Thursday, 20 February 2020

On This Day in Math - February 20

A mathematician will recognise Cauchy, Gauss, Jacobi or Helmholtz after reading a few pages, just as musicians recognise, from the first few bars, Mozart, Beethoven or Schubert.
~Ludwig Boltzmann

The 51st day of the year; 51 is the number of different paths from (0,0) to (6,0) made up of segments connecting lattice points that can only have slopes of 1, 0, or -1 but so that they never go below the x-axis. These are called Motzkin Numbers.

\(\pi(51) = 15\), the number of primes less than 51 is given by it's reversal, 15.

Jim Wilder pointed out that 51 is the smallest number that can be writtenas a sum of primes  with the digits 1 to 5 each used once  2 + 3 + 5 + 41 = 51 (Students might explore similar problems using first n digits 2-9)

A triangle with sides 51, 52 and 53 has an integer area 1170 units2.

And like any odd number, it is the sum of two consecutive numbers, 25+26 , and the difference of their squares \(26^2 - 25^2\)

And I just found this unusual reference, "Don’t be baffled if you see the number 51 cropping up in Chinese website names, since 51 sounds like 'without trouble' or 'carefree' in Chinese." at the Archimedes Lab


1639  Responding to Mersene's comment that the sum of the divisors of 360 form a ratio of 9/4 with 360, Fermat responds that 2016 has the same property. 

1648 A letter from Fermat through Frenicle to Digby reached Wallis saying that Fermat had solved equations of the type x2-Ay2 = 1 for all non-square values up to 150. Thus begins the saga of the mis-naming of Pell's equation. *Edward Everett Whitford, The Pell Equation

1729 A Letter from Gabriel Cramer, Prof. Math. Genev. to James Jurin, M. D. and F. R. S. to be read at the Royal Society, gives an “account of an Aurora Borealis Attended with Unusual Appearances” . The borealis occurred on Feb 15, and the letter was sent on Feb 20. *Transactions of RSI

1807 Sophie Germain writes to Gauss informing him that she is the person who had written to him using the name M. LeBlanc. In closing she writes her hope that this will not change their correspondence. His Response on April 30 would assure her it had not.
*Sophie Germain: An Essay in the History of the Theory of Elasticity

In 1835, Charles Darwin, on his H.M.S. Beagle voyage reached Chile, and experienced a very strong earthquake and shortly afterward saw evidence of several feet of uplift in the region. He repeated measurement a few days later, and found the land had risen several feet. He had proved that geological changes occur even in our own time. Lyell's principles were based on the concept of a steady-state, nondirectional earth whereby uplift, subsidence, erosion, and deposition were all balanced. Thereby, Darwin coupled in his mind this dramatic evidence of elevation with accompanying subsidence and deposition. Thus he hypothesized that coral reefs of the Pacific developed on the margins of subsiding land masses, in the three stages of fringing reef, barrier reef, and atoll.*TIS

1913 It was on, or around, this day that the Three Sisters Radio towers near Arlington, Va went into service. In an area called Radio, near the Columbia Pike and Courthouse Road. Virginia. It was a neighborhood named for the old U.S. Navy Wireless Station. The tallest of the three towers was 45 feet taller than the Washington Monument, and second only to the Eiffel Tower in the world.
The Navy opened Radio Arlington, call sign NAA, in 1913, launching the U.S. military’s global communications system on Fort Myers. A streetcar stop was even named “Radio.’’ Old Radio Arlington marked the first time the term “radio’’ was used in communications, according to Nan and Ross Netherton’s book “Arlington County in Virginia: A Pictorial History,” which was published in 1987. In the days of Marconi and other radio pioneers, the new communications mode was called “wireless telegraphy.’’
*The 625 Sentinal

At Tenwatts Blog I found that there is a marker outside the present Dept. of Defense facility there:
"Three radio towers similar to the Eiffel tower were erected here in 1913. One stood 600 feet, and the other two 450 feet above the 200-foot elevation of the site. The word "radio" was first used instead of "wireless" in the name of this naval communications facility. The first trans-Atlantic voice communication was made between this station and the Eiffel tower in 1915. The nation set its clocks by the Arlington Radio time signal and listened for its broadcast weather reports. The towers were dismantled in 1941, as a menace to aircraft approaching the new Washington National Airport."
I also found the nice postcard showing the three sisters (and some additions) taken from Arlington National Cemetery. His post suggests that the towers were eventually dismantled.

1947 Computer pioneer Alan Turing suggests testing artificial intelligence with the game of chess in a lecture to the London Mathematical Society. Computers, he argued, must like humans be given training before their IQ is tested. A human mathematician has always undergone an extensive training. This training may be regarded as not unlike putting instruction tables into a machine, he said. One must therefore not expect a machine to do a very great deal of building up of instruction tables on its own.*CHM

1966 The only verified example of a family producing five single children with coincidental birthdays is that of Catherine (1952), Coral (1953), Charles (1956), Claudia (1961), and Cecelia (1966), born to Ralph and Carolyn Cummins of Clintwood, VA. All on Feb 20th.  What is the probability of this happening? *VFR (RALPH? He should have changed his name.)

1979 The German Democratic Republic issued a stamp commemorating the centenary of Einstein’s birth. It shows the Einstein tower in Potsdam and his famous formula E = mc2. [Scott #1990]*VFR

In 1996, a bright "new" star was discovered in Sagittarius by Japanese amateur astronomer Yukio Sakurai. It was found not to be a usual nova, but instead was a star going through a dramatic evolutionary state, re-igniting its nuclear furnace for one final blast of energy called the "final helium flash." It was only the second to be identified in the twentieth century. A star like the Sun ends its active life as a white dwarf star gradually cooling down into visual oblivion. Sakurai's Object had a mass a few times that of the Sun. Its collapse after fusing most of its hydrogen fuel to helium raised its temperature so much higher it began nuclear fusion of its helium remains. This was confirmed using its light spectrum to identify the elements present.*TIS

2013 In celebration of the 100th anniversary of the publication of the three-volume version of Bertrand Russell and Alfred North Whitehead's Principia Mathematica, a London theater company staged the world premiere of a musical based on the epic mathematics text.
Performed by the Conway Collective based out of London's historic Conway Hall and written by Tyrone Landau, the play was described as "fascinating and unusual." *MAA DL


1844 Ludwig Eduard Boltzmann (February 20, 1844 – September 5, 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. He was one of the most important advocates for atomic theory at a time when that scientific model was still highly controversial. *Wik Trivia: Boltzmann's famous equation S = K log W (where S = entropy, K = Boltzmann's constant, and W = probability of a particular state) was inscribed as an epitaph on Boltzmann's tombstone. *Wik After obtaining his doctorate, he became an assistant to his teacher Josef Stefan. Boltzmann's fame is based on his invention of statistical mechanics, independently of Willard Gibbs. Their theories connected the properties and behaviour of atoms and molecules with the large scale properties and behaviour of the substances of which they were the building blocks. He also worked out a kinetic theory of gases, and the Stefan-Boltzmann law concerning a relationship between the temperature of a body and the radiation it emits. His firm belief and defense of atomism (that all matter is made of atoms) against hostile opposition to this new idea, may have contributed to his suicide in 1906. *TIS

1860 Mathias Lerch​ (20 February 1860, Milínov - 3 August 1922, Schüttenhofen) was an eminent Czech mathematician who published about 250 papers, largely on mathematical analysis and number theory. He studied in Prague and Berlin, and held teaching positions at the Czech Technical Institute in Prague, the University of Fribourg in Switzerland, the Czech Technical Institute in Brno, and Masaryk University in Brno; he was the first mathematics professor at Masaryk University when it was founded in 1920. In 1900, he was awarded the Grand Prize of the French Academy of Sciences for his number-theoretic work. The Lerch zeta-function is named after him as is the Appell–Lerch sum.*Wik

1926 Kenneth Harry Olsen (February 20, 1926 – February 6, 2011) was an American engineer who co-founded Digital Equipment Corporation (DEC) in 1957 with colleague Harlan Anderson *Wik

1929 Madan Lal Puri ( Sialkot in Pakistan , 20 February 1929 ) is a statistical Indian important in the context of nonparametric statistics and also occupied the fuzzy sets .*Wik

1931 John Willard Milnor (20 Feb 1931, )American mathematician who was awarded the Fields Medal in 1962 for his his proof that a 7-dimensional sphere can have 28 different differential structures. This work opened up the new field of differential topology. Milnor's theorem shows that the total curvature of a knot is at least 4. In the 1950's, Milnor did a substantial amount of work on algebraic topology in which he constructed the classifying space of a topological group and gave a geometric realisation of a semi-simplicial complex. Since the 1970's his interest is in dynamics, especially holomorphic dynamics. Milnor served the American Mathematical Society as vice president (1975-76) and was awarded the Wolf Prize in 1989. *TIS

1948 Andrew Christopher Fabian, OBE, FRS (20 February 1948 - ) is a British astronomer and astrophysicist. He is a Royal Society Research Professor at the Institute of Astronomy, Cambridge, and Vice-Master of Darwin College, Cambridge. He was the President of the Royal Astronomical Society from May 2008 through to 2010. He is an Emeritus Professor of Astronomy at Gresham College, a position in which he delivered free public lectures within the City of London between 1982 and 1984. He was also editor-in-chief of the astronomy journal Monthly Notices of the Royal Astronomical Society. He was educated at King's College London (BSc, Physics) and University College London (PhD).
His current areas of research include galaxy clusters, active galactic nuclei, strong gravity, black holes and the X-ray background. He has also worked on X-ray binaries, neutron stars and supernova remnants in the past. Much of his research involves X-ray astronomy and high energy astrophysics. His notable achievements include his involvement in the discovery of broad iron lines emitted from active galactic nuclei, for which he was jointly awarded the Bruno Rossi Prize. He is author of over 800 refereed articles and head of the X-ray astronomy group at the Institute of Astronomy. Fabian was awarded the Dannie Heineman Prize for Astrophysics by the American Astronomical Society in 2008 and the Gold Medal of the Royal Astronomical Society in 2012 *Wik


1762 Tobias Meyer (17 Feb 1723; 20 Feb 1762 at age 38) German astronomer who developed lunar tables that greatly assisted navigators in determining longitude at sea. Mayer also discovered the libration (or apparent wobbling) of the Moon. Mayer began calculating lunar and solar tables in 1753 and in 1755 he sent them to the British government. These tables were good enough to determine longitude at sea with an accuracy of half a degree. Mayer's method of determining longitude by lunar distances and a formula for correcting errors in longitude due to atmospheric refraction were published in 1770 after his death. The Board of Longitude sent Mayer's widow a payment of 3000 pounds as an award for the tables. *TIS Leonhard Euler described him as 'undoubtedly the greatest astronomer in Europe'. More notes on Meyer can be found on this blog at the Board of Longitude Project from the Royal Museums at Greenwich. Another nice blog by Thony Christie, The Renaissance Mathematicus tells of Meyer's measurement of the Moon's distance, and the importance of that measurement.

1778 Laura Maria Catarina Bassi (31 Oct 1711 in Bologna, Papal States, 20 Feb 1778 in Bologna, Papal States) was an Italian physicist and one of the earliest women to gain a position in an Italian university. *SAU She was the first woman in the world to earn a university chair in a scientific field of studies. She received a doctoral degree from the University of Bologna in May 1732, only the third academic qualification ever bestowed on a woman by a European university, and the first woman to earn a professorship in physics at a university in Europe. She was the first woman to be offered an official teaching position at a university in Europe.
In 1738, she married Giuseppe Veratti, a fellow academic with whom she had twelve children. After this, she was able to lecture from home on a regular basis and successfully petitioned the University for more responsibility and a higher salary to allow her to purchase her own equipment.
One of her principal patrons was Pope Benedict XIV. He supported less censorship of scholarly work, such as happened with Galileo, and he supported women figures in learning, including Agnesi.
She was mainly interested in Newtonian physics and taught courses on the subject for 28 years. She was one of the key figures in introducing Newton's ideas of physics and natural philosophy to Italy. She also carried out experiments of her own in all aspects of physics. In order to teach Newtonian physics and Franklinian electricity, topics that were not focused in the university curriculum, Bassi gave private lessons.[6] In her lifetime, she authored 28 papers, the vast majority of these on physics and hydraulics, though she did not write any books. She published only four of her papers.[2] Although only a limited number of her scientific works were left behind, much of her scientific impact is evident through her many correspondents including Voltaire, Francesco Algarotti, Roger Boscovich, Charles Bonnet, Jean Antoine Nollet, Giambattista Beccaria, Paolo Frisi, Alessandro Volta. Voltaire once wrote to her saying "There is no Bassi in London, and I would be much happier to be added to your Academy of Bologna than that of the English, even though it has produced a Newton". *Wik

1928 Antonio Abetti (19 Jun 1846, 20 Feb 1928 at age 81) Italian astronomer who was an authority on minor planets. At first a civil engineer, he became an astronomer at the University of Padua (1868-93), with an interest in positional astronomy and made many observations of small planets, comets and star occultations. In 1874, Abetti went to Muddapur, Bengal, to observe the transit of Venus across the sun's disk where his use of a spectroscope was the first use of this kind. Later, he became director at the Arcetri Observatory and Professor of astronomy at the University of Florence (1894-1921). The observatory had been founded by G. B. Donati in 1872, and Abetti equipped it with a new telescope that he had built in the workshops at Padua. He was active after retirement, until his death, and was followed by his son Giorgio.*TIS

1955 Arthur Lee Dixon FRS (27 November 1867 — 20 February 1955) was a British mathematician and holder of the Waynflete Professorship of Pure Mathematics at the University of Oxford. The younger brother of Alfred Cardew Dixon, he was educated at Kingswood School and Worcester College, Oxford, becoming a Tutorial Fellow at Merton College in 1898 and the Waynflete Professor in 1922. Dixon was the last mathematical professor at Oxford to hold a life tenure, and although he was not particularly noted for his mathematical innovations he did publish many papers on analytic number theory and the application of algebra to geometry, elliptic functions and hyperelliptic functions. Elected a Fellow of the Royal Society in 1912 and serving as President of the London Mathematical Society from 1924 to 1926, *Wik

1972 Maria Goeppert-Mayer (28 Jun 1906, 20 Feb 1972 at age 65) German physicist who shared one-half of the 1963 Nobel Prize for Physics with J. Hans D. Jensen of West Germany for their proposal of the shell nuclear model. (The other half of the prize was awarded to Eugene P. Wigner of the United States for unrelated work.) In 1939 she worked at Columbia University on the separation of uranium isotopes for the atomic bomb project. In 1949, she devised the shell nuclear model, which explained the detailed properties of atomic nuclei in terms of a structure of shells occupied by the protons and neutrons. This explained the great stability and abundance of nuclei that have a particular number of neutrons (such as 50, 82, or 126) and the same special number of protons. *TIS

2005 Esther (Klein) Szekeres (20 February 1910 – 28 August 2005) was a Hungarian–Australian mathematician with an Erdős number of 1. She was born to Ignaz Klein in a Jewish family in Budapest, Kingdom of Hungary in 1910. As a young woman in Budapest, Klein was a member of a group of Hungarians including Paul Erdős, George Szekeres and Paul Turán that convened over interesting mathematical problems.
In 1933, Klein proposed to the group a combinatorial problem that Erdős named as the Happy Ending problem as it led to her marriage to George Szekeres in 1937, with whom she had two children.
Following the outbreak of World War II, Esther and George Szekeres emigrated to Australia after spending several years in Hongkew, a community of refugees located in Shanghai, China. In Australia, they originally settled in Adelaide before moving to Sydney in the 1960s.
In Sydney, Esther lectured at Macquarie University and was actively involved in mathematics enrichment for high-school students. In 1984, she jointly founded a weekly mathematics enrichment meeting that has since expanded into a program of about 30 groups that continue to meet weekly and inspire high school students throughout Australia and New Zealand.
In 2004, she and George moved back to Adelaide, where, on 28 August 2005, she and her husband passed away within an hour of each other *Wik

2005 Edward Maitland Wright (13 Feb 1906 in Farnley, near Leeds, England - 2 Feb 2005 in Reading, England) was initially self-taught in Mathematics but was able to go and study at Oxford. He spent a year at Göttingen and returned to Oxford. He was appointed to the Char at Aberdeen where he stayed for the rest of his career, eventually becoming Principal and Vice-Chancellor of the University. He is best known for the standard work on Number Theory he wrote with G H Hardy. One of Wright's first papers, published in 1930, was on Bernstein polynomials. Also among his early work was a series of three papers titled Asymptotic partition formulae. The third in the series Asymptotic partition formulae, III. Partitions into kth powers was published by Acta Mathematica in 1934. *SAU

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Wednesday, 19 February 2020

On This Day in Math - February 19

Copernicus statue at Olsztyn Castle

It is true that a mathematician who is not somewhat of a poet, will never be a perfect mathematician.
~Karl Weierstrass

The 50th day of the year; 50 is the smallest number that can be written as the sum of two squares in two distinct ways 50 = 49 + 1 = 25 + 25. *Tanya Khovanova, Number Gossip (What is the next, or what is the smallest number that can be written as the sum of two squares in three distinct ways? For solution from Ben Vitale, see bottom of post)

50 is also expressible as the sum of distinct primes in two ways so that all consecutive primes 2-23 are used :50 = 2 + 5 + 7 + 17 + 19 = 3 + 11 + 13 + 23.
The number 50 is somewhat responsible for the area of number theory about partitions. In 1740 Philip Naudé the younger (1684-1747) wrote Euler from Berlin to ask “how many ways can the number 50 be written as a sum of seven different positive integers?” Euler would give the answer, 522, within a few days but would return to the problem of various types of partitions throughout the rest of his life.

1512 The French invaded Brescia, in Northern Italy, during the War of the League of Cambrai. The militia of Brescia defended their city for seven days. When the French finally broke through, they took their revenge by massacring the inhabitants of Brescia. By the end of battle, over 45,000 residents were killed. During the massacre, a French soldier sliced Niccolò's jaw and palate with a saber. This made it impossible for Niccolò to speak normally, prompting the nickname "Tartaglia" Tartaglia is perhaps best known today for his conflicts with Gerolamo Cardano over the solution of cubics. (see this blog for the unfortunate common mistake about Tartaglia's family name.)

1549 Osiander wrote of Michael Stifel: “He has devised new numbers for the alphabet, namely the triangular numbers, and his fantasies are more absurd than before.” *VFR

1600 The Inquisition brought Giordano Bruno to the Campo dei Fiori in Rome’s center where they chained him to an iron stake and burned him alive for his beliefs that the earth rotated on its axis. *Amir Aczel, Pendulum, pg 9 (This date seems wrong. Thony Christie noted that " Bruno was executed on 17th Feb and not for his cosmology but for his heretical theology." Thanks... several other sources agree with Feb 17th date))

1616 On February 19, 1616, the Inquisition asked a commission of theologians, known as qualifiers, about the propositions of the heliocentric view of the universe after Nicollo Lorin had accused Galileo of Heretical remarks in a letter to his former student, Benedetto Castelli. On February 24 the Qualifiers delivered their unanimous report: the idea that the Sun is stationary is "foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture..."; while the Earth's movement "receives the same judgement in philosophy and ... in regard to theological truth it is at least erroneous in faith."At a meeting of the cardinals of the Inquisition on the following day, Pope Paul V instructed Bellarmine to deliver this result to Galileo, and to order him to abandon the Copernican opinions; should Galileo resist the decree, stronger action would be taken. On February 26, Galileo was called to Bellarmine's residence, and accepted the orders.*Wik

1671/72 Newton’s first publication appears as a letter in the Philosophical Transactions. It deals with his new theory of light, showing that a prism separates white light into its component colors. Huygens, Hooke and others objected so strongly that he vowed not to publish again. Fortunately that vow was not kept. *VFR The full text of that publication is here.

In 1855, M. Le Verrier presented the first weather map at the French Academy of Sciences.*TIS A storm on November 14, 1854 destroyed the French warship Henri IV and damaged other British and French vessels on the Black Sea involved in the Crimean War. A report from the state-supported Paris Observatory indicated that barometric readings showed that the storm had passed across Europe in about four days. Urban Leverrier, director of the Paris Observatory, concluded that had there been a telegraph line between Vienna and the Crimea, the British and French fleets could have received warnings. An earlier map is mentioned, but not shown in a letter dated Dec 1, 1816 in Gilbert's Annalen der Physik from Heinrich Wilhelm Brandes *Report of The International Meterological Congress, 1893

1876 Sylvester began his duties at the newly founded Johns Hopkins, *TIS

1901 Messages from Mars reported in Collier's Magazine. While conducting experiments on high-frequency electrical transmission in 1899 in his Colorado Springs, Colorado laboratory, Nikola Tesla picked up cosmic radio waves on his instruments. Announcing this development, he publicly opined that the messages came from outer space, possibly from inhabitants of Mars. In a Collier’s Weekly article dated February 19, 1901, Tesla wrote, “At the present stage of progress, there would be no insurmountable obstacle in constructing a machine capable of conveying a message to Mars … What a tremendous stir this would make in the world! How soon will it come?” Later discoveries revealed that Tesla had actually picked up common radio waves emitted by interstellar gas clouds. *History. Com

1940Edwin Hubble wrote in a letter to Harlow Shapley that he had determined the distance to the "Andromeda nebula". He included this graph. HT Massimo

1946 Alan Turing Presents the “Proposal for the Development in the Mathematics Division of an Automatic Computing Engine (ACE).”
This research proposal was presented to a meeting of the Executive Committee of the National Physical Laboratory (NPL) in Teddington, England, and approved at a second meeting held a month later.
Turing based this research on von Neumann’s First Draft of a Report on the EDVAC. He had studied it in summer 1945 when he was recruited by J.R. Womersley to join the staff of the NPL. *CHM

1971 The first warrant is issued to search a computer storage. Although the requirements for obtaining such a warrant were similar to those for searching a home, they ushered in a new era that would lead to increasingly sophisticated methods of encryption to hide computer files from law enforcement agents.*CHM

1972 The New Yorker published an article by A. Adler on “Mathematics and Creativity” that was not well received by the mathematical community. See The [old] Mathematical Intelligencer, no. 2. *VFR An abstract is here

1473 Nicolaus Copernicus Polish astronomer who proposed that the planets have the Sun as the fixed point to which their motions are to be referred; that the Earth is a planet which, besides orbiting the Sun annually, also turns once daily on its own axis; and that very slow, long-term changes in the direction of this axis account for the precession of the equinoxes *TIS
An advance copy of his work De revolutionibus orbium coelestium was presented to Copernicus. On the same day he died. *VFR
Over 450 years after his death, Copernicus was reburied in the cathedral at Frombork on Poland’s Baltic coast. The astronomer whose ideas were once declared heresy by the Vatican—was reburied with full religious honors.

1837 Aleksandr Nikolayevich Korkin (3 March [O.S. 19 February] 1837–September 1, 1908, all New Style) was a Russian mathematician. He made contribution to the development of partial differential equations. After Chebyshev, Korkin was the most important initiator of the formation of the Saint Petersburg Mathematical School*Wik

1863 Axel Thue(19 Feb 1863 in Tönsberg, Norway - 7 March 1922 in Oslo, Norway) Thue studied Diophantine equations, showing that, for example, y3 - 2x2 = 1 cannot be satisfied by infinitely many pairs of integers. Edmund Landau, in 1922, described Thue's work as, ".. the most important discovery in elementary number theory that I know. "
Thue's Theorem states, " If f (x, y) is a homogeneous polynomial with integer coefficients, irreducible in the rationals and of degree > 2 and c is a non-zero integer then f (x, y) = c has only a finite number of integer solutions." *SAU

1866 Thomas Jefferson Jackson See (19 Feb 1866 in Montgomery City, Missouri - 4 July 1962 in Oakland, California, USA) was an U S astronomer who studied in the University of Missouri and in Berlin. He fell out with his astronomical colleagues and was eventually banned from publishing. He spend the last part of his life arguing against Einstein's Theory of Relativity. *SAU

1889 Sir Ernest Marsden (19 Feb 1889, 15 Dec 1970) British-born New Zealand nuclear physicist who worked under Ernest Rutherford investigating atomic structure with Hans Geiger. Marsden visually counted scintillations from alpha particles after passing through gold foil and striking a phosphorescent screen. That some of these were observed scattered at surprisingly large angles led to Rutherford's theory of the nucleus as the massive, tiny centre of the atom. Later, Marsden's own experiments, working in New Zealand, hinted suggested transmutation of elements was possible when alpha particles bombarding nitrogen nuclei produced scattered particles of greater speed than the original radiation. *TIS

1553 Erasmus Reinhold (October 22, 1511 – February 19, 1553) was a German astronomer and mathematician, considered to be the most influential astronomical pedagogue of his generation. He was born and died in Saalfeld, Saxony.
He was educated, under Jacob Milich, at the University of Wittenberg, where he was first elected dean and later became rector. In 1536 he was appointed professor of higher mathematics by Philipp Melanchthon. In contrast to the limited modern definition, "mathematics" at the time also included applied mathematics, especially astronomy. His colleague, Georg Joachim Rheticus, also studied at Wittenberg and was appointed professor of lower mathematics in 1536.
Reinhold catalogued a large number of stars. His publications on astronomy include a commentary (1542, 1553) on Georg Purbach's Theoricae novae planetarum. Reinhold knew about Copernicus and his heliocentric ideas prior to the publication of De revolutionibis and made a favourable reference to him in his commentary on Purbach. However, Reinhold (like other astronomers before Kepler and Galileo) translated Copernicus' mathematical methods back into a geocentric system, rejecting heliocentric cosmology on physical and theological grounds.
It was Reinhold's heavily annotated copy of De revolutionibus in the Royal Observatory, Edinburgh that started Owen Gingerich on his search for copies of the first and second editions which he describes in The Book Nobody Read.[5] In Reinhold's unpublished commentary on De revolutionibus, he calculated the distance from the Earth to the sun. He "massaged" his calculation method in order to arrive at an answer close to that of Ptolemy.*Wik

1622 Sir Henry Savile (30 Nov 1549 in Bradley (near Halifax), Yorkshire, England - 19 Feb 1622 in Eton, Berkshire, England) Savile was an English mathematician who founded professorships of geometry and astronomy at Oxford. It is interesting to read Savile's comments in these lectures on why he felt that mathematics at that time was not flourishing. Students did not understand the importance of the subject, Savile wrote, there were no teachers to explain the difficult points, the texts written by the leading mathematicians of the day were not studied, and no overall approach to the teaching of mathematics had been formulated. Of course, as we shall see below, fifty years later Savile tried to rectify these shortcomings by setting up two chairs at the University of Oxford. *SAU

1799 Jean-Charles Borda, (4 May 1733 in Dax, France - 19 Feb 1799 in Paris, France) a major figure in the French navy who participated in sev­eral scientific voyages and the American revolution. Besides his contributions to navigational instruments he did important work on fluid mechanics, even showing that Newton’s theory of fluid resistance was untenable. He is best known for the voting system he created in 1770.*VFR (The Borda count is a single-winner election method in which voters rank candidates in order of preference. The Borda count determines the winner of an election by giving each candidate a certain number of points corresponding to the position in which he or she is ranked by each voter. Once all votes have been counted the candidate with the most points is the winner. Because it sometimes elects broadly acceptable candidates, rather than those preferred by the majority, the Borda count is often described as a consensus-based electoral system, rather than a majoritarian one.The Borda count is a popular method for granting awards for sports in the United States, and is used in determining the Most Valuable Player in Major League Baseball, and by the Associated Press and United Press International to rank teams in NCAA sports, to determine the winner of the Heisman Trophy.) [He was one of the main driving forces in the introduction of the decimal system. Borda made good use of calculus and experiment to unify areas of physics. For his surveying, he also developed a series of trigonometric tables. In 1782, while in command of a flotilla of six French ships, he was captured by the British. Borda's health declined after his release. He is one of 72 scientists commemorated by plaques on the Eiffel tower.]*TIS

1897 Karl (Theodor Wilhelm) Weierstrass (31 Oct 1815, 19 Feb 1897 at age 81) was a German mathematician who is known as the "father of modern analysis" for his rigour in analysis led to the modern theory of functions, and considered one of the greatest mathematics teachers of all-time. He was doing mathematical research while a secondary school teacher, when in 1854, he published a paper on Abelian functions in the famous Crelle Journal. The paper so impressed the mathematical community that he shortly received an honorary doctorate and by 1856, he had a University appointment in Berlin. In 1871, he demonstrated that there exist continuous functions in an interval which have no derivatives nowhere in the interval. He also did outstanding work on complex variables.*TIS Weierstrass died peacefully at the age of 82 at his home in Berlin after a long illness culminating in influenz. It is reported that his last wish was that the priest say nothing in his praise at the funeral, but to restrict the services to the customary prayers. *VFR

1908 Paul Matthieu Hermann Laurent (2 Sept 1841 in Echternach, Luxembourg - 19 Feb 1908 in Paris, France) He developed statistical formulas for the calculation of actuarial tables and studied heat conduction. *VFR

1916 Ernst Mach (18 Feb 1838; 19 Feb 1916 at age 77) Austrian physicist and philosopher who established important principles of optics, mechanics, and wave dynamics. His early physical works were devoted to electric discharge and induction. Between 1860 and 1862 he studied in depth the Doppler Effect by optical and acoustic experiments. He introduced the "Mach number" for the ratio of speed of object to speed of sound is named for him. When supersonic planes travel today, their speed is measured in terms that keep Mach's name alive. His lifetime interest, however, was in psychology and human perception. He supported the view that all knowledge is a conceptual organization of the data of sensory experience (or observation). *TIS

1929 Joseph Valentin Boussinesq (13 March 1842 – 19 February 1929) was a French mathematician and physicist who made significant contributions to the theory of hydrodynamics, vibration, light, and heat.
In 1897 he published Théorie de l' écoulement tourbillonnant et tumultueux des liquides, a work that greatly contributed to the study of turbulence and hydrodynamics.*Wik

1938 Edmund Georg Hermann Landau (14 Feb 1877 in Berlin, Germany - 19 Feb 1938 in Berlin, Germany) Although famous as a number theorist, he is best known for his textbooks which are written in an austere definition-theorem-proof style. His Grundlagen der Analysis is an excellent treatment of the development of our number systems from the Peano postualates. Reading this book is a good way to learn mathematical German. But if you are lazy, it has been translated into English. *VFR Landau gave the first systematic presentation of analytic number theory and wrote important works on the theory of analytic functions of a single variable.*SAU Legend has it that at the age of three, when is mother forgot her umbrella in a carriage, he replied, "It was number 354," and the umbrella was quickly re-acquired.

1940 Otto Toeplitz died in Jerusalem, after having left Germany in the Spring of 1939. He made lasting contributions to the theory of integral equations and the theory of functions of infinitely many variables. Today he is best remembered for two popular works which have been translated into English: The Enjoyment of Mathematics (original 1930, 1957), and The Calculus: A Genetic Approach (first published 1949; English 1963). These are some of the most successful attempts to bring higher mathematics to the general public. The later shows his deep interest in the history of mathematics; every calculus teacher could profit from reading it. *VFR

1990 Otto Neugebauer, historian of ancient and medieval mathematics and astronomy. *VFR
(May 26, 1899 – February 19, 1990) He was an Austrian-American mathematician and historian of science who became known for his research on the history of astronomy and the other exact sciences in antiquity and into the Middle Ages. By studying clay tablets he discovered that the ancient Babylonians knew much more about mathematics and astronomy than had been previously realized. The National Academy of Sciences has called Neugebauer "the most original and productive scholar of the history of the exact sciences, perhaps of the history of science, of our age." *Wik

@BenVitale: smallest number w/ 3 representations: \( 325 = 1^2 + 18^2 = 6^2 + 17^2 = 10^2+ 15^2\)

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Tuesday, 18 February 2020

On This Day in Math - February 18

Leon Battista Alberti, De pictura and Elementa *Museo Galileo
The power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental operations.
~Ernst Mach

The 49th day of the year; lots of numbers are squareful (divisible by a square number) but 49 is the smallest number so that it, and both its neighbors are squareful. (Many interesting questions arise for students.. what's next, can there be four in a row?, etc)

And Prof. William D Banks of the University of Missouri has recently proved that every integer in base ten is the sum of 49 or less palindromes. (August 2015) (Building on Prof. Banks groundbreaking work, by February 22, 2016 JAVIER CILLERUELO AND FLORIAN LUCA had proved that for any base > 4

The 49th Mersenne prime is discovered. On Jan 19th, 2016 The GIMPS program announced a new "largest known" prime, 274,207,281 -1. called M74,207,281 for short, the number has 22,338,618 digits.

3102 B.C. The Kaliyuga begins according to the Indian mathematician Aryabhata (born A.D. 476). He believed all astronomical phenomena were periodic, with period 4,320,000= 20 × 603 years, and that all the planets had mean longitude zero on this date. [College Mathematics Journal, 16 (1985), p. 169.] *VFR

1670 “Joannes Georgius Pelshower [Regimontanus Borussus] giving me a visit, and desiring an example of the like, I did that night propose to myself in the dark without help to my memory a number in 53 places: 2468135791011121411131516182017192122242628302325272931 of which I extracted the square root in 27 places: 157103016871482805817152171 proxim´e; which numbers I did not commit to paper till he gave me another visit, March following, when I did from memory dictate them to him.” So wrote John Wallis. [American Journal of Psychology, 4(1891), 38] *VFR

1673: Robert Hooke writes in his Journal: "Bought Copernicus tower hill 2sh " *‏@HookesLondon Thony Christie points out that current first editions run about \( 2,500,000 \) GB Pounds.

1727 Leonhard Euler defends his De Sono essay in a public disputation at the law auditorium at Basal. His paper had been submitted as his "habilitationsschrift", part of his application for the Physics Professorship at Basal. Fortunately, he did not get the position, and soon departed for a position at Petersburg Academy of Science in Russia. Among other competitors overlooked for the position was Jakob Hermann. *Ronald S. Calinger; Leonhard Euler: Mathematical Genius in the Enlightenment

1772 the Royal Danish Academy of Sciences and Letters presented Alexander Wilson with a gold medal for his work on sunspots. Wilson was a Scottish surgeon, type-founder, astronomer, mathematician and meteorologist and the first scientist to record the use of kites in meteorological investigations. Wilson noted that sunspots viewed near the edge of the Sun's visible disk appear depressed below the solar surface, a phenomenon referred to as the Wilson effect. When the Royal Danish Academy of Sciences and Letters announced a prize to be awarded for the best essay on the nature of solar spots, Wilson submitted an entry which won. *Wik

1879 “I will do the same for the young women that I do for the young men. I shall take pleasure in giving gratuitous instruction to any person whom I find competent to receive it. I give no elementary instruction, but only in the higher mathematics.” Benjamin Peirce to Arthur V. Gilman, president of Harvard. [Scripta Mathematica, 11(1945), 259

1879 J. J. Sylvester, in a lecture at the Peabody Institute in Baltimore, read “Rosalind”, a mock-sentimental poem of four hundred lines all ending in “ind”. For the first few lines of this dreadful poem, see Osiris, 1(1936), p. 106. *VFR says that Sylvester was the author of this poem, and another which had two hundred lines rhyming with “Winn.” These were products of his later residence in Baltimore. Sylvester had perhaps a better appreciation of music.

In 1913, chemist Frederick Soddy introduced the term "isotope". Soddy was an English chemist and physicist who received the Nobel Prize for Chemistry in 1921 for investigating radioactive substances. He suggested that different elements produced in different radioactive transformations were capable of occupying the same place on the Periodic Table, and on 18 Feb 1913 he named such species "isotopes" from Greek words meaning "same place." He is credited, along with others, with the discovery of the element protactinium in 1917. *TIS He also wrote the mathematical poem, The Kiss Precise, which includes a solution to Descartes Circle Problem. the poem begins:
For pairs of lips to kiss maybe
Involves no trigonometry.
'Tis not so when four circles kiss
Each one the other three.
To bring this off the four must be
As three in one or one in three.
If one in three, beyond a doubt
Each gets three kisses from without.
If three in one, then is that one
Thrice kissed internally.
The complete poem and more about the history of the problem can be found here.

1930 Clyde Tombaugh (1906–1997) discovered Pluto on photographic plates under the direction of V M Slipher at the Lowell Observatory at Flagstaff, Az. For 45 minutes, before he showed his superiors, he was the only person in the world who knew it existed. When he later went to college he was not allowed to take Astronomy I, the instructor thinking it unsuitable for the discoverer of a planet. (On August 24th of 2006 the International Astronomical Union decided to rescind Pluto’s status as a planet and reclassify it as another entity called a “dwarf planet”. ) *FFF, pg 537

2006 The game of Connect Four was first solved by James D. Allen (Oct 1, 1988), and independently by Victor Allis (Oct 16, 1988). First player can force a win. Strongly solved by John Tromp's 8-ply database (Feb 4, 1995). It was weakly solved for all boardsizes where width+height is at most 15 (Feb 18, 2006). *Wik


1201 Muhammad ibn Muhammad ibn al-Hasan al-Tusi (18 Feb 1201; 26 Jun 1274 at age 73) Persian philosopher, scientist, mathematician and astronomer who made outstanding contributions in his era. When The Mongol invasion, started by Genghis Khan, reached him in 1256, he escaped likely death by joining the victorious Mongols as a scientific adviser. He used an observatory built at Maragheh (finished 1262), assisted by Chinese astronomers. It had various instruments such as a 4 meter wall quadrant made from copper and an azimuth quadrant which was Tusi's own invention. Using accurately plotted planetary movements, he modified Ptolemy's model of the planetary system based on mechanical principles. The observatory and its library became a center for a wide range of work in science, mathematics and philosophy. He was known by the title Tusi from his place of birth (Tus)*TIS

1404 Leon Battista Alberti (18 Feb 1404; 25 Apr 1472 at age 68) Italian artist and geometrist who “wrote the book,” the first general treatise Della Pictura (1434) on the the laws of perspective, establishing the science of projective geometry. Alberti also worked on maps (again involving his skill at geometrical mappings) and he collaborated with Toscanelli who supplied Columbus with the maps for his first voyage. He also wrote the first book on cryptography which contains the first example of a frequency table. *TIS
. This noted architect took up the study of mathematics for relaxation. He contributed to the study of perspective. *VFR

1677 Jacques Cassini (18 Feb 1677; 16 Apr 1756 at age 79) French astronomer whose direct measurement of the proper motions of the stars (1738) disproved the ancient belief in the unchanging sphere of the stars. He also studied the moons of Jupiter and Saturn and the structure of Saturn's rings. His two major treatises on these subject appeared in 1740: Elements of Astronomy and Astronomical Tables of the Sun, Moon, Planets, Fixed Stars, and Satellites of Jupiter and Saturn. He also wrote about electricity, barometers, the recoil of firearms, and mirrors. He was the son of astronomer, mathematician and engineer Giovanni Cassini (1625-1712) with whom he made numerous geodesic observations. Eventually, he took over his father's duties as head of the Paris Observatory.*TIS Cassini was born at the Paris Observatory and died at Thury, near Clermont. Admitted at the age of seventeen to membership of the French Academy of Sciences, he was elected in 1696 a fellow of the Royal Society of London, and became maître des comptes in 1706. *Wik

1745 Count Alessandro Giuseppe Antonio Anastasio Volta (18 Feb 1745; 5 Mar 1827 at age 82) Italian physicist who invented the electric battery (1800), which for the first time enabled the reliable, sustained supply of current. His voltaic pile used plates of two dissimilar metals and an electrolyte, a number of alternated zinc and silver disks, each separated with porous brine-soaked cardboard. Previously, only discharge of static electricity had been available, so his device opened a new door to new uses of electricity. Shortly thereafter, William Nicholson decomposed water by electrolysis. That same process later enabled Humphry Davy to isolate potassium and other metals. Volta also invented the electrophorus, the condenser and the electroscope. He made important contributions to meteorology. His study of gases included the discovery of methane. The volt, a unit of electrical measurement, is named after him.*TIS

1832 Octave Chanute(18 Feb 1832, 23 Nov 1910) U.S. aeronaut whose work and interests profoundly influenced Orville and Wilbur Wright and the invention of the airplane. Octave Chanute was a successful engineer who took up the invention of the airplane as a hobby following his early retirement. Knowing how railroad bridges were strengthened, Chanute experimented with box kites using the same basic strengthening method, which he then incorporated into wing design of gliders. Through thousands of letters, he drew geographically isolated pioneers into an informal international community. He organized sessions of aeronautical papers for the professional engineering societies that he led; attracted fresh talent and new ideas into the field through his lectures; and produced important publications. *TIS The town of Chanute, Kansas is named after him, as well as the former Chanute Air Force Base near Rantoul, Illinois, which was decommissioned in 1993. The former Base, now turned to peacetime endeavors, includes the Octave Chanute Aerospace Museum, detailing the history of aviation and of Chanute Air Force base. He was buried in Springdale Cemetery, Peoria, Illinois. *Wik

1838 Ernst Mach (18 Feb 1838; 19 Feb 1916 at age 77) Austrian physicist and philosopher who established important principles of optics, mechanics, and wave dynamics. His early physical works were devoted to electric discharge and induction. Between 1860 and 1862 he studied in depth the Doppler Effect by optical and acoustic experiments. He introduced the "Mach number" for the ratio of speed of object to speed of sound is named for him. When supersonic planes travel today, their speed is measured in terms that keep Mach's name alive. His lifetime interest, however, was in psychology and human perception. He supported the view that all knowledge is a conceptual organization of the data of sensory experience (or observation). *TIS

1844 Jacob Lüroth (18 Feb 1844 in Mannheim, Germany - 14 Sept 1910 in Munich, Germany) Lüroth was taught by Hesse and Clebsch and continued to develop their work on geometry and invariants. He published results in the areas of analytic geometry, linear geometry and continued the directions of his teachers in his publications on invariant theory. In 1869 Lüroth discovered the "Lüroth quartic". This came out of an investigation he was carrying out into when a ternary quartic form could be represented as the sum of five fourth powers of linear forms.
Some of his work on rational curves, published in Mathematische Annalen in 1876, was extended to surfaces by Castelnuovo in 1895. In 1883 Lüroth published his method on constructing a Riemann surface for a given algebraic curve.
Lüroth also worked on the big problem of the topological invariance of dimension. He made some useful progress but this difficult problem was not completely solved until the work of Brouwer in 1911.
Among his other work, Lüroth undertook editing. He was an editor of the complete works of Hesse and of Grassmann. He also has some fine results on logic, a topic he worked on in collaboration with his friend Ernst Schröder.
Von Staudt's ideas of geometry interested Lüroth and he further developed von Staudt's complex geometry. He published Grundriss der Mechanik in 1881. This mechanics book makes heavy use of the vector calculus. *sau

1871 George Udny Yule (18 Feb 1871 in Morham (near Haddington), Scotland - 26 June 1951 in Cambridge, Cambridgeshire, England) graduated in Engineering from University College London and then studied in Bonn. He worked with Karl Pearson on the statistics of regression and correlation. He took a post with an examinations board before being appointed to a Cambridge fellowship. He is best known for his book: Introduction to the Theory of Statistics.*SAU


901 Al-Sabi Thabit ibn Qurra al-Harrani (born c. 836, 18 Feb 901) was a Mesopotamian scholar and mathematician who greatly contributed to preparing the way for such important mathematical discoveries as the extension of the concept of number to (positive) real numbers, integral calculus, theorems in spherical trigonometry, analytic geometry, and non-euclidean geometry. In astronomy he was one of the first reformers of the Ptolemaic system, writing Concerning the Motion of the Eighth Sphere. He believed (wrongly) that the motion of the equinoxes oscillates. Including observations of the Sun, eight complete treatises by Thabit on astronomy have survived. In mechanics he was a founder of statics. He wrote The Book on the Beam Balance in which he finds the conditions for the equilibrium of a heavy beam. *TIS

1851 Karl Gustav Jacob Jacobi (10 Dec 1804; 18 Feb 1851) German mathematician who, with the independent work of Niels Henrik Abel of Norway, founded the theory of elliptic functions. He also worked on Abelian functions and discovered the hyperelliptic functions. Jacobi applied his work in elliptic functions to number theory. He also investigated mathematical analysis and geometry. Jacobi carried out important research in partial differential equations of the first order and applied them to the differential equations of dynamics. His work on determinants is important in dynamics and quantum mechanics and he studied the functional determinant now called the Jacobian. *TIS He died from smallpox, in his 47th year.*VFR

1856 Baron Wilhelm von Biela (19 Mar 1782, 18 Feb 1856 at age 73) Austrian astronomer who was known for his measurement (1826) of a previously known comet as having an orbital period of 6.6 years. Subsequently, known as Biela's Comet, it was observed to break in two (1846), and in 1852 the fragments returned as widely separated twin comets that were not seen again. However, in 1872 and 1885, bright meteor showers (known as Andromedids, or Bielids) were observed when the Earth crossed the path of the comet's known orbit. This observation provided the first concrete evidence for the idea that some meteors are composed of fragments of disintegrated comets.*TIS

1877 Charles Henry Davis (16 Jan 1807; 18 Feb 1877) U.S. naval officer and scientist who published several hydrographic studies, was a superintendent of the Naval Observatory (1865–67, 1874–77) and worked to further scientific progress. Between his naval duties at sea, he studied mathematics at Harvard. He made the first comprehensive survey of the coasts of Massachusetts, Rhode Island, and Maine, including the intricate Nantucket shoals area. He helped establish and then supervised the preparation of the American Nautical Almanac (1849) for several years. Davis was a co-founder of the National Academy of Sciences (1863), and wrote several scientific books.*TIS

1899 (Marius) Sophus Lie (17 Dec 1842; 18 Feb 1899) was a Norwegian mathematician who made significant contributions to the theories of algebraic invariants, continuous groups of transformations and differential equations. Lie groups and Lie algebras are named after him. Lie was in Paris at the outbreak of the French-German war of 1870. Lie left France, deciding to go to Italy. On the way however he was arrested as a German spy and his mathematics notes were assumed to be coded messages. Only after the intervention of French mathematician, Gaston Darboux, was Lie released and he decided to return to Christiania, Norway, where he had originally studied mathematics to continue his work. *TIS

1900 Eugenio Beltrami (November 16, 1835, Cremona – February 18, 1900, Rome) was an Italian mathematician notable for his work concerning differential geometry and mathematical physics. His work was noted especially for clarity of exposition. He was the first to prove consistency of non-Euclidean geometry by modeling it on a surface of constant curvature, the pseudosphere, and in the interior of an n-dimensional unit sphere, the so-called Beltrami–Klein model. He also developed singular value decomposition for matrices, which has been subsequently rediscovered several times. Beltrami's use of differential calculus for problems of mathematical physics indirectly influenced development of tensor calculus by Gregorio Ricci-Curbastro and Tullio Levi-Civita.*Wik
Beltrami studied elasticity, wave theory, optics, thermodynamics, and potential theory, and was among the first to explore the concepts of hyperspace and time as a fourth dimension. His investigations in the conduction of heat led to linear partial differential equations. Some of Beltrami's last work was on a mechanical interpretation of Maxwell's equations. *TIS

1944 Charles Benedict Davenport (1 Jun 1866, 18 Feb 1944 at age 77) American zoologist who contributed substantially to the study of eugenics (the improvement of populations through breeding) and heredity and who pioneered the use of statistical techniques in biological research. Partly as a result of breeding experiments with chickens and canaries, he was one of the first, soon after 1902, to recognize the validity of the newly discovered Mendelian theory of heredity. In Heredity in Relation to Eugenics (1911), he compiled evidence concerning the inheritance of human traits, on the basis of which he argued that the application of genetic principles would improve the human race. These data were at the heart of his lifelong promotion of eugenics, though he muddled science with social philosophy. *TIS

1957 Henry Norris Russell (25 Oct 1877; 18 Feb 1957) American astronomer and astrophysicist who showed the relationship between a star's brightness and its spectral type, in what is usually called the Hertzsprung-Russell diagram, and who also devised a means of computing the distances of binary stars. As student, professor, observatory director, and active professor emeritus, Russell spent six decades at Princeton University. From 1921, he visited Mt. Wilson Observatory annually. He analyzed light from eclipsing binary stars to determine stellar masses. Russell measured parallaxes and popularized the distinction between giant stars and "dwarfs" while developing an early theory of stellar evolution. Russell was a dominant force in American astronomy as a teacher, writer, and advisor. *TIS

1967 Julius Robert Oppenheimer (22 Apr 1904, 18 Feb 1967 at age 62) was an American theoretical physicist and science administrator, noted as director of the Los Alamos laboratory during development of the atomic bomb (1943-45) and as director of the Institute for Advanced Study, Princeton (1947-66). Accusations as to his loyalty and reliability as a security risk led to a government hearing that resulted the loss of his security clearance and of his position as adviser to the highest echelons of the U.S. government. The case became a cause célèbre in the world of science because of its implications concerning political and moral issues relating to the role of scientists in government. *TIS

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

A Serendipitous Coincidence? and The First-Ever Pursuit Problem.

Thoughts after a visit to the Needham Research Institute in Cambridge about a decade ago, worth sharing again I hope: Enjoy!

Just reading through some old copies of the Mathematical Spectrum from my great source of mathematical periodicals, Dave Renfro. Intrigued by a couple of posts about a problem from the ancient Chinese Chiu Chang Suan Shu or Jiuzhang suanshu (Nine Chapters of Mathematical Art...about 150 BC) submitted by David Singmaster.

The problem: "A water weed grows 3 feet on the first day, and its growth on each succeeding day is half that on the preceding day. A reed grows 1 foot on the first day and its growth on each successive day is twice that of the preceding day? When are they of equal size?"

Go ahead, stop reading for a minute and try to solve it because I give an answer (actually two different ones) below and I don't want to spoil the fun.

The interesting thing to me, was the two letters of solution. My pre-calc students came through exponential growth and decay a few chapters ago, so they would approve of the first solution that was submitted. It suggested that we assume that the height of the water weed was growing according to the exponential function hw= 3 (1.5)d-1. The reed would reach a height of hr=3d-1. Setting these equal we would find the heights are equal when d= log26; or at about 2.585 days. They also pointed out that the mutual heights would be 5.705 feet.

Simple, quick, and "Wrong" according to the next commenter. They pointed out that a careful reading of the problem stated that the water weed "growth on any succeeding day is half that of the preceding day", would meant that it grew 3 feet the first day, and then successively it would grow 3/2, 3/4, 3/8 ... feet on each day.. to find the height we should sum this geometric series. So he suggests the height of the water weed would be hw=. This would result in the weed being somewhat shorter after each day than in the previous solution. In the same way, the reed should, on successive days, change by 1, 2, 4, 8 etc feet, so it would have a height of 2d-1 after d days. Setting these equal we see that the two plants will both reach a height of five feet (exactly) after d= log26; or at about 2.585 days.???? WAIT, that sounds familiar....where have I ... Oh YEAH!!!, that was the answer to the problem done the first way? WOW, what a lucky coincidence........ Well, NO... the good Professor who posed the problem stepped up to assure us that, in fact, if you used those same two approaches to similar problems they would always reach equal heights at the same time... (can you prove that???)

Try for yourself. I assumed similar means that the shorter grows at r times its previous days amount, and the taller at 1/r times the previous day. Try a few. In fact, it is frequently the case that the second method gives an integer solution, and when it is not, it seems pretty easy to adjust the growth on the first day of the two plants to make it come out an integer. If we call the first day growths W and R, then the solution works out to logr(rb/a); where r is the common ratio of the plant whose growth each day is increasing.

Dr Singmaster points out that this ancient text solves both quadratics and cubics, as well as systems of equations (including indeterminate systems with more unknowns than equations) using the "modern" method of elimination. It also is the earliest known text to have used negative numbers, and includes the rules for all the arithmetic operations. It is also the oldest know source of chase or pursuit problems, such as this one. This is problem 11 of the 7th chapter. I had the good fortune to sit with my beautiful Jeannie as the only two non-Chinese speakers at a discussion about the text at the Needham Research Institute in Cambridge by a group of English and Chinese experts. The amount I was able to take in is a credit to the patience of the gracious hosts.

Monday, 17 February 2020

On This Day in Math - February 17

Statue of Quetelet in Brussels

Inductive inference is the only process known to us by which essentially new knowledge comes into the world.
~Sir Ronald Aylmer Fisher

The 48th day of the year; 48 is the smallest number with exactly ten divisors. (This is an interesting sequence, and students might search for others. Finding the smallest number with twelve divisors will be easier than finding the one with eleven.)

48 is also the smallest even number that can be expressed as a sum of two primes in 5 different ways:

If n is greater than or equal to 48, then there exists a prime between n and 9n/8 This is an improvement on a conjecture known as Bertrand's Postulate. In spite of the name, many students remember it by the little rhyme, "Chebyshev said it, but I'll say it again; There's always a prime between n and 2n ." Mathematicians have lowered the 2n down to something like n+n.6 for sufficiently large numbers.

48 is the smallest betrothed (quasi-amicable) number. 48 and 75 are a betrothed pair since the sum of the proper divisors of 48 is 75+1 = 76 and the sum of the proper divisors of 75 is 48+1=49. (There is only a single other pair of betrothed numbers that can be a year day)

And 48 x 48 = 2304 but 48 x 84 = 4032.

In 1719 Paul Halcke observed that the product of the aliquot divisors of 48 is equal to the fourth power of 48. 1*2*3*4*6*8*12*16*24= 5,308,416= 484.   48 and 80 are the only two year dates for which this is true.

1600 The Inquisition brought Giordano Bruno to the Campo dei Fiori in Rome’s center where they chained him to an iron stake and burned him alive for his beliefs that the earth rotated on its axis. *Amir Aczel, Pendulum, pg 9 (Aczel gives this date as the 19th but this date seems wrong. Thony Christie noted that " Bruno was executed on 17th Feb and not for his cosmology but for his heretical theology." Thanks... several other sources agree with Feb 17th date))

In 1857, the City of New York passed a charter to enable Peter Cooper to found a scientific institution in the city. He established the Cooper Union for the Advancement of Science and Art for the express purpose of improving the working classes by providing free education. Courses included algebra, geometry, calculus, chemistry, physics, mechanics, architectural and mechanical drawing. It also provided a School of Design for Women, a Musical Department, and a Free Library and Reading Room with all the periodicals of the day. By 1868, an article in the New York Times stated there were nearly 1500 students attached to the instiution, and the classes, which included night classes, were universally full. *TIS

In 1869, Dmitri Mendeleev cancelled a planned visit to a factory and stayed at home working on the problem of how to arrange the chemical elements in a systematic way. To begin, he wrote each element and its chief properties on a separate card and arranged these in various patterns. Eventually he achieved a layout that suited him and copied it down on paper. Later that same day he decided a better arrangement by properties was possible and made a copy of that, which had similar elements grouped in vertical columns, unlike his first table, which grouped them horizontally. These historic documents still exist, and mark the beginning of the form of the Periodic Table as commonly used today. (The date is given by the Julian calendar in use in Russia at the time. The Gregorian date is March 1) *TIS

1994 A small satellite named Dactyl was found which orbits the asteroid Ida. This was the first discovery of a satellite orbiting and asteroid. Dactyl was discovered in images taken by the Galileo spacecraft during its flyby in 1993. Dactyl was found on 17 February 1994 by Galileo mission member Ann Harch, while examining delayed image downloads from the spacecraft.
It was named by the International Astronomical Union in 1994, for the mythological dactyls who inhabited Mount Ida on the island of Crete. It is only 1.4 kilometres (4,600 ft) in diameter. *Wik

In 1996, world chess champion Gary Kasparov defeated Deep Blue, IBM's chess-playing computer, by winning a six-game match 4-2, in a regulation-style match held in Philadelphia, as part of the ACM Computer Science Conference. Deep Blue is an improved version of the older Deep Thought, augmented by parallel special-purpose hardware. Deep Blue uses a selectively deepening search strategy, using improvements of the alpha-beta search strategy, with powerful evaluation functions. Transposition tables help avoid unnecessarily calculating the same position more than once. Two powerful databases further augment Deep Blue's play. *TIS On May 11, 1997, the machine won a six-game match by two wins to one with three draws against world champion Garry Kasparov, the first time the grandmaster ever lost a six-game match in championship play. *Wik

2015 After a weekend of celebrating, the 65th annual International Pancake race will take place in Liberal, Kansas, USA and Olney, England. The celebration is associated with Pancake day, which is often used as a name for Shrove Tuesday in many Western countries. History of the event, and a schedule of the (now) week-long activities is here. The race in 2016 was won by a woman from Olney,  The score now stands with Liberal winning 37 times, Olney 29.although according to legend, Olney Pancake Race began in 144, so Lliberal has to win a bunch of races to catch up. In 2020 the race will occur on Feb 25th, So you still have time to get there and run (or watch).

1201 Khawaja Muhammad ibn Muhammad ibn Hasan Tūsī (17 February 1201; Ṭūs, Khorasan – 25 June 1274; Baghdad), better known as Nasīr al-Dīn Tūsī was a Persian polymath and prolific writer: An architect, astronomer, biologist, chemist, mathematician, philosopher, physician, physicist, scientist, and theologian
Tusi convinced Hulegu Khan to construct an observatory for establishing accurate astronomical tables for better astrological predictions. Beginning in 1259, the Rasad Khaneh observatory was constructed in Azarbaijan, west of Maragheh, the capital of the Ilkhanate Empire.
Based on the observations in this for the time being most advanced observatory, Tusi made very accurate tables of planetary movements as depicted in his book Zij-i ilkhani (Ilkhanic Tables). This book contains astronomical tables for calculating the positions
of the planets and the names of the stars. His model for the planetary system is believed to be the most advanced of his time, and was used extensively until the development of the heliocentric model in the time of Nicolaus Copernicus.
For his planetary models, he invented a geometrical technique called a Tusi-couple, which generates linear motion from the sum of two circular motions. He used this technique to replace Ptolemy's problematic equant for many planets, but was unable to find a solution to Mercury. The Tusi couple was later employed in Ibn al-Shatir's geocentric model and Nicolaus Copernicus' heliocentric Copernican model.
Al-Tusi was the first to write a work on trigonometry independently of astronomy. In his Treatise on the Quadrilateral he gave an extensive exposition of spherical trigonometry, distinct from astronomy. It was in the works of Al-Tusi that trigonometry achieved the status of an independent branch of pure mathematics distinct from astronomy, to which it had been linked for so long. He was also the first to list the six distinct cases of a right triangle in spherical trigonometry.
In his On the Sector Figure, appears the famous law of sines for plane triangles.

\( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \)

He also stated the law of sines for spherical triangles,discovered the law of tangents for spherical triangles, and provided proofs for these laws. *Wik

1723 Tobias Meyer (17 Feb 1723; 20 Feb 1762 at age 38) German astronomer who developed lunar tables that greatly assisted navigators in determining longitude at sea. Mayer also discovered the libration (or apparent wobbling) of the Moon. Mayer began calculating lunar and solar tables in 1753 and in 1755 he sent them to the British government.
 These tables were good enough to determine longitude at sea with an accuracy of half a degree. Mayer's method of determining longitude by lunar distances and a formula for correcting errors in longitude due to atmospheric refraction were published in 1770 after his death. The Board of Longitude sent Mayer's widow a payment of 3000 pounds as an award for the tables. *TIS Leonhard Euler described him as 'undoubtedly the greatest astronomer in Europe'. More notes on Meyer can be found on this blog at the Board of Longitude Project from the Royal Museums at Greenwich.
In 1758, Mayer attempted to define the number of colors that the eye can distinguish with accuracy. His color triangle was first published in 1775 by the Göttinger physicist Georg Christoph Lichtenberg — more than 12 years after Mayer’s death.

1765 Sir James Ivory (17 February 1765 – 21 September 1842) was a Scottish mathematician born in Dundee. He was essentially a self-trained mathematician, and was not only deeply versed in ancient and modern geometry, but also had a full knowledge of the analytical methods and discoveries of the continental mathematicians.
His earliest memoir, dealing with an analytical expression for the rectification of the ellipse, is published in the Transactions of the Royal Society of Edinburgh (1796); and this and his later papers on Cubic Equations (1799) and Kepler's Problem (1802) evince great facility in the handling of algebraic formulas. In 1804 after the dissolution of the flax-spinning company of which he was manager, he obtained one of the mathematical chairs in the Royal Military College at Marlow (afterwards removed to Sandhurst); and until the year 1816, when failing health obliged him to resign, he discharged his professional duties with remarkable success.*Wik It has been suggested that Ivory may have suffered from schizophrenia (*ALEX D. D. CRAIK) of some type throughout his life.

Ivory, because of his mental problems, tended to quarrel with his fellow mathematicians. His relations with Wallace deteriorated with arguments over Ivory's Attraction article to Encyclopaedia Britannica. Ivory's article on Capillary action for the same publication led to an argument with Thomas Young. Many other cases were simply caused by Ivory suffering from a quite incorrect belief that he was being persecuted by others. In fact he never joined the Royal Astronomical Society, despite his interests in astronomy, since he believed that members of that Society were systematically working against him. As De Morgan wrote that Ivory was of
... thoroughly sound judgement in every other respect seemed to be under a complete chain of delusions about the conduct of others to himself. But the paradox is this: - I never could learn that Ivory, passing his life under the impression that secret and unprovoked enemies were at work upon his character, ever originated a charge, imputed a bad motive, or allowed himself an uncourteous expression.

1874 Thomas J. Watson Sr. is born. A shrewd businessman, Watson started his career as a cash register salesman, eventually taking the helm of IBM and directing it to world leadership in punch card equipment sales. Watson died in 1956 and control of IBM passed on to his son, Thomas Watson, Jr. who brought IBM into the electronic age and, after several bold financial risks, to dominance in the computer industry.*CHM

1888 Otto Stern (17 Feb 1888; 17 Aug 1969 at age 81) German-American scientist and winner of the Nobel Prize for Physics in 1943 for his development of the molecular beam as a tool for studying the characteristics of molecules and for his measurement of the magnetic moment of the proton. *TIS

1890 Ronald Aylmer Fisher FRS (17 February 1890 – 29 July 1962) was an English statistician, evolutionary biologist, eugenicist and geneticist. Among other things, Fisher is well known for his contributions to statistics by creating Fisher's exact test and Fisher's equation. Anders Hald called him "a genius who almost single-handedly created the foundations for modern statistical science" while Richard Dawkins called him "the greatest of Darwin's successors". In 2010 Dawkins named him "the greatest biologist since Darwin". Fisher was opposed to the conclusions of Richard Doll and A.B. Hill that smoking caused lung cancer. He compared the correlations in their papers to a correlation between the import of apples and the rise of divorce in order to show that correlation does not imply causation.
To quote Yates and Mather, "It has been suggested that the fact that Fisher was employed as consultant by the tobacco firms in this controversy casts doubt on the value of his arguments. This is to misjudge the man. He was not above
accepting financial reward for his labours, but the reason for his interest was undoubtedly his dislike and mistrust of puritanical tendencies of all kinds; and perhaps also the personal solace he had always found in tobacco."
After retiring from Cambridge University in 1957 he spent some time as a senior research fellow at the CSIRO in Adelaide, Australia. He died of colon cancer there in 1962.
He was awarded the Linnean Society of London's prestigious Darwin–Wallace Medal in 1958.
Fisher's important contributions to both genetics and statistics are emphasized by the remark of L.J. Savage, "I occasionally meet geneticists who ask me whether it is true that the great geneticist R.A. Fisher was also an important statistician"*Wik The stained glass window is from the Greatroom at Caius College.

1891 Abraham Halevi (Adolf) Fraenkel (February 17, 1891, Munich, Germany – October 15, 1965, Jerusalem, Israel) known as Abraham Fraenkel, was an Israeli mathematician born in Germany. He was an early Zionist and the first Dean of Mathematics at the Hebrew University of Jerusalem. He is known for his contributions to axiomatic set theory, especially his addition to Ernst Zermelo's axioms which resulted in Zermelo–Fraenkel axioms.*Wik

1905 Rózsa Péter (orig.: Politzer) (17 February 1905–16 February 1977) was a Hungarian mathematician. She is best known for her work with recursion theory.
Péter was born in Budapest, Hungary, as Rózsa Politzer (Hungarian: Politzer Rózsa). She attended Eötvös Loránd University, where she received her PhD in 1935. After the passage of the Jewish Laws of 1939 in Hungary, she was forbidden to teach because of her Jewish origin. After the war she published her key work, Recursive Functions.
She taught at Eötvös Loránd University from 1955 until her retirement in 1975. She was a corresponding member of the Hungarian Academy of Sciences (1973).*Wik In 1951 she wrote the first monograph on recursive function theory.

1950 Viktor Aleksandrovich Gorbunov (17 Feb 1950 in Russia - 29 Jan 1999 in Novosibirsk, Russia) He published his first paper in 1973 being a joint work with A I Budkin entitled Implicative classes of algebras (Russian). The implicative class of algebras is a generalisation of quasivarieties. The structural characteristics of the implicative class are studied in this paper. A second join paper with Budkin On the theory of quasivarieties of algebraic systems (Russian) appeared in 1975. In the same year he published Filters of lattices of quasivarieties of algebraic systems (Russian), this time written with V P Belkin. In fact he had written six papers before his doctoral thesis On the Theory of Quasivarieties of Algebraic Systems was submitted. He received the degree in 1978. Gorbunov continued working at Novosibirsk State University, being promoted to professor. He also worked as a researcher in the Mathematics Institute of the Siberian Branch of the Russian Academy of Sciences. *SAU

1600 Giordano Bruno (born 1548 - 17 Feb 1600)Italian philosopher, astronomer, mathematician and occultist whose theories anticipated modern science. The most notable of these were his theories of the infinite universe and the multiplicity of worlds, in which he rejected the traditional geocentric (or Earth-centred) astronomy and intuitively went beyond the Copernican heliocentric (sun-centred) theory, which still maintained a finite universe with a sphere of fixed stars. Although one of the most important philosophers of the Italian Renaissance, Bruno's various passionate utterings led to opposition. In 1592, after a trial he was kept imprisoned for eight years and interrogated periodically. When, in the end, he refused to recant, he was burned at the stake in Rome for heresy.*TIS Professor Rickey of USMA disagrees about Bruno's "failure to recant." "It is a nineteenth century myth that he refused to recant his view that the earth moves." *VFR

1680 Jan Swammerdam (February 12, 1637, Amsterdam – February 17, 1680) was a Dutch biologist and microscopist. His work on insects demonstrated that the various phases during the life of an insect—egg, larva, pupa, and adult—are different forms of the same animal. As part of his anatomical research, he carried out experiments on muscle contraction. In 1658, he was the first to observe and describe red blood cells. He was one of the first people to use the microscope in dissections, and his techniques remained useful for hundreds of years.*Wik

1865 George Phillips Bond (20 May 1825, 17 Feb 1865 at age 39) American astronomer who made the first photograph of a double star, discovered a number of comets, and with his father discovered Hyperion, the eighth moon of Saturn. *TIS

1867 Alexander Dallas Bache (19 Jul 1806, 17 Feb 1867 at age 60) was an American physicist who was Ben Franklin's great grandson and trained at West Point. Bache became the second Superintendent of the Coast Survey (1844-65). He made an ingenious estimate of ocean depth (1856) by studying records of a tidal wave that had taken 12 hours to cross the Pacific. Knowing that wave speeds depend on depth, he calculated a 2.2- mile average depth for the Pacific (which is within 15% of the presently accepted value). Bache created the National Academy of Sciences, securing greater government involvement in science. Through the Franklin Institute he instituted boiler tests to promote safety for steamboats. *TIS

1874 (Lambert) Adolphe (Jacques) Quetelet (22 Feb 1796, 17 Feb 1874 at age 78) was a Belgian mathematician, astronomer, statistician, and sociologist known for his pioneering application of statistics and the theory of probability to social phenomena, especially crime. At an observatory in Brussels that he established in 1833 at the request of the Belgian government, he worked on statistical, geophysical, and meteorological data, studied meteor showers and established methods for the comparison and evaluation of the data. In Sur l'homme et le developpement de ses facultés, essai d'une physique sociale (1835) Quetelet presented his conception of the average man as the central value about which measurements of a human trait are grouped according to the normal curve. *TIS Quetelet created the Body Mass Index in a paper in 1832.  It was known as the Quetelet Index until it was termed the Body Mass Index in 1972 by Ancel Keys.

1875 Friedrich Wilhelm August Argelander (22 Mar 1799, 17 Feb 1875 at age 75)
German astronomer who established the study of variable stars as an independent branch of astronomy and is renowned for his great catalog listing the positions and brightness of 324,188 stars of the northern hemisphere above the ninth magnitude. He studied at the University of Königsberg, Prussia, where he was a pupil and later the successor of Friedrich Wilhelm Bessel. In 1837, Argelander published the first major investigation of the Sun's motion through space. In 1844 he began studies of variable stars.*TIS

1947 Ettore Bortolotti (6 March 1866 in Bologna, Kingdom of Sardinia (now Italy) - 17 Feb 1947 in Bologna, Italy) Italian mathematician who worked in various areas in analysis. He was interested in the history of mathematics. *SAU

1974 Heinrich Franz Friedrich Tietze contributed to the foundations of general topology and developed important work on subdivisions of cell complexes. The bulk of this work was carried out after he took up the chair at Munich in 1925.*SAU

2012 Nicolaas Govert "Dick" de Bruijn (9 July 1918 – 17 February 2012) was a Dutch mathematician, affiliated as professor emeritus with the Eindhoven University of Technology. He received his Ph.D. in 1943 from Vrije Universiteit Amsterdam.
De Bruijn covered many areas of mathematics. He is especially noted for the discovery of the De Bruijn sequence. He is also partly responsible for the De Bruijn–Newman constant, the De Bruijn–Erdős theorem (in both incidence geometry and graph theory) and the BEST theorem. He wrote one of the standard books in advanced asymptotic analysis (De Bruijn, 1958). De Bruijn also worked on the theory of Penrose tilings. In the late sixties, he designed the Automath language for representing mathematical proofs, so that they could be verified automatically (see automated theorem checking). Lately, he has been working on models for the human brain.*Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Sunday, 16 February 2020

On This Day in Math - February 16

The Goose Girl Fountain in Gottingen

Whenever you can, count.
~Sir Francis Galton

The 47th day of the year; 47 is a Thabit number, named after the Iraqi mathematician Thâbit ibn Kurrah number, of the form 3 * 2n -1 (sometimes called 3-2-1 numbers). He studied their relationship to Amicable numbers. All Thabit numbers expressed in binary end in 10 followed by n ones, 47 in binary is 101111.
(The rule is that if p=3*2n-1 -1, q= 3*2n -1, and r = 9*2n-1 -1, are all prime, then 2npq and 2nr are amicable numbers.

3^3^3^3^3^3^3 has 47 distinct values depending on parentheses. *Math Year-Round ‏@MathYearRound

"The 47 Society is an international interest-group that follows the occurrence and recurrence of the quintessential random number: 47. Many suspect that the coincidental nature of 47 carries some mystical, metaphysical and/or scientific significance." *

Mario Livio has pointed out that this date written month day as 216, 216=63 and also 216=33+43+53

The 47th day gives me a reason to include this brief story of Thomas Hobbes from Aubrey's "Brief Lives". The 47th proposition of Libre I of The Elements (The Pythagorean Theorem) seemed so obviously false to him that, in following the reasoning back, his life was changed:
He was (vide his life) 40 yeares old before he looked on geometry; which happened accidentally. Being in a gentleman’s library in . . . , Euclid’s Elements lay open, and ’twas the 47 El. libri I. He read the proposition. ‘By† G—,’ sayd he, ‘this is impossible!’So he reads the demonstration of it, which referred him back to such a propo- sition; which proposition he read. That referred him back to another, which he also read. Et sic deinceps,(and so back to the beginning) that at last he was demonstratively convinced of that trueth. This made him in love with geometry.


1615 Galileo sends Piero Dini a modified copy of his letter to Castelli which had been the basis of an accusation of heresy by Nicolo Lorini to the Holy office in Rome. He included a cover letter on this date downplaying some of the points in his original and asked Dini to show it to Cardial Bellarmine, the chief theologian of the church. *Brody & Brody, The Science Class You Wish You Had

1745 Euler in a letter to Goldbach, first mentions factorization of a number using the representation of the sum of two squares . *Oystein Orr, Number Theory and Its History
Included in the letter is the proof that all integers that are the sum of two squares in more than one way must be composite; there are no prime numbers that can be expressed as the sum of two squares in more than one way.

In 1880, the American Society of Mechanical Engineers was founded when 40 engineers from eight states met in New York City in the office of American Machinist. In the same year, an organizational meeting was held on Apr 7, and the first annual meeting took place 4-5 Nov. Robert Henry Thurston was its first president. Thurston had established an engineering school at the new Stevens Institute of Technology in New Jersey and would later create an engineering school at Cornell. *TIS

1910 At 6pm Richard Courant was administered his oral exams by Hilbert (who left early), Voight (who did not appear), and Husserl (who arrived late). Afterwards, “the little Courant” as he was known, gave the customary kiss to the little goose girl in the fountain in the square, and then hired a droschke and his two friends drove him around the city announcing to all “Dr. Courant, Summa Cum Laude.” *Reid, Hilbert, pg 124

1912 ‏Thomas Jennings, hanged 16 Feb 1912, was the first US murder case decided with fingerprint evidence. *@executedtoday

In 1948, Miranda, a famous moon of Uranus, was photographed for first time. It was discovered by Gerard Kuiper, the Dutch astronomer, who also found Neptune's moon Nereid (1949). Miranda is the smallest of the five 5 major satellites of Uranus, and has a diameter of 480 km. When Voyager 2 passed closely by Miranda in 1986, it showed it was one of the most interesting satellites in the solar system, with a complex geological history. The numerous pictures it took of the surface showed a vast and diverse array of fractures, faults, grooves and craters unlike anything ever seen before. The large (318 km diam.) circular region is named the Arden Corona. Miranda is named after a character in Shakespeare's "The Tempest." Arden is the name of a forest, in which his play "As You Like It." is set.*TIS

1982 Sweden issued three stamps picturing impossible figures. Does this twisted triangle have a name? [Scott #1396–8] *VFR  Yes, The figure is called a Tribar, and sometimes a Penrose Triangle.  It was firstly painted in 1934 by swedish painter Oscar Reutersvärd. He drew his version of triangle as a set of cubes in parallel projection.  Roger Penrose, and his father, Lionel also independently discovered the triangle in the 1950's.  Maurice Escher used and popularized the idea even more in his drawings. 
There are at least two sculptures depicting the tribar when viewed from the right perspective.  One is in Perth Australia (shown below), and another in  Gotschuchen, Austria.

1984 In a Dungeons of Doom computer adventure game at the University of Texas at Austin, the Rogue, manipulated by an expert system, descended through the 26 levels of the dungeons, fought off all monsters, seized the Amulet of Yendor, amassed a considerable pile of gold and returned safely to the surface, being the first ever to do so. See Scientific American, February 1985, esp. p. 19. *VFR

1993 Great Britain issues a set of stamps with four views (dial and hands; train remontoire; temperature compensation-curb; top plate and balance-brake) of Harrison’s Marine Timekeeper number four to commemorate the 300th anniversary of Harrison’s birth year (his birthdate and date of death were both March 24). Harrison was a self-educated English clockmaker. He invented the marine chronometer, a long-sought device in solving the problem of establishing the East-West position or longitude of a ship at sea, thus revolutionizing and extending the possibility of safe long distance sea travel in the Age of Sail. The problem was considered so intractable that the British Parliament offered a prize of £20,000 (comparable to £2.87 million in modern currency) for the solution.*Wik

1514 Georg Joachim Rheticus (16 Feb 1514; 4 Dec 1576 at age 62) German astronomer and mathematician who was among the first to adopt and spread the heliocentric theory of Nicolaus Copernicus. He was first taught by his father, a physician, who was beheaded for sorcery (1528) while Rheticus was still a teenager. He is best known as the first disciple of Copernicus. In 1540, Rheticus published the first account of the heliocentric hypothesis which had been elaborated by Copernicus, entitled Narratio prima, which was explicitly authorised by Copernicus, who also asked for his friend's aid in editing the edition of his De revolutionibus orbium coelestium ("On the revolutions of the heavenly spheres"). Rheticus was the first mathematician to regard the trigonometric functions in terms of angles rather than arcs of a circle.*TIS

For much of his life, Rheticus displayed a passion for the study of triangles, the branch of mathematics now called trigonometry. In 1542 he had the trigonometric sections of Copernicus' De revolutiobis published separately under the title De lateribus et angulis triangulorum (On the Sides and Angles of Triangles). In 1551 Rheticus produced a tract titled Canon of the Science of Triangles, the first publication of six-function trigonometric tables (although the word trigonometry was not yet coined). Neither did he use the current names for any of them. Prior to Rheticus, European mathematicians used only the sine, and the versed sine (although Johannes Regiomontanus, Tabulae directionum et profectionum, Augsburgii 1490 had calculated what is essentially the tangent.) Rheticus seems to have had an aversion to the term sine. He called his principal units the perpendicular of the first species (sine), the base of the first species (cosine) with the hypotenuse being the hypotenuse was the radius for the first species triangle. Then, he decided to construct a triangle of the second species with the base as a radius. Then the perpendicular of the second species (tangent) and the hypotenuse of the second species(secant). For the third species he chooses the perpendicular of the triangle as the radius, and so the base of the third species (cotangent) and hypotenuse of the thrid species (cosecant) are found.
This pamphlet was to be an introduction to Rheticus' greatest work, a full set of tables to be used in angular astronomical measurements.
At his death, the Science of Triangles was still unfinished. However, paralleling his own relationship with Copernicus, Rheticus had acquired a student who devoted himself to completing his teacher's work. Valentin Otto oversaw the hand computation of approximately 100,000 ratios to at least ten decimal places. When completed in 1596, the volume, Opus palatinum de triangulis, filled nearly 1,500 pages. Its tables were accurate enough to be used in astronomical computation into the early twentieth century. *Wik

1698 Pierre Bouguer (16 Feb 1698; 15 Aug 1758 at age 60) In 1727 he won the prize competition of the Acad´emie Royal des Sciences on the masting of ships. In this competition Euler only received the “accessit.” *VFR
Two days before (Aug 13)Charles-Etienne-Louis Camas was elected to the French Academy of Sciences because he had earlier won half the prize money in their competition for the best manner of masting vessels. (did Bouguer get the other half? Did Euler get any? is one, or more of these three pieces of information incorrect?)*PB
French physicist whose work founded photometry, the measurement of light intensity. He was a child prodigy, a professor at age 15, following his father, Jean Bouguer, in hydrography - the study of bodies of water, both salt and fresh. He participated on the expedition to Peru (1735-44) to measure an arc of the meridian near the equator. In 1729, he invented a photometer to compare the intensity of two light sources illuminating separate halves of translucent paper. The eye itself, he determined, could not be used as a meter, but could establish the equality of brightness of adjacent surfaces. He determined the sun was 300 times brighter the moon. Bouguer's law gives the attenuation of a beam of light by an optically homogeneous (transparent) medium.*TIS

1822 Sir Francis Galton (16 Feb 1822, 17 Jan 1911) English scientist, founder of eugenics, statistician and investigator of intellectual ability. He explored in south-western Africa. In meteorology, he was first to recognise and name the anticyclone. He interpreted the theory of evolution of (his cousin) Charles Darwin to imply inheritance of talent could be manipulated. Galton had a long-term interest in eugenics - a word he coined for scientifically selected parenthood to enable inheritance of beneficial characteristics. He coined the phrase "nature versus nurture." Galton experimentally verified the uniqueness of fingerprints, and suggested the first classification based on grouping the patterns into arches, loops, and whorls. On 1 Apr 1875, he published the first newspaper weather map in The Times *TIS

1838 Henry Adams born. In his autobiography, The Education of Henry Adams, he wrote in the third person: “At best he would never have been a mathematician; at worst he would never have cared to be one; But he needed to read mathematics, like any other universal language, and he never reached the alphabet.” *VFR

1903 Beniamino Segre (16 February 1903 – 2 October 1977) was an Italian mathematician who is remembered today as a major contributor to algebraic geometry and one of the founders of combinatorial geometry. Among his main contributions to algebraic geometry are studies of birational invariants of algebraic varieties, singularities and algebraic surfaces. His work was in the style of the old Italian School, although he also appreciated the greater rigour of modern algebraic geometry. Another contribution of his was the introduction of finite and non-continuous structures into geometry. In his best known paper he proved the following theorem: In a Desarguesian plane of odd order, the ovals are exactly the irreducible conics. Some critics felt that his work was no longer geometry, but today it is recognized as a separate sub-discipline: combinatorial geometry.
In 1938 he lost his professorship as a result of the anti-Jewish laws enacted under Benito Mussolini's government; he spent the next 8 years in Great Britain (mostly at the University of Manchester), then returned to Italy to resume his academic career *Wik

1937 Yuri Ivanovitch Manin (1937, Simferopol - ) is a Soviet/Russian/German mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics.
Manin's early work included papers on the arithmetic and formal groups of abelian varieties, the Mordell conjecture in the function field case, and algebraic differential equations. The Gauss–Manin connection is a basic ingredient of the study of cohomology in families of algebraic varieties. He wrote an influential book on cubic surfaces and cubic forms, showing how to apply both classical and contemporary methods of algebraic geometry, as well as nonassociative algebra. He also indicated the role of the Brauer group, via Grothendieck's theory of global Azumaya algebras, in accounting for obstructions to the Hasse principle, setting off a generation of further work. He has also written on Yang-Mills theory, quantum information, and mirror symmetry.*Wik

1636 Henry Gellibrand (17 Nov 1597, 16 Feb 1636 at age 38) English astronomer and mathematician who co-discovered (with John Marr) the geomagnetic secular variation. This refers to the magnetic declination of the earth's magnetic field, the angle between magnetic north and true north, changing on a long-term time scale over years. He detected the direction of a compass needle in London had changed by seven degrees over a period of a half-century. He became professor of astronomy at Gresham College, London on 2 Jan 1627. His navigation textbooks helped improve English navigation at the time.Using manuscripts left unfinished when his friend Henry Briggs died (1630), he completed volume two of Briggs's Trigonometrica Britannica, in 1633. Gellibrand published A Discourse Mathematicall on the Variation of the Magneticall Needle, in 1635. He died the following year, at age 39.*TIS He was Professor at Gresham College, succeeding Edward Gunter in 1626. He was buried in St Peter Le Poer. (London, demolished in 1907) *Wik

1892 Thomas Archer Hirst FRS (22 April 1830 – 16 February 1892) was a 19th century mathematician, specializing in geometry. He was awarded the Royal Society's Royal Medal in 1883.Hirst was a projective geometer in the style of Poncelet and Steiner. He was not an adherent of the algebraic geometry approach of Cayley and Sylvester, despite being a personal friend of theirs. His specialty was Cremona transformations.*Wik

1956 Meghnad Saha FRS (6 October 1893 – 16 February 1956) was an Indian astrophysicist best known for his development of the Saha ionization equation, used to describe chemical and physical conditions in stars. Saha was the first scientist to relate a star's spectrum to its temperature, developing thermal ionization equations that have been foundational in the fields of astrophysics and astrochemistry. He was repeatedly and unsuccessfully nominated for the Nobel Prize in Physics. Saha was also politically active and was elected in 1952 to India's parliament. *Wik

1957 Sir John Sealy Edward Townsend (7 Jun 1868, 16 Feb 1957 at age 88) British physicist who pioneered in the study of electrical conduction in gases. In 1898 he made the first direct measurement of the unit electrical charge (e). As a postgraduate, he was a research student of J. J. Thomson. In 1897, Townsend developed the falling-drop method for measuring e, using saturated clouds of charged water droplets (extended by Robert Millikan's highly accurate oil-drop method). He was first to explain how electric discharges pass through gases (Electricity in Gases, 1915) whereby motion of electrons in an electric field releases more electrons by collision. These in turn collide releasing even more electrons in a multiplication of charges known as an avalanche. *TIS

1977 Rózsa Péter (orig.: Politzer), Hungarian name Péter Rózsa, (17 February 1905–16 February 1977) was a Hungarian mathematician. She is best known for her work with recursion theory.
Péter was born in Budapest, Hungary, as Rózsa Politzer (Hungarian: Politzer Rózsa). She attended Eötvös Loránd University, where she received her PhD in 1935. After the passage of the Jewish Laws of 1939 in Hungary, she was forbidden to teach because of her Jewish origin. After the war she published her key work, Recursive Functions.
She taught at Eötvös Loránd University from 1955 until her retirement in 1975. She was a corresponding member of the Hungarian Academy of Sciences (1973).*Wik

1980 Edward Copson (21 Aug 1901; 16 Feb 1980) English mathematician known for his studies in classical analysis, differential and integral equations, and their use in mathematical physics. After graduating from Oxford University with a B.A. degree in 1922, he moved to Scotland where he spent the nearly all of his career. His first book, The Theory of Functions of a Complex Variable (1935) was immediately successful. He was a co-author for his next book, The Mathematical Theory of Huygens' Principle (1939). By 1975, he had published four more books, on asymptotic expansions, metric spaces and partial differential equations. Many of the papers he wrote bridged mathematics and physics, of which his last showed his interest in astrophysics, Electrostatics in a Gravitational Field (1978) which was relevant to Black Holes.*TIS

1997 Chien-Shiung Wu (simplified Chinese: 吴健雄; traditional Chinese: 吳健雄; pinyin: Wú Jiànxióng, May 31, 1912 – February 16, 1997) was a Chinese American experimental physicist who made significant contributions in the field of nuclear physics. Wu worked on the Manhattan Project, where she helped develop the process for separating uranium metal into uranium-235 and uranium-238 isotopes by gaseous diffusion. She is best known for conducting the Wu experiment, which contradicted the hypothetical law of conservation of parity. This discovery resulted in her colleagues Tsung-Dao Lee and Chen-Ning Yang winning the 1957 Nobel Prize in physics, and also earned Wu the inaugural Wolf Prize in Physics in 1978. Her expertise in experimental physics evoked comparisons to Marie Curie. Her nicknames include "the First Lady of Physics", "the Chinese Madame Curie", and the "Queen of Nuclear Research".*Wik

1997 Leon Bankoff (December 13, 1908, New York City, NY -February 16, 1997, Los Angeles, CA), was an American dentist and mathematician.
After a visit to the City College of New York, Bankoff studied dentistry at New York University. Later, he moved to Los Angeles, California, where he taught at the University of Southern California; while there, he completed his studies. He practiced over 60 years as a dentist in Beverly Hills. Many of his patients were celebrities.
Along with Bankoff's interest in dentistry were the piano and the guitar. He was fluent in Esperanto, created artistic sculptures, and was interested in the progressive development of computer technology. Above all, he was a specialist in the mathematical world and highly respected as an expert in the field of flat geometry. Since the 1940s, he lectured and published many articles as a co-author. Bankoff collaborated with Paul Erdős in a mathematics paper and therefore has an Erdős number 1.
From 1968 to 1981, Bankoff was the editor of the Problem Department of Pi Mu Epsilon Journals, where he was responsible for the publication of some 300 top problems in the area of plane geometry, particularly Morley's trisector theorem, and the arbelos of Archimedes. Among his discoveries with the arbelos was the Bankoff circle, which is equal in area to Archimedes' twin circles. Martin Gardner called Bankoff, “one of the most remarkable mathematicians I have been privileged to know.” *Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell