## Saturday, 20 February 2016

### 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.

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

EVENTS
1648 A letter from Fermat through Frenicle to Digby reached Wallis saying that Fermat had solve 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

BIRTHS
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

DEATHS
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