Monday, 18 March 2019

On This Day in Math - March 18

Steiner eircumellipse *wolfram  alpha

Scientific discovery consists in the interpretation for our own convenience of a system of existence which has been made with no eye to our convenience at all.
~Norbert Wiener


The 77th day of the year; 77 is the only number less than 100 with a multiplicative persistence of 4. Can you find the next? (Multiply all the digits of a number n, repeating with the product until a single digit is obtained. The number of steps required is known as the multiplicative persistence, and the final digit obtained is called the multiplicative digital root of n.) There is not another year day that will have a multiplicative persistence greater than four. [7x7=49, 4x9=36, 3x6=18, 1x8=8]

772 is the smallest square number that can be the sum of consecutive squares greater than 1, \(sum_{k=18}^{28}k^2 = 77^2\)

The concatenation of all palindromes from one up to 77 is prime.

77 is equal to the sum of three consecutive squares, \(4^2 + 5^2 + 6^2= 77\) and also the sum of the first 8 primes. *Prime Curios


EVENTS

2012 The Sunday following March 15 is "Buzzard Sunday" at the Hinckley Reservation (Near Cleveland, Ohio) a family fun day celebrating the buzzards (a common name for the "turkey vulture,"). Every year on March 15 since 1957, the city of Hinckley Ohio has eagerly awaited the return of the buzzards at "Buzzards' Roost" at the Hinckley Reservation, part of the Cleveland Metroparks. *about.com

1973 Comet Kohoutek, formally designated C/1973 E1, 1973 XII, and 1973f, was first discovered on this date while examining photographic plates taken on 7 March 1973 by Czech astronomer Luboš Kohoutek. It attained perihelion on 28 December that same year. Will not be back for a really, really long time.

In 1987, the discovery of "high-temperature" superconductivity was announced to thousands of scientists at a packed meeting of the American Physical Society in New York City. The phenomenon, discovered 1911, was at first known to occur at only 4 degrees above absolute zero, when all electrical resistance in a metal sample disappeared. In 1986, researchers discovered a ceramic material that was a superconductor at a temperature of more than 30 degrees above absolute zero. When published in September of that year, that news stirred the wider scientific community into action. By the time of the APS meeting, further discoveries had been made. The scene of excitement at the meeting was dubbed the "Woodstock of Physics." *TIS

1990 The Mathematische Gesellschaft, the world’s oldest existing mathematical society (founded 1690) began a seven day meeting in Hamburg to celebrate its third centenary. *VFR

2010 It was announced that Grigori Yakovlevich Perelman had met the criteria to receive the first Clay Millennium Prize for resolution of the Poincaré conjecture. On 1 July 2010, he turned down the prize of one million dollars, saying that he considers his contribution to proving the Poincaré conjecture to be no greater than that of Richard Hamilton, who introduced the theory of Ricci flow with the aim of attacking the geometrization conjecture. *Wik

2011 The Pluto-bound New Horizons spacecraft flew past Uranus’ orbit at about 6 p.m. EDT, 1.8 billion miles from Earth. New Horizons is now well over halfway through its journey to Pluto. Motoring along at 57,9000 km/hr (36,000 mph), it will travel more than 4.8 billion km (3 billion miles) to fly past Pluto and its moons Nix, Hydra and Charon in July 2015.The next planetary milestone for New Horizons will be the orbit of Neptune, which it crosses on Aug. 25, 2014, exactly 25 years after Voyager 2 made its historic exploration of that giant planet. *Universe Today (Hat tip to David Dickinson@Astroguyz


BIRTHS

1602 Jacques de Billy (18 March 1602 in Compiègne, France - 14 Jan 1679 in Dijon, France) was a French Jesuit. Billy corresponded with Fermat and produced a number of results in number theory which have been named after him. Billy had collected many problems from Fermat's letters and, after the death of his father, Fermat's son appended de Billy's collection under the title Doctrinae analyticae inventum novum (New discovery in the art of analysis) as an annex to his edition of the Arithmetica of Diophantus (1670). *SAU . At the College de Dijon he taught privately Jacques Ozanam, in whom he instilled a love of the calculus. *VFR

1640 Philippe de La Hire (or Lahire or Phillipe de La Hire) (March 18, 1640 – April 21, 1718) was a French mathematician and astronomer. According to Bernard le Bovier de Fontenelle he was an "academy unto himself". La Hire wrote on graphical methods, 1673; on conic sections, 1685; a treatise on epicycloids, 1694; one on roulettes, 1702; and, lastly, another on conchoids, 1708. His works on conic sections and epicycloids were founded on the teaching of Desargues, of whom he was his favourite pupil. He also translated the essay of Manuel Moschopulus on magic squares, and collected many of the theorems on them which were previously known; this was published in 1705. He also published a set of astronomical tables in 1702. La Hire's work also extended to descriptive zoology, the study of respiration, and physiological optics.
Two of his sons were also notable for their scientific achievements: Gabriel-Philippe de La Hire (1677–1719), mathematician, and Jean-Nicolas de La Hire (1685–1727), botanist.
The mountain Mons La Hire on the Moon is named for him. *Wik He was also the first to find the arc length of the cardioid in 1708.

1690 Christian Goldbach (18 Mar 1690, 20 Nov 1764) Russian mathematician whose contributions to number theory include Goldbach's conjecture, formulated in a letter to Leonhard Euler dated 7 Jul 1742. Stated in modern terms it proposes that: "Every even natural number greater than 2 is equal to the sum of two prime numbers." It has been checked by computer for vast numbers - up to at least 4 x 1014 - but still remains unproved. Goldbach made another conjecture that every odd number is the sum of three primes, on which Vinogradov made progress in 1937. (It has been checked by computer for vast numbers, but remains unproved.) Goldbach also studied infinite sums, the theory of curves and the theory of equations. *TIS

1796 Jakob Steiner (18 Mar 1796; 1 Apr 1863 at age 67) Swiss mathematician who was one of the greatest, contributors to projective geometry. He discovered the Steiner surface which has a double infinity of conic sections on it. The Steiner theorem states that the two pencils by which a conic is projected from two of its points are projectively related. He is also known for the Poncelet-Steiner theorem which shows that only one given circle and a straight edge are required for Euclidean constructions. His work included conic sections and surfaces, the theory of second-degree surfaces and centre-of-gravity problems. He developed the principle of symmetrization (1840-41). In 1848 he ws the first to define various polar curves with respect to a given curve, and introduced the “Steiner Curves.” *TIS

1839 Joseph Émile Barbier (18 March 1839 in St Hilaire-Cottes, Pas-de-Calais, France - 28 Jan 1889 in St Genest, Loire, France)
He was offered a post at the Paris Observatory by Le Verrier and Barbier left Nice to begin work as an assistant astronomer. For a few years he applied his undoubted genius to problems of astronomy. He proved a skilled observer, a talented calculator and he used his brilliant ideas to devise a new type of thermometer. He made many contributions to astronomy while at the observatory but his talents in mathematics were also to the fore and he looked at problems in a wide range of mathematical topics in addition to his astronomy work.
As time went by, however, Barbier's behaviour became more and more peculiar. He was clearly becoming unstable and exhibited the fine line between genius and mental problems which are relatively common. He left the Paris Observatory in 1865 after only a few years of working there. He tried to join a religious order but then severed all contacts with his friends and associates. Nothing more was heard of him for the next fifteen years until he was discovered by Bertrand in an asylum in Charenton-St-Maurice in 1880.
Bertrand discovered that although Barbier was clearly unstable mentally, he was still able to make superb original contributions to mathematics. He encouraged Barbier to return to scientific writing and, although he never recovered his sanity, he wrote many excellent and original mathematical papers. Bertrand, as Secretary to the Académie des Sciences, was able to find a small source of income for Barbier from a foundation which was associated with the Académie. Barbier, although mentally unstable, was a gentle person and it was seen that, with his small income, it was possible for him to live in the community. This was arranged and Barbier spent his last few years in much more pleasant surroundings.
Barbier's early work, while at the Observatory, consists of over twenty memoirs and reports. These cover topics such as spherical geometry and spherical trigonometry. We mentioned above his work with devising a new type of thermometer and Barbier wrote on this as well as on other aspects of instruments. He also wrote on probability and calculus.
After he was encouraged to undertake research in mathematics again by Bertrand, Barbier wrote over ten articles between the years 1882 and 1887. These were entirely on mathematical topics and he made worthwhile contributions to the study of polyhedra, integral calculus and number theory. He is remembered for Barbier's theorem, nicely explained here by Alex Bogomolny.*SAU

1870 Agnes Sime Baxter (Hill) (18 March 1870 – 9 March 1917) was a Canadian-born mathematician. She studied at Dalhousie University, receiving her BA in 1891, and her MA in 1892. She received her Ph.D. from Cornell University in 1895; her dissertation was “On Abelian integrals, a resume of Neumann’s ‘Abelsche Integrele’ with comments and applications." *Wik

1891 Walter Andrew Shewhart (March 18, 1891 - March 11, 1967) was an American physicist, engineer and statistician, sometimes known as the father of statistical quality control.
W. Edwards Deming said of him, "As a statistician, he was, like so many of the rest of us, self-taught, on a good background of physics and mathematics. "
His more conventional work led him to formulate the statistical idea of tolerance intervals and to propose his data presentation rules, which are listed below:

Data have no meaning apart from their context.
Data contain both signal and noise. To be able to extract information, one must separate the signal from the noise within the data.
Walter Shewhart visited India in 1947-48 under the sponsorship of P. C. Mahalanobis of the Indian Statistical Institute. Shewhart toured the country, held conferences and stimulated interest in statistical quality control among Indian industrialists
*SAU

1911 Walter Ledermann (18 March 1911 in Berlin, Germany - 22 May 2009 in London, England) graduated from Berlin but was forced to leave Germany in 1933 to avoid Nazi persecution. He came to St Andrews and studied under Turnbull. He worked at Dundee and St Andrews until after World War II when he moved to Manchester and then to the University of Sussex. He is especially known for his work in homology, group theory and number theory. *SAU

1928 Lennart Axel Edvard Carleson (18 March 1928 in Stockholm, Sweden - ) is a Swedish mathematician who solved one of the most important problems in the theory of Fourier series. He was director of the Mittag-Leffler Institute, Stockholm, from 1968 to 1984, during which time he built the Institute from a small base into one of the leading mathematical research institutes in the world.*SAU


DEATHS

1871 Augustus de Morgan  (born 27 Jun 1806, 18 Mar 1871 at age 64) Born in Madura (now Madurai), India, son of a colonel in the Indian Army. He is best known for his work in Formal Logic. “De Morgan’s Laws”, are contained in his first book (1847), although they were known to Peter of Spain in the fourteenth century. *VFR
In formal logic, De Morgan's laws are rules relating the logical operators "and" and "or" in terms of each other via negation. With two operands A and B:
\overline{A \cdot B} = \overline A + \overline B
\overline{A + B} = \overline {A} \cdot \overline {B}
In another form:
NOT (P AND Q) = (NOT P) OR (NOT Q)
NOT (P OR Q) = (NOT P) AND (NOT Q)
The rules can be expressed in English as:
"The negation of a conjunction is the disjunction of the negations." and
"The negation of a disjunction is the conjunction of the negations."
*Wik
When he defined and introduced the term "mathematical induction" (1838), he gave the process a rigorous basis and clarity that it had previously lacked. He originated the use of the slash to represent fractions, as in 1/5 or 3/7. In Trigonometry and Double Algebra (1849) he gave a geometric interpretation of complex numbers. *TIS  A nice blog about De Morgan's life and relationships is at The Renaissance Mathematicus.
Teachers might give students the opportunity to find the date of his birth using De Morgan's own clues; “I was x years old in the year x2” *VFR

1907 Pierre-Eugène-Marcellin Berthelot (27 Oct 1827, 18 Mar 1907 at age 79) was a French chemist and science historian and government official whose creative thought and work significantly influenced the development of chemistry in the late 19th century. He helped to found the study of thermochemistry, introduced a standard method for determining the latent heat of steam, measured hundreds of heats of reactions and coined the words exothermic and endothermic. Berthelot systematically synthesized organic compounds, including some not found in nature. His syntheses of many fundamental organic compounds helped to destroy the classical division between organic and inorganic compounds. *TIS

1964 Norbert Wiener (26 Nov 1894; 18 Mar 1964) U.S. mathematician, who established the science of cybernetics, a term he coined, which is concerned with the common factors of control and communication in living organisms, automatic machines, and organizations. He attained international renown by formulating some of the most important contributions to mathematics in the 20th century. His work on generalised harmonic analysis and Tauberian theorems won the Bôcher Prize in 1933 when he received the prize from the American Mathematical Society for his memoir Tauberian theorems published in Annals of Mathematics in the previous year. His extraordinarily wide range of interests included stochastic processes, quantum theory and during WW II he worked on gunfire control. *TIS Cybernetics, published in 1948, was a major influence on later research into artificial intelligence. In the book, Wiener drew on World War II experiments with anti-aircraft systems that anticipated the course of enemy planes by interpreting radar images. Wiener also did extensive analysis of brain waves and explored the similarities between the human brain and a modern computing machine capable of memory association, choice, and decision making.*CHM (Wiener is somewhat revered as the ultimate absent-minded professor. An anecdote I used to share with my classes, almost certainly exaggerated, went something like this: Wiener had moved to a new address, and his wife knowing of his forgetfulness wrote a note with his new address and put it in his coat pocket. During the day struck by a mathematical muse he whipped out the piece of paper and scribbled notes on the back, then realizing his idea had been wrong, he tossed the piece of paper away and went about his day. In the afternoon he returned to his old house out of habit and coming up to the empty house remembered that he had moved, but not where. As he started to leave a young girl walked up and he stopped here. "Young lady, I am the famous mathematician Wiener. Do you know where I live?" The lass replied, "Yes, father, I'll show you the way home."... )
Wiener is buried in Vittum Hill Cemetery in Sandwich, Carroll County, New Hampshire, USA
reader Tom ‏@umacf24 told me that "Before this guy, 'kyber' was an obscure Greek word for 'steering.' " (seems very appropriate root) Thanks Tom.


1989 Sir Harold Jeffreys (22 Apr 1891, 18 Mar 1989 at age 97)English astronomer, geophysicist and mathematician who had diverse scientific interests. In astronomy he proposed models for the structures of the outer planets, and studied the origin of the solar system. He calculated the surface temperatures of gas at less than -100°C, contradicting then accepted views of red-hot temperatures, but Jeffreys was shown to be correct when direct observations were made. In geophysics he researched the circulation of the atmosphere and earthquakes. Analyzing earthquake waves (1926), he became the first to claim that the core of the Earth is molten fluid. Jeffreys also contributed to the general theory of dynamics, aerodynamics, relativity theory and plant ecology.*TIS

2001 Dirk Polder (August 23, 1919, The Hague — March 18, 2001, Iran) was a Dutch physicist who, together with Hendrik Casimir, first predicted the existence of what today is known as the Casimir-Polder force, sometimes also referred to as the Casimir effect or Casimir force. He also worked on the similar topic of radiative heat transfer at nanoscale. *Wik

2013 Mary Ellen Rudin (born December 7, 1924, Hillsboro, Texas - March 18, 2013, Madison, Wisconsin) was an American mathematician.
Born Mary Ellen Estill, she attended the University of Texas, completing her B.A. in 1944 and her Ph.D. in 1949, under Robert Lee Moore. In 1953, she married the mathematician Walter Rudin. Following her mentor Moore, her research centers on point-set topology. She was appointed as Professor of Mathematics at the University of Wisconsin in 1971, and is currently a Professor Emerita there. She served as vice-president of the American Mathematical Society, 1980–1981. In 1984 she was selected to be a Noether Lecturer. She is an honorary member of the Hungarian Academy of Sciences (1995).
Rudin is best known in topology for her constructions of counterexamples to well-known conjectures. Most famously, she was the first to construct a Dowker space, thus disproving a conjecture of Dowker's that had stood, and helped drive topological research, for more than twenty years. She also proved the first Morita conjecture and a restricted version of the second. Her latest major result is a proof of Nikiel's conjecture. Rudin's Erdős number is 1.
"Reading the articles of Mary Ellen Rudin, studying them until there is no mystery takes hours and hours; but those hours are rewarded, the student obtains power to which few have access. They are not hard to read, they are just hard mathematics, that's all." (Steve Watson)
She lived in Madison, Wisconsin, in the Rudin House, a home designed by architect Frank Lloyd Wright, and died at the age of 88. *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 & Campbel

Sunday, 17 March 2019

On This Day in Math - March 17

*WolframAlpha

St. Patrick’s Day. The equation of the day is the four-leaved rose r = sin(2θ). Work on this curve was first published by the Italian priest Guido Grandi in 1723. *VFR

"Spirit of '76" by Archibald McNeal Willard, 189

The 76th day of the year; 76 is an automorphic number because the square of 76 ends in 76. (5 and 6 are automorphic because 52 ends in five and 62 ends in six).
There is one other two digit automorphic number (it should be easy to find) but can you find the three digit ones?

76= 8 + 13 + 21 + 34 the sum of four consecutive Fibonacci numbers

76 is the number of 6 X 6 symmetric permutation matrices.

Seventy Six is an unincorporated community in Clinton County, Kentucky, United States. Seventy Six is 6.9 miles north of Albany( and 46 miles west of 88, ky.). Its post office has been closed.



EVENTS

1694 L’Hospital hires his former tutor Johann Bernoulli to “work on what I shall ask you ... and also to communicate to me your discoveries, with the request not to mention them to others.” The first calculus text resulted in 1696. It contained the famous “L’Hospital’s rule,” which, we now know, is the work of Bernoulli. [Eves, Circles, 208◦] VFR
(Because L'Hospital is so often discredited by Intro Calculus teachers for his role, I wanted to add more detail in the hopes they will share a more enlightened presentation of his work.)
In a letter from March 17, 1694, l'Hôpital made the following proposal to Johann Bernoulli: in exchange for an annual payment of 300 Francs, Bernoulli would inform L'Hôpital of his latest mathematical discoveries, withholding them from correspondence with others, including Varignon. Bernoulli's immediate response has not been preserved, but he must have agreed soon, as the subsequent letters show. L'Hôpital may have felt fully justified in describing these results in his book, after acknowledging his debt to Leibniz and the Bernoulli brothers, "especially thle younger one" (Johann). Johann Bernoulli grew increasingly unhappy with the accolades bestowed on l'Hôpital's work and complained in private correspondence about being sidelined. After l'Hôpital's death, he publicly revealed their agreement and claimed credit for the statements and portions of the text of Analyse, which were supplied to l'Hôpital in letters. Over a period of many years, Bernoulli made progressively stronger allegations about his role in the writing of Analyse, culminating in the publication of his old work on integral calculus in 1742: he remarked that this is a continuation of his old lectures on differential calculus, which he discarded since l'Hôpital had already included them in his famous book. For a long time, these claims were not regarded as credible by many historians of mathematics, because l'Hôpital's mathematical talent was not in doubt, while Bernoulli was involved in several other priority disputes. For example, both H. G. Zeuthen and Moritz Cantor, writing at the cusp of the 20th century, dismissed Bernoulli's claims on these grounds. However, in 1921 Paul Schafheitlin discovered a manuscript of Bernoulli's lectures on differential calculus from 1691–1692 in the Basel University library. The text showed remarkable similarities to l'Hôpital's writing, substantiating Bernoulli's account of the book's origin.
L'Hôpital's pedagogical brilliance in arranging and presenting the material remains universally recognized. Regardless of the exact authorship (one should also note that the book was first published anonymously), Analyse was remarkably successful in popularizing the ideas of differential calculus stemming from Leibniz. *Wik

1856 Joseph Lacomme, a French well-sinker, and illiterate laborer who asked a mathematics professor to tell him the amount of stone needed to cover the bottom of a circular cistern, and unsatisfied with the reply that it would be impossible to tell him exactly, set about experimenting and determined the "True" ratio of the circumference to diameter of a circle. Teaching himself arithmetic and writing to confirm the results he obtained by experimentation he shared his computation with the commissioner of police in Paris. The commissioner introduced Lacomme to his father, who presented him to the Academie and after consideration by a committee, Lacomme received a silver medal from the French Academie for his discovery of the true ratio of diameter to circumfrence of a circle. He would later receive three more medals from other societies for his value of 3 1/8. *Augustus DeMorgan, A Budget of Paradoxes, pgs 46-47
The Kindle edition of A Budget of Paradoxes, Volume I is currently free.

1889 A political cartoon in the New York World lampooned President Benjamin Harrison's advisers and cabinet members showing the group sitting around playing the game, Pigs in Clover which had recently been invented by Charles Martin Crandall. The caption read "Will Mr. Harrison be able to get all these hungry pigs in the official pen?"
The events which prompted the story were related in a New York Tribune's March 13, 1889 issue:
Senator William M. Evarts purchased one from a street fakir in order to get rid of him. He took the puzzle home and worked it for hours. The following morning he brought it with him into senate chambers where Senator George Graham Vest stopped by Evarts' desk, borrowed the puzzle and took it to a cloak room. Soon thereafter he was joined by Senators James L. Pugh, James B. Eustis, Edward C. Walthall and John E. Kenna. A page was sent out to buy five of the puzzles and upon his return, the group engaged in a "pig driving contest". About 30 minutes later, Senator Vest announced his accomplishment of driving the last pig in the pen.
*Antique Toy Collectors of America *Wik (Will negotiate trade of my off-spring or other not-to-valuable property for a imageof this cartoon. )

1905 Albert Einstein submits his paper "On a Heuristic Point of View Concerning the Production and Transformation of Light" to the Annalen der Physik. In this revolutionary paper he proposes that light can be conceived both as waves and as discrete quanta (later to be called photons) which are localized at points in space. This paper was the primary reason for his Nobel Prize.

1914 Ramanujan boarded the S.S. Nevasa on 17 March 1914, and at 10 o'clock in the morning, the ship departed from Madras. He arrived in London on 14 April, with E. H. Neville waiting for him with a car. A tweet from @amanicdroid pointed out that, "this was significant for him culturally as a high-caste Hindu as crossing the ocean was taboo. "

1941 The National Gallery of Art opened its doors on the mall in Washington D.C. The gallery was a gift of Pittsburgh financier Andrew W. Mellon. His personal collection of 152 masterpieces has grown to 80,000 priceless works today. Today it is a good place to see some mathematics, from the lack of perspective in its medieval works, to The Lady in the Red Hat with its camera obscura technique, to the geometric starkness of the East Wing. *VFR

1988 Apple Computer sues Microsoft Corporation for copyright infringement in its Windows design. After Apple developed a highly successful graphical user interface for its Macintosh computer released in 1984, Microsoft fought back with an operating system of its own, called "Windows." In 1995, Apple lost the lawsuit, in which it claimed that the similarities of the Windows and Macintosh environments extended too far.*CHM

2013 Flash of Meteor hitting moon visible to naked eye. Scientists monitoring the moon for meteorite impacts spotted the biggest impact event to date: a space rock the size of a basketball slammed into the lunar surface at a speed of 56,000 miles per hour (90,000 km/hr), creating a new crater around 20 meters wide.
The flash was impressive — it unleashed the equivalent energy of 5 tons of TNT exploding and would have been visible to anyone casually looking at the moon, no telescope required. *NASA The impact hit almost exactly on a crater already present. This animated gif shows before and after shots of the site.



BIRTHS
1733 Carsten Niebuhr(March 17, 1733 Lüdingworth – April 26, 1815 Meldorf, Dithmarschen), German mathematician, cartographer, and explorer in the service of Denmark. Niebuhr's first book, Beschreibung von Arabien, was published in Copenhagen in 1772, the Danish government providing subsidies for the engraving and printing of its numerous illustrations. This was followed in 1774 and 1778 by the two volumes of Niebuhr's Reisebeschreibung von Arabien und anderen umliegenden Ländern. These works (particularly the one published in 1778), and most specifically the accurate copies of the cuneiform inscriptions found at Persepolis, were to prove to be extremely important to the decipherment of cuneiform writing. Before Niebuhr's publication, cuneiform inscriptions were often thought to be merely decorations and embellishments, and no accurate decipherments or translations had been made up to that point. Niebuhr demonstrated that the three trilingual inscriptions found at Persepolis were in fact three distinct forms of cuneiform writing (which he termed Class I, Class II, and Class III) to be read from left to right. His accurate copies of the trilingual inscriptions gave Orientalists the key finally crack the cuneiform code, leading to the discovery of Old Persian, Akkadian, and Sumerian. *Wik

1876 Ernest Benjamin Esclangon (March 17, 1876 – January 28, 1954) was a French astronomer and mathematician. During World War I, he worked on ballistics and developed a novel method for precisely locating enemy artillery. When a gun is fired, it initiates a spherical shock wave but the projectile also generates a conical wave. By using the sound of distant guns to compare the two waves, Escaglon was able to make accurate predictions of gun locations.
After the armistice, Esclangon became director of the Strasbourg Observatory and professor of astronomy at the university the following year. In 1929, he was appointed director of the Paris Observatory and of the International Time Bureau, and elected to the Bureau des Longitudes in 1932. In 1933, he initiated the talking clock telephone service in France. He was elected to the Académie des Sciences in 1939.
Serving as director of the Paris Observatory throughout World War II and the German occupation of Paris, he retired in 1944. He died in Eyrenville, France.
The binary asteroid 1509 Esclangona and the lunar crater Esclangon are named after him.*Wik

1915 Wolfgang Döblin, known in France as Vincent Doblin, (17 March 1915 – 21 June 1940) was a German-French mathematician. Wolfgang was the son of the Jewish-German novelist, Alfred Döblin. His family escaped from Nazi Germany to France where he became a citizen. Studying probability theory at the Institute Henri Poincaré under Fréchet, he quickly made a name for himself as a gifted theorist. He became a doctor at age 23. Drafted in November 1938, after refusing to be exempted of military service, he had to stay in the active Army when World War II broke out in 1939, and was quartered at Givet, in the Ardennes, as a telephone operator. There, he wrote down his latest work on the Chapman-Kolmogorov equation, and sent this as a "pli cacheté" (sealed envelope) to the French Academy of Sciences. His company, sent to the sector of the Saare on the ligne Maginot in April 1940, was caught in the German attack in the Ardennes in May, withdrew to the Vosges, and capitulated on June 22, 1940. On June 21, Doblin had committed suicide in Housseras (a small village near to Epinal), at the moment where German troops came in sight of the place. In his last moments, he burned his mathematical notes.
The sealed envelope was opened in 2000, revealing that Döblin was ahead of his time in the development of the theory of Markov processes. In recognition of his results, Itō's lemma is now referred to as the Itō–Doblin Theorem.
His life was recently the subject of a movie by Agnes Handwerk and Harrie Willems, A Mathematician Rediscovered. *Wik

1972 Kalpana Chawla (March 17, 1962 – February 1, 2003) was an American astronaut and the first indian woman in space. She first flew on Space Shuttle Columbia in 1997 as a mission specialist and primary robotic arm operator. In 2003, Chawla was one of the seven crew members killed in the Space Shuttle Columbia disaster. *Wik


DEATHS
1652 Benjamin Bramer (15 Feb 1588 in Felsberg, Germany - 17 March 1652 in Ziegenhain, Germany) was an architect who published work on the calculation of sines. He was tutored by Jost Bürgi in a wide range of subjects but it was mathematics that he loved and he passed this love on to Bramer. (Bramer married Bürgi's daughter) Bramer followed Alberti (1435), Dürer (1525) and Bürgi (1604) when in 1630 he constructed a device that enabled one to draw accurate geometric perspective. The instrument had been described in a 1617 publication Trigonometrica planorum mechanica oder Unterricht und Beschreibung eines neuen und sehr bequemen geometrischen Instrumentes zu allerhand Abmessung. Bramer designed several other mathematical instruments, for example a description of the pantograph appears in the same 1617 publication. The instrument is designed to copy a geometric shape and reproduce it at a reduced or enlarged scale. It consists of an assemblage of rigid bars adjustably joined by pin joints; as the point of one bar is moved over the outline to be duplicated, the motion is translated to a point on another bar, which makes the desired copy according to the predetermined scale. Bramer has not been recognised as the inventor of the pantograph, this distinction going to the Jesuit Christoph Scheiner who describes a similar instrument in his 1631 publication Pantographice seu acre delineandi res quaslibet by parallelogrammum linear seu cavum mechanicum, mobile. Although Scheiner's publication did much to spread knowledge of the pantograph, the instrument he describes is technically inferior to the earlier instrument as described by Bramer. *SAU

1767 George Parker (born 1697, 17 Mar 1764) [2nd Earl of Macclesfield] English astronomer who was instrumental in changing the computation of current chronology, subsequently enacted as the British Calendar Act of 1751 which co-authored and co-promoted. (Shortly thereafter, he was elected President of the Royal Society, 1752-1764). Since 1582, the new calendar of Pope Gregory XIII had been used in most of Europe. In England the new calendar was rejected as popish. By 1750, the old calendar became 11 days out of sequence with the position of the Earth in its orbit due to its lack of leap years. Parker was assisted in these calculations by his friend James Bradley, the astronomer royal, and received influential support from Philip Dormer Stanhope, 4th Earl of Chesterfield. *TIS

1771 Chester Moor Hall, (Dec. 9, 1703, Leigh, Essex, Eng.— March 17, 1771, Sutton, Surrey), English jurist and mathematician who invented the achromatic lens, which he utilized in building the first refracting telescope free from chromatic aberration (colour distortion).
Convinced from study of the human eye that achromatic lenses were feasible, Hall experimented with different kinds of glass until he found (1729) a combination of crown glass and flint glass that met his requirements. In 1733 he built several telescopes with apertures of 2.5 inches (6.5 cm) and focal lengths of 20 inches (50 cm).*britannica.com

1782 Daniel Bernoulli (29 January 1700 (8 Feb new style), 8 March 1782) was a Dutch-Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. Bernoulli's work is still studied at length by many schools of science throughout the world. The son of Johann Bernoulli (one of the "early developers" of calculus), nephew of Jakob Bernoulli (who "was the first to discover the theory of probability"), and older brother of Johann II, He is said to have had a bad relationship with his father. Upon both of them entering and tying for first place in a scientific contest at the University of Paris, Johann, unable to bear the "shame" of being compared as Daniel's equal, banned Daniel from his house. Johann Bernoulli also plagiarized some key ideas from Daniel's book Hydrodynamica in his own book Hydraulica which he backdated to before Hydrodynamica. Despite Daniel's attempts at reconciliation, his father carried the grudge until his death.
He was a contemporary and close friend of Leonhard Euler. He went to St. Petersburg in 1724 as professor of mathematics, but was unhappy there, and a temporary illness in 1733 gave him an excuse for leaving. He returned to the University of Basel, where he successively held the chairs of medicine, metaphysics and natural philosophy until his death.
In May, 1750 he was elected a Fellow of the Royal Society. He was also the author in 1738 of Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk), in which the St. Petersburg paradox was the base of the economic theory of risk aversion, risk premium and utility.
One of the earliest attempts to analyze a statistical problem involving censored data was Bernoulli's 1766 analysis of smallpox morbidity and mortality data to demonstrate the efficacy of vaccination. He is the earliest writer who attempted to formulate a kinetic theory of gases, and he applied the idea to explain Boyle's law. He worked with Euler on elasticity and the development of the Euler-Bernoulli beam equation. *Wik

1846 Friedrich Wilhelm Bessel (22 Jul 1784, 17 Mar 1846 at age 61). He is noted for the special class of functions that have become an indispensable tool in applied mathematics. This, like all of his mathematical work, was motivated by his work in astronomy. *VFR In 1809, at the age of 26, Bessel was appointed director of Frederick William III of Prussia's new Königsberg Observatory and professor of astronomy, where he spent the rest of his career. His monumental task was determining the positions and proper motions for about 50,000 stars, which allowed the first accurate determination of interstellar distances. Bessel's work in determining the constants of precession, nutation and aberration won him further honors. Other than the sun, he was the first to measure the distance of a star, by parallax, of 61 Cygni (1838). In mathematical analysis, he is known for his Bessel function. *TIS


1853 Christian Doppler (29 Nov 1803; 17 Mar 1853) Austrian physicist who first described how the observed frequency of light and sound waves is affected by the relative motion of the source and the detector, known as the Doppler effect. In 1845, to test his hypothesis, Doppler used two sets of trumpeters: one set stationary at a train station and one set moving on an open train car, all holding the same note. As the train passed the station, it was obvious that the frequency of the notes from the two groups didn't match. Sound waves would have a higher frequency if the source was moving toward the observer and a lower frequency if the source was moving away from the observer. Edwin Hubble used the Doppler effect of light from distant stars to determine that the universe is expanding.*TIS


1922 Heinrich Suter (4 January 1848, Hedingen near Zurich, Switzerland – 17 March 1922) was a historian of science specializing in Islamic mathematics and astronomy.*Wik

1956 Irène Joliot-Curie (12 Sep 1897; 17 Mar 1956) French physicist and physical chemist, wife of Frédéric Joliot-Curie, who shared the 1935 Nobel Prize for Chemistry "in recognition of their synthesis of new radioactive elements." For example, in their joint research they discovered that aluminium atoms exposed to alpha rays transmuted to radioactive phosphorus atoms. She was the daughter of Nobel Prize winners Pierre and Marie Curie. From 1946, she was director of the Radium Institute, Paris, founded by her mother. She died of leukemia, like her mother, resulting from radiation exposure during research.*TIS

1956 Henry Frederick Baker FRS (3 July 1866 – 17 March 1956) was a British mathematician, working mainly in algebraic geometry, but also remembered for contributions to partial differential equations (related to what would become known as solitons), and Lie groups.
Baker was born in Cambridge, England and educated at The Perse School before winning a scholarship to St John's College, Cambridge in October 1884. Baker graduated as Senior Wrangler in 1887, bracketed with 3 others.
Baker was elected Fellow of St John's in 1888 where he remained for 68 years.
In June, 1898 he was elected a Fellow of the Royal Society. In 1911, he gave the presidential address to the London Mathematical Society.
In January 1914 he was appointed Lowndean Professor of Astronomy. *Wik
In the 1920's and 30's before the war Baker's graduate students would meet at what they called Professor Baker’s "Tea Party". They met each Saturday to discuss the areas of research in which they were working. It was to one of these meetings that a young Donald Coxeter brought his "Aunt Alice", the 69 year old Alicia Boole to co-present on the subject of Polytopes in higher dimensions.

1962 Wilhelm Blaschke (13 Sep 1885; 17 Mar 1962) German mathematician whose major contributions to geometry concerned kinematics and differential geometry. Kinetic mapping (important later in the axiomatic foundations of various geometries) he both discovered and established it as a tool in kinematics. He also initiated topological differential geometry (the study of invariant differentiable mappings)*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

Saturday, 16 March 2019

On This Day in Math - March 16


Memorial for Ohm ,

Whenever I meet in Laplace with the words 'Thus it plainly appears', I am sure that hours and perhaps days, of hard study will alone enable me to discover how it plainly appears.
~Nathaniel Bowditch



The 75th day of the year; the aliquot divisors of 75 are 1,3,5,15, and 25. Their sum is a perfect square, 49. Their product is also a perfect square, 5625. (Can you find other numbers with this property?)

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

75 and 76 form the first pair of adjacent numbers in base ten which are NOT a palindrome in any base \( 2 \leq b \leq 10 \)

275 + 75 is prime

75 is a Keith # or repfigit (75 appears in a Fibonacci-like sequence created by its digits) 7, 5, 12, 17, 29, 46, 75 ...  (75 is the sixth of seven year days which are repfigits.  Can you find the others?)






EVENTS

1713 Saunderson to Jones: “There has been nothing published here since my last to you, excepting a treatise, which is not worth mentioning, by one Mr. Green, fellow of Clare Hall of this university. If there had been anything in it instructive or diverting I should have sent it to you; but I can find nothing in it but ill manners and elaborate nonsense from one end to the other. The gentelman has been reputed mad for these two years last past, but never gave the world such ample testimony of it before.” [Rigaud, Correspondence of Scientific Men of the Seventeenth Century, I, *263] *VFR

1763 Jerome Lalande writes in his diary about a visit to England, and "I went to see the Tower, and from there by water to Surrey Street to see Mr Short (James Short FRS was an optician who had been called to London to teach mathematics to William, Duke of Cumberland)
who spoke to me about the difficulty in giving his mirrors a parabolic figure. It is done only by guess-work." *Richard Watkins

1802 The United States Military Academy at West Point established by act of congress. This school was the first engineering school in the U.S. Charles Davies, a noted math textbook writer, taught there.*VFR (The academy opened on July 4, 1802. Before 1812 it was conducted as an apprentice school for military engineers and, in effect, as the first U.S. school of engineering.)

1830 The New York Stock Exchange had its slowest trading day, only 31 shares trading hands. *VFR

1916 On his seventieth birthday in 1916, Mittag-Leffler and his wife signed their last will and testament. They gave their entire fortune to found a Mathematical Institute which now bears their names. It is in their villa in Djursholm, near Stockholm, Sweden. A sumptuous volume giving a complete calatogue of Mittag-Leffler’s library was also published at this time, and this library is now housed in the Institute. Naturally it is a favorite haunt of historians of mathematics. *VFR (See Births,1846 below)

1926 Clark University Physics Professor, Robert H. Goddard, conducted the first successful open-air test of a liquid-fuel rocket. “The rocket soared only forty-one feet, hardly the ‘extreme altitudes’ Goddard had envisioned, yet the occasion was anologous to the first flight of the Wright brothers at Kitty Hawk nearly a quarter of a century earlier.” *William A. Koelsch, Clark University, 1887–1987
He thought stable flight could be obtained by mounting the rocket ahead of the fuel tank. The tank was shielded from the flame by a metal cone and was pulled behind the rocket by the lines for gasoline fuel and oxygen. The design worked, but did not produce the hoped-for stability. The rocket burned about 20 seconds before reaching sufficient thrust (or sufficiently lightening the fuel tank) for taking off. During that time it melted part of the nozzle. It took off to a height of 41-ft, leveled off and within 2.5 seconds hit the ground 184 feet away, averaging about 60 mph. The camera ran out of film, so no photographic record of that flight remains. *TIS

1928 Chandrasekhara Raman presented the results from his Feb 28 ground breaking experiments in light scattering at a meeting of scientists in Bangalore on 16 March 1928. The results would lead to his wining the Nobel Prize in Physics in 1930. *Wik

1986 The Manchester Guardian Weekly announces that Colin Rourke of Warwick and his student Eduardo Rego of Oporto University in Portugal have solved the 82 year old Poincare conjecture which states that loops on spheres in n-dimensions can be shrunk to points. Obviously, Mr. Rego will get his Ph.D. *VFR The article in the Guardian was by Ian Stewart. In November 1986, Rourke was at the University of California, Berkeley, conducting a seminar to explain and defend his proof. By the end of the week, Rourke's audience, which included some of the world's top topologists, had pointed out a gap in his proof, one that Rourke could not fill. In the end, there was no valid proof. The problem was solved by the reclusive Russian mathematician Grigori Perelman in November of 2002

1990 Internet Extends Beyond U.S. to Europe: The National Science Foundation announces it will extend its network with a high-speed data link to Europe. Five years earlier, the Internet in its modern form had started to develop rapidly thanks to the formation of the NSFNET, which linked five supercomputer centers in the United States. Later in 1990, Europe contributed to the growth of the Internet when CERN's Tim Berners-Lee developed HTML, the language used for the World Wide Web.*CHM

BIRTHS

1750 Caroline Lucretia Herschel (16 Mar 1750, 9 Jan 1848) German-born British astronomer, sister of Sir William Herschel, who assisted in his astronomical researches making calculations associated with his studies. In her own telescope observations, she found three nebulae (1783) and eight comets (1786-97). In 1787, King George III gave Caroline a salary of 50 pounds per year as assistant to William. She published the Index to Flamsteed's Observations of the Fixed Stars and a list of his mistakes in 1797. At the age of 10 she had been struck with typhus, which subsequently stunted her growth. She never grew taller than 4' 3" and remained frail throughout her life. *TIS
[The following inscription is engraved on Miss Herschel's tomb. It begins: "Hier ruhet die irdische Hülle von CAROLINA HERSCHEL, Geboren zu Hannover den 16ten Marz 1750, Gestorben, den 9ten Januar 1848." But, for the convenience of our young readers, we give it in English:—

HERE RESTS THE EARTHLY CASE OF

CAROLINE HERSCHEL.

BORN AT HANOVER, MARCH 10, 1750.

DIED JANUARY 9, 1848.

"The eyes of her now glorified were, while here below, directed towards the starry heavens. Her own discoveries of comets, and her share in the immortal labours of her brother, William Herschel, bear witness of this to succeeding ages.

"The Royal Irish Academy of Dublin, and the Royal Astronomical Society of London, enrolled her name among their members.

"At the age of 97 years 10 months, she fell asleep in calm rest, and in the full possession of her faculties; following into a better life her father, Isaac Herschel, who lived to the age of 60 years, 2 months, 17 days, and has lain buried not far off since the 29th of March 1767."

This epitaph was mainly written by Miss Herschel herself, and the allusion to her brother is characteristic.]
*from The Project Gutenberg EBook of The Story of the Herschels, by Anonymous

1789 Georg Simon Ohm (16 Mar 1789; 6 Jul 1854 at age 65) German physicist (high school teacher) who showed by experiment (1825) that there are no “perfect” electrical conductors. All conductors have some resistance. He stated the famous Ohm's law (1826): “If the given temperature remains constant, the current flowing through certain conductors is proportional to the potential difference (voltage) across it.” or V=iR. *Tis

1821 Heinrich Eduard Heine (16 March 1821 in Berlin, Germany - 21 Oct 1881 in Halle, Germany) Heine is best remembered for the Heine-Borel theorem. He was responsible for the introduction of the idea of uniform continuity.*SAU

1846 Magnus Gösta Mittag-Leffler (16 Mar 1846; 7 Jul 1927 at age 81) Swedish mathematician who founded the international mathematical journal Acta Mathematica and whose contributions to mathematical research helped advance the Scandinavian school of mathematics. Mittag-Leffler made numerous contributions to mathematical analysis (concerned with limits and including calculus, analytic geometry and probability theory). He worked on the general theory of functions, concerning relationships between independent and dependent variables. His best known work concerned the analytic representation of a one-valued function, this work culminated in the Mittag-Leffler theorem. *TIS One of the stories that circulates from time to time about Mittag-Leffler and the fact that there is no Nobel Prize in mathematics is that Nobel disliked Mittag-Leffler for having an affair with Nobel's wife and so he did not create a prize in Mathematics. Only problem; Nobel never married, and there is little if any evidence that Mittag-Leffler ever met Nobel's mistress, Sophie Hess.

1853 Heinrich (Gustav Johannes) Kayser (16 Mar 1853, 14 Oct 1940) was a German physicist who discovered the presence of helium in the Earth's atmosphere. Prior to that scientists had detected helium only in the sun and in some minerals. Kayser's early research work was on the properties of sound. In collaboration with the physicist and mathematician Carl D.T. Runge, Kayser carefully mapped the spectra of a large number of elements. He wrote a handbook of spectroscopy (1901–12) and a treatise on the electron theory (1905).*TIS

1915 Kunihiko Kodaira(16 Mar 1915; 26 Jul 1997 at age 82) Japanese mathematician who was awarded the Fields Medal in 1954 for his work in algebraic geometry and complex analysis. Kodaira's work includes applications of Hilbert space methods to differential equations which was an important topic in his early work and was largely the result of influence by Weyl. Through the influence of Hodge, he also worked on harmonic integrals and later he applied this work to problem in algebraic geometry. Another important area of Kodaira's work was to apply sheaves to algebraic geometry. In around 1960 he became involved in the classification of compact, complex analytic spaces. One of the themes running through much of his work is the Riemann-Roch theorem. He won the 1985 Wolf Prize. *TIS

1947 Dr. Keith Devlin (March 16, 1947, Kingston upon Hull, UK; ) is a co-founder and Executive Director of Stanford University's H-STAR institute, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition. He has written 32 books and over 80 published research articles. Recipient of the Pythagoras Prize, the Peano Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. In 2003, he was recognized by the California State Assembly for his "innovative work and longtime service in the field of mathematics and its relation to logic and linguistics." He is "the Math Guy" on National Public Radio. *Stanford Edu

1954 John E. Laird (March 16, 1954 Ann Arbor, Michigan - ) is a computer scientist who, with Paul Rosenbloom and Allen Newell, created the Soar cognitive architecture at Carnegie Mellon University. Laird is a Professor of the Computer Science and Engineering Division of the Electrical Engineering and Computer Science Department of the University of Michigan. He was the director of the Artificial Intelligence Laboratory there from 1994 to 1999. *Wik

DEATHS

 Bowditch gravestone,Mount Auburn Cemetery
Cambridge
Middlesex County
Massachusetts, USA

1838 Nathaniel Bowditch (26 Mar 1773, 16 Mar 1838 at age 65) Self-educated American mathematician and astronomer. He learned Latin to study Newton's Principia and later other languages to study mathematics in these languages. Between 1795 and 1799 he made four sea voyages and in 1802 he was in command of a merchant ship. He was author of the best book on navigation of his time, New American Practical Navigator (1802), and his translation (assisted by Benjamin Peirce) of Laplace's Mécanique céleste gave him an international reputation. Bowditch was the discoverer of the Bowditch curves (more often called Lisajous figures for their co-discoverer), which have important applications in astronomy and physics.*TIS Bowditch was a navigator on the Wilkes Expedition and an island in the Stork Archipelago in the South Pacific is named for him (and sometimes called Fakaofu)
(I can give no explanation for the discrepancy in the date of death on his tombstone.)

1841 Félix Savart (30 Jun 1791, 16 Mar 1841 at age 49)French physicist who researched various manifestations of vibration. With Jean-Baptiste Biot, he developed the Biot-Savart Law (1820) concerning the magnetic field intensity around a current-carrying wire. After earning a degree in medicine (1816), he took an interest in physics, beginning with a study of the violin to explain the contributions from its components to the sound from the strings. He presented a memoir on the subject to the Paris Academy of Sciences in 1819. He conducted extensive research in acoustics, the nodal patterns of vibrating systems (including air columns), and related enquiries into the elasticity of substances. He also investigated the voice and hearing. He devised a rotating toothed wheel to produce a sound of any frequency by a reed held against it, to measure high frequency hearing limits. *TIS

1914 Edward Singleton Holden (November 5, 1846 – March 16, 1914) was an American astronomer. Born in St. Louis, Missouri in 1846 to Jeremiah and Sarah Holden. From 1862-66, he attended Washington University in St. Louis, where he obtained a B.S. degree. He later trained at West Point in the class of 1870.In 1873 he became professor of mathematics at the US Naval Observatory, where he made a favorable impression on Simon Newcomb. He was director of Washburn Observatory at the University of Wisconsin–Madison from 1881 to 1885. He was elected a member of the American National Academy of Sciences in 1885.
On August 28, 1877, a few days after Asaph Hall discovered the moons of Mars Deimos and Phobos, he claimed to have found a third satellite of Mars. Further analysis showed large mistakes in his observations.
He was president of the University of California from 1885 until 1888, and the first director of the Lick Observatory from 1888 until the end of 1897. Meanhwile in 1893 while at the observatory he published a book on Mughal Emperors, The Mogul emperors of Hindustan, A.D. 1398- A.D. 1707. He resigned as a result of internal dissent over his management among his subordinates. While at the Lick Observatory, he was the founder of the Astronomical Society of the Pacific and its first President (1889–1891).
In 1901 he became the librarian of the United States Military Academy at West Point, where he remained until his death.
His cousin, George Phillips Bond, was director of Harvard College Observatory.
He discovered a total of 22 NGC objects during his work at Washburn Observatory.
He wrote many books on popular science (and on other subjects, such as flags and heraldry), including science books intended for children. For example the book Real Things In Nature. A Reading Book of Science for American Boys and Girls published in 1916.*Wik

1922 George Bruce Halsted (23 Nov 1853 in Newark, New Jersey, USA - 16 March 1922 in New York, USA) His main interests were the foundations of geometry and he introduced non-euclidean geometry into the United States, both through his own research and writings as well as by his many important translations. Halsted gave commentaries on the work of Lobachevsky, Bolyai, Saccheri and Poincaré and made translations of their works into English. His work on the foundations of geometry led him to publish Demonstration of Descartes's theorem and Euler's theorem in the Annals of Mathematics in 1885. His other main interest was in mathematical education and, as a mathematics educator, he criticised the careless way that mathematics was presented in the textbooks of the time. He contributed over ninety article to the American Mathematical Monthly and wrote many biographies of mathematicians such as Lambert, Farkas Bolyai, Lobachevsky, De Morgan, Sylvester, Chebyshev, Cayley, Hoüel and Klein. *SAU

1933 Alfréd Haar (11 Oct 1885 in Budapest, Hungary - 16 March 1933 in Szeged, Hungary) was a Hungarian mathematician who is best remembered for his work on analysis on groups, introducing a measure on groups, now called the Haar measure. *SAU

1940 Sir Thomas Little Heath (5 October 1861 – 16 March 1940) was a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer. Heath translated works of Euclid of Alexandria, Apollonius of Perga, Aristarchus of Samos, and Archimedes of Syracuse into English.
He was distinguished for his work in Greek Mathematics and author several books on Greek mathematicians. It is primarily through Heath's translations that modern English-speaking readers are aware of what Archimedes did.
He died in Ashtead, Surrey. *Wik

1941 Edward Lindsay Ince (30 Nov 1891 in Amblecote, Staffordshire, England
- 16 March 1941 in Edinburgh, Scotland) Ince graduated from Edinburgh and researched at Edinburgh and Cambridge. He worked at universities in Leeds, Liverpool, Cairo, Edinburgh and Imperial College London before moving back to Edinburgh as Head of Technical Mathematics. He worked on Special Functions. *SAU

1980 William Prager (May 23, 1903, Karlsruhe - 16 March 1980 in Zurich, Switzerland) was a German-born US applied mathematician. He was a lecturer at Darmstadt, a deputy director at University of Göttingen, professor at Karlsruhe, University of Istanbul, the University of California, San Diego and Brown University, where he advised Bernard Budiansky.
The Society of Engineering Science has awarded the Wiliam Prager Medal in Solid Mechanics since 1983 in his honor.*Wik

1992 Yves-André Rocard (22 May 1903 in Vannes, France - 16 March 1992 in Paris, France) French mathematician and physicist who


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

Friday, 15 March 2019

On This Day in Math - March 15

1659 title page of one of Argoli's books.*Wik


...there is no study in the world which brings into more harmonious action all the faculties of the mind than [mathematics], ... or, like this, seems to raise them, by successive steps of initiation, to higher and higher states of conscious intellectual being ...
~James J Sylvester

The 74th day of the year.
74 is related to an open question in mathematics since 742 + 1 is prime. Hardy and Littlewood conjectured that asymptotic number of elements in this sequence, primes = n2 + 1, not exceeding n is approximately \(c \frac {\sqrt{n}} {log(n)}\) for some constant c. There was a $1000 prize for best solution to an open sequence during 2015 and submitting it to OEIS, details here

74 is the sum of the squares of two consecutive prime numbers.
A hungry number is number in the form 2n  that eats as much pi as possible, for example 25 is the smallest power of two that contains a 3.  The smallest power that contains the first three digits of pi, 314 is 27 4
(eating e seems much harder for powers of 2)

22796996699 is the 999799787th prime. Note that the sum of digits of the nth prime equals the sum of digits of n. The number 74 is the largest known digit sum with this property (as of August 2004). *Prime Curios





EVENTS
44 B.C. Julius Caesar assassinated on the Ides of March, a phrase which came to denote an ill omen. The word “ides” is from the Etruscan for one-half (it is the middle of the lunar month).

1758 March 15th was the earliest date in the prediction of the return of Halley's comet by the team of Clairaut, La Lande and Lepaute. After incremental computations of the gravitational influences and motion of Jupiter and Saturn on the predicted return of Halley's comet, Alexis-Claude Clairaut presents the results to the Academies de Sciences. The computational work of the team of Clairaut, with La Lande and Nicole-Reine Lepaute, (having removed Saturn from the last few months calculations to speed the results) had predicted a window of arrival between March 15 and May 15 (1758).
The unruly comet reached perihelion on the 13th of March. *David A Grier, When Computers Were Human

In 1806, a 6-kg chondritemeteorite - carrying carbon-based, organic chemicals - was unequivocally identified for the first time. Its arrival on earth was noted at 5:30 pm, outside Alais, France. The organic chemicals it carried suggested the possibility of life on whatever body was the source, somewhere in the universe. According to the observations of Berzelius and a commission appointed by the French Academy it "emits a faint bituminous substance" when heated. Berzelius reported his analysis of the Alais meteorite in 1833 that destructive distillation yielded a blackish substance, indiginous water, carbon dioxide gas, a soluble salt containing ammonia, and a blackish-brown sublimate, which Berzelius confessed was unknown to him. *TIS

1871 James Clerk Maxwell in a letter to C. J. Monro comments on the fourth dimension, "The peculiarity of our space is that of its three dimensions, none is before or after another. As is x, so is y, and so is z."
Later in the same message he adds, "I am quite sure that the kind of continuity which has four dimensions all co-equal is not to be discovered by merely generalizing Cartesian space equations." Alfred M. Bork, The Fourth Dimensions in Ninetenth-Century Physics, Isis, Sept. 1964, pg 326-338
Matt Parkers fun book on the Fourth Dimension


1873 Lewis Carroll in a letter to fourteen year old Helen Fielden offers a tempting geometric problem,
I don’t know if you’re fond of puzzles, or not. If you are, try this. If not, never mind. A gentlemen (a nobleman let us say, to make it more interesting) had a sitting-room with only one window in it — a square window, 3 feet high and 3 feet wide. Now, he had weak eyes, and the window gave too much light,  so (don’t you like “so” in a story?) he sent for the builder, and told hm to alter it, so  as to give half the light. Only, he was to keep it square — he was to keep it 3 feet high — and he was to keep it 3 feet wide. How did he do it? Remember, he wasn’t allowed to use curtains, or shutters, or colored glass, or anything of that sort.

I must tell you an awful story of my trying to set a puzzle to a little girl the other day. It was at a dinner party, at dessert. I had never seen her before, but, as she was sitting next me, I rashly proposed to her to try the puzzle (I daresay you know of it) of “the fox, the goose, and bag of corn.” And I got some biscuits to represent the fox and the other things. Her mother was sitting on the other side, and said, “Now you take pains, my dear, and do it right!” The consequences were awful! She shrieked out, “I can’t do it! I can’t do it! Oh, Mamma! Mamma!” threw herself into her mother’s lap, and went off into a fit of sobbing which lasted several minutes! That was a lesson to me about trying children with puzzles. I do hope the square window won’t produce any awful effect on you! I am.

*Robin Wilson, Lewis Carroll in Numberland: His Fantastical Mathematical Logical Life (If the puzzle stumps you, I put a helpful hint at the bottom after credits.)


1955 John von Neumann sworn in as one of the first Atomic Energy Commissioners. In August he learned that he had bone cancer. *Goldstein, The Computer from Pascal to von Neumann

1933 Winston Churchill was very interested in science and wrote often and popularly on the subject. He chaired a conference in on the atomic discoveries in the Cavendish Laboratory in Cambridge. On this date his scientific friend, Frederick Lindemann said of him, "All the qualities … of the scientist are manifest in him. The readiness to face realities, even though they contradict a favourite hypothesis; the recognition that theories are made to fit facts, not facts to fit the theories; the interest in phenomena and the desire to explore them, and above all the underlying conviction that the world is not just a jumble of events but that there must be some higher unity." *Graham Farmelo, Churchills Bomb


1994 Aldus Corporation and Adobe Systems Inc. Merge:
Aldus Corporation and Adobe Systems Inc. announce they will merge. Aldus revolutionized desktop publishing (DTP) when founder Paul Brainerd released the PageMaker program in 1985. Computer Scientists John Warnock and Charles Geschke applied knowledge learned in their graduate work to similar products and founded Adobe in 1982.CHM

2012 Every year on March 15 since 1957, the city of Hinckley, Ohio has eagerly awaited the return of the buzzards at "Buzzards' Roost" at the Hinckley Reservation, part of the Cleveland Metroparks. *about.com


BIRTHS
1570 Andrea Argoli a versatile Italian scholar. He was a jurist, mathematician, astronomer and astrologer, and medical writer.
He was professor of mathematics at the University of Rome La Sapienza, from 1622 to 1627, and then the University of Padua 1632 to 1657. His astrology pupils may have included Placido Titi, and Giambattista Zenno, astrologer to Wallenstein.*Wik
From 1622 to 1627 he held a chair of mathematics in Rome, but lost it because of his enthusiasm for astrology. *VFR

1713 Abbé Nicolas Louis de La Caille (15 Mar 1713; 21 Mar 1762 at age 48) was a French astronomer who named 15 of the 88 constellations in the sky. He spent 1750-1754 mapping the constellations visible from the Southern Hemisphere, as observed from the Cape of Good Hope, the southernmost part of Africa. In his years there, he was said to have observed over 10,000 stars using just his 1/2-inch refractor. He established the first southern star catalogue containing 9776 stars (Caelum Australe Stelliferum, published partly in 1763 and completely in 1847), and a catalogue of 42 nebulae in 1755 containing 33 true deep sky objects (26 his own discoveries).*TIS

1855 Sir Charles Vernon Boys (15 Mar 1855; 30 Mar 1944 at age 88) English physicist and inventor of sensitive instruments. He graduated in mining and metallurgy, self-taught in a wide knowledge of geometrical methods. In 1881, he invented the integraph, a machine for drawing the antiderivative of a function. Boys is known particularly for his utilization of the torsion of quartz fibres in the measurement of minute forces, enabling him to elaborate (1895) on Henry Cavendish's experiment to improve the values obtained for the Newtonian gravitational constant. He also invented an improved automatic recording calorimeter for testing manufactured gas (1905) and high-speed cameras to photograph rapidly moving objects, such as bullets and lightning discharges. Upon retirement in 1939, he grew weeds.*TIS

A reproduction of his wonderful book, Soap-Bubbles: Their Colours and the Forces Which Mould Them : Being the Substance of Many Lectures Delivered to Juvenile and Popular Audiences with the Addition of Several New and Original Sections


1860 Walter Frank Raphael Weldon DSc FRS (Highgate, London, 15 March 1860 – Oxford, 13 April 1906) generally called Raphael Weldon, was an English evolutionary biologist and a founder of biometry. He was the joint founding editor of Biometrika, with Francis Galton and Karl Pearson.*Wik Pearson said of him, "He was by nature a poet, and these give the best to science, for they give ideas." *SAU

1868 Grace Chisholm Young (née Chisholm; 15 March 1868 – 29 March 1944) was an English mathematician. She was educated at Girton College, Cambridge, England and continued her studies at Göttingen University in Germany, where in 1895 she became the first woman to receive a doctorate in any field in that country. Her early writings were published under the name of her husband, William Henry Young, and they collaborated on mathematical work throughout their lives. For her work on calculus (1914–16), she was awarded the Gamble Prize.
Her son, Laurence Chisholm Young, was also a prominent mathematician. One of her living granddaughters, Sylvia Wiegand (daughter of Laurence), is also a mathematician (and a past president of the Association for Women in Mathematics.)*Wik


DEATHS
1897 James Joseph,(Sylvester) (3 Sep 1814; 15 Mar 1897) youngest child of Abraham Joseph, born in London. The eldest son, an actuary, eventually migrated to the U.S. where, for unknown reasons, he took the surname Sylvester. The rest of the family soon followed suit, so that is how James Joseph Sylvester got his name. *VFR British mathematician who, with Arthur Cayley, founded the theory of algebraic invariants, algebraic-equation coefficients that are unaltered when the coordinate axes are translated or rotated. Beginning in 1833, he studied at St John's College, Cambridge. However, at this time signing a religious oath to the Church of England was required to graduate. Being Jewish, he refused and so he did not graduate. He taught physics at the University of London (1838-41), one of the few places which did not bar him because of his religion. Sylvester did important work on matrix theory, in particular, to study higher dimensional geometry. In 1851 he discovered the discriminant of a cubic equation. Earlier in his life, he tutored Florence Nightingale.*TIS (This idea of Sylvester tutoring Nightingale, to the best of my knowledge, originates from the Herbert Baker obituary. Karen Hunger Parshall, among others, has questioned the accuracy of this statement.)
James Joseph Sylvester died, at age 83, after earlier suffering a paralytic stroke while working at his mathematics. *VFR
I came across a nice story about Sylvester on the wonderful "Cut-the-Knot" blog of Alexander Bogomolny. He writes, "Sylvester was one the greatest British mathematicians of the 19th century. He was known for his absentmindedness and poor memory; on one occasion he even denied the truth of one of his own theorems."

1900 Elwin Bruno Christoffel (November 10, 1829 in Montjoie, now called Monschau – March 15, 1900 in Strasbourg) was a German mathematician and physicist. Christoffel worked on conformal maps, potential theory, invariant theory, tensor analysis, mathematical physics, geodesy, and shock waves. The Christoffel symbol, Riemann–Christoffel tensor, and Schwarz–Christoffel mapping are named after him. *Enotes.com

1960 Eduard Cech,(29 June 1893 in Stracov, Bohemia (now Czech Republic)- 15 March 1960 in Prague, Czechoslovakia (now Czech Republic)) Czech topologist. His research interests included projective differential geometry and topology. In 1921–1922 he collaborated with Guido Fubini in Turin. He died in Prague. *Wik

1955 Michele Angelo Besso (25 May 1873 Riesbach – 15 March 1955 Genoa) was a Swiss/Italian engineer of Jewish Italian (Sephardi) descent. He was a close friend of Albert Einstein during his years at the Federal Polytechnic Institute in Zurich, today the ETH Zurich, and then at the patent office in Bern. Besso is credited with introducing Einstein to the works of Ernst Mach, the sceptical critic of physics who influenced Einstein's approach to the discipline. Einstein called Besso "the best sounding board in Europe" for scientific ideas.
In a letter of condolence to the Besso family Albert Einstein wrote his now famous quote "Now Besso has departed from this strange world a little ahead of me. That means nothing. People like us, who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion" *Wik

1962 Arthur Holly Compton (10 Sep 1892; 15 Mar 1962) American physicist and engineer. He was a joint winner, with C.T.R. Wilson of England, of the Nobel Prize for Physics (1927) for his discovery and explanation of the change in the wavelength of X rays when they collide with electrons in metals. This so-called Compton effect is caused by the transfer of energy from a photon to a single electron, then a quantum of radiation is re-emitted in a definite direction by the electron, which in so doing must recoil in a direction forming an acute angle with that of the incident radiation. During WW II, in 1941, he was appointed Chairman of the National Academy of Sciences Committee to Evaluate Use of Atomic Energy in War, assisting in the development of the atomic bomb.*TIS

1992 Deane Montgomery (2 Sept 1909 - 15 March 1992 in Chapel Hill, North Carolina, USA) was a mathematician specializing in topology who was one of the contributors to the final resolution of Hilbert's fifth problem in the 1950s. He served as President of the American Mathematical Society from 1961 to 1962.
Born in the small town of Weaver, Minnesota, he received his B.S. from Hamline University in St. Paul, MN and his Masters and Ph.D. from the University of Iowa in 1933; his dissertation advisor was Edward Chittenden.
In 1941 Montgomery was awarded a Guggenheim Fellowship. In 1988, he was awarded the American Mathematical Society Leroy P. Steele Prize for Lifetime Achievement.*Wik

2004 William Hayward Pickering (24 Dec 1910; 15 Mar 2004) Engineer and physicist, head of the team that developed Explorer 1, the first U.S. satellite. He collaborated with Neher and Robert Millikan on cosmic ray experiments in the 1930s, taught electronics in the 1930s, and was at Caltech during the war. He spent the rest of his career with the Jet Propusion Laboratory, becoming its Director (1954) with responsibility for the U.S. unmanned exploration of the planets and the solar system. Among these were the Mariner spacecraft to Venus and Mercury, and the Viking mission to Mars. The Voyager spacecraft yielded stunning photographs of the planets Jupiter and Saturn.*TIS

2004 John A. Pople (31 Oct 1925; 15 Mar 2004) British mathematician and chemist who, (with Walter Kohn), received the 1998 Nobel Prize in Chemistry for his work on computational methodology to study the quantum mechanics of molecules, their properties and how they act together in chemical reactions. Using Schrödinger's fundamental laws of quantum mechanics, he developed a computer program which, when provided with particulars of a molecule or a chemical reaction, outputs a description of the properties of that molecule or how a chemical reaction may take place - often used to illustrate or explain the results of different kinds of experiment. Pople provided his GAUSSIAN computer program to researchers (first published in 1970). Further developed, it is now used by thousands of chemists the world over. *TIS

2006 George Whitelaw Mackey (February 1, 1916 in St. Louis, Missouri – March 15, 2006 in Belmont, Massachusetts) was an American mathematician.
Mackey's main areas of research were in the areas of representation theory, ergodic theory, and related parts of functional analysis. Earlier in his career Mackey did significant work in the duality theory of locally convex spaces, which provided tools for subsequent work in this area, including Alexander Grothendieck's work on topological tensor products.
He has written numerous survey articles connecting his research interests with a large body of mathematics and physics, particularly quantum mechanics and statistical mechanics. He was among the first five recipients of William Lowell Putnam fellowships in 1938.*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

(Hint for the Lewis Carroll puzzle, think of diamonds.)