## Saturday, 10 September 2016

### On This Day in Math - September 10

This branch of mathematics [Probability] is the only one, I believe, in which good writers frequently get results which are entirely erroneous.
~Charles S Peirce

The 254th day of the year; 254 is the maximum number of pieces a flat pizza could be cut into with n straight lines.... find n. (for help, see bottom of this post, a good quadratic problem)

254 is the average of consecutive primes,

and 254 = 28 - 21

EVENTS

1542 In an apocryphal letter to Rabelais, Charles V of Spain offered 1000 escudos for the solution of the quadrature of the circle problem. This letter was one of 27,345 forged by Denis Vrain-Lucas between 1861 and 1869 and sold to Michel Chasles for 140,000 franks. [Mathematics Magazine 61 (1988), pp. 159-160].*VFR

The Berlin competition, like other prize competitions of this time, involved anonymous entries, identified only by a motto or dévise. It would not have been difficult for Euler to identify d'Alembert's distinctive mathematical style, so the story has at least some credibility. In any case, d'Alembert believed that he had been treated unfairly, and broke off his correspondence with Euler in an angry letter of September 10, 1751

1858: The asteroid 55 Pandora was discovered by George Mary Searle from the Dudley Observatory. *David Dickinson ‏@Astroguyz It is named after Pandora, the first woman in Greek mythology, who unwisely opened a box that released evil into the world. The name was apparently chosen by Blandina Dudley, widow of the founder of the Dudley Observatory, who had been involved in an acrimonious dispute with astronomer B. A. Gould. Gould felt that the name had an "apt significance". The asteroid shares its name with Pandora, a moon of Saturn *Wik

1885 Galton introduced regression. *SAU The statistical concept of regression has its origins in an attempt by Francis Galton (1822-1911) to find a mathematical law for one of the phenomena of heredity. His model (as it would be called today) was extended by Karl Pearson and G. Udny Yule and the biological reference eventually disappeared. The Pearson-Yule notion of regression was based on the multivariate normal distribution but R. A. Fisher re-founded regression using the model Gauss had proposed for the theory of errors and method of least squares. *Jeff Miller, Earliest Known Uses of Some of the Words of Mathematics

1931 Ernst Eduard Kummer (1810–1893) solved a prize problem dealing with the expanding sin(nx) in powers of sin and cos which was posed by his professor Heinrich Ferdinand Scherk, and consequently was awared his Ph.D. degree at age 21 from the University of Halle. He taught as a Gymnasium teacher for 11 years before he became a professor at the University of Breslau. *SAU

2009 UK apologizes to Turing.  Alan Turing committed suicide in 1954 because he was persecuted by the British Government for his homosexuality. The Government feared he might be a security risk as many (almost all) of his actions on behalf of the war effort at Bletchley Park were still classified. On 10 September 2009, following an Internet campaign, British Prime Minister Gordon Brown made an official public apology on behalf of the British government for the way in which Turing was treated after the war.

2016 A thirty ton meteorite found in Argentina buried only 3 meters deep, is probably the second largest known. The largest is the 66-ton Hoba meteorite discovered in Namibia, Africa. *Universe Today

BIRTHS

1838 Charles Sanders Peirce (10 Sep 1839; 19 Apr 1914) American scientist, logician, and philosopher who is noted for his work on the logic of relations and on pragmatism as a method of research. He was the first modern experimental psychologist in the Americas, the first metrologist to use a wave-length of light as a unit of measure, the inventor of the quincuncial projection of the sphere, the first known conceiver of the design and theory of an electric switching-circuit computer, and the founder of "the economy of research." He is the only system-building philosopher in the Americas who has been both competent and productive in logic, in mathematics, and in a wide range of sciences.*TIS He was elected to the National Academy of Sciences (United States) in April 1877 and published the results of his earlier research in astronomy in a book Photometric Researches (1878). Although his work had been wide ranging in the sciences, he had always been interested in philosophy and logic and, in 1879, he was appointed as Lecturer in Logic in the Department of Mathematics at Johns Hopkins University. Sylvester was Head of Mathematics at Johns Hopkins University at this time and for a while things went well for Peirce. He became interested in the Four Colour Problem, and problems of knots and linkages studied by Kempe. He then extended his father's work on associative algebras and worked on mathematical logic, topology and set theory. However by now Peirce was living with Juliette Froissy Pourtalès, a French gypsy. He was divorced from his first wife Melusina on 24 April 1883 and married Juliette six days later. In 1884 Simon Newcomb, who had just been appointed professor of mathematics and astronomy at Johns Hopkins University, reported to the trustees of the university that Peirce had been living with a French gypsy while still married to Melusina. Not wishing to be involved in a scandal, the trustees chose not to renew Peirce's contract. Peirce would never hold another academic post. *SAU

1857 James Edward Keeler (10 Sep 1857; 12 Aug 1900) was an American astronomer who confirmed Maxwell's theory that the rings of Saturn were not solid (requiring uniform rotation), but composed of meteoric particles (with rotational velocity given by Kepler's 3rd law). His spectrogram of 9 Apr 1895 of the rings of Saturn showed the Doppler shift indicating variation of radial velocity along the slit. At the age of 21, he observed the solar eclipse of Jul 1878, with the Naval Observatory expedition to Colorado. He directed the Allegheny Observatory (1891-8) and the Lick Observatory from 1898, where, working with the Crossley reflector, he observed large numbers of nebulae whose existence had never before been suspected. He died unexpectedly of a stroke, age 42*TIS

1861 Theodor Molien​ or Fedor Eduardovich Molin​ (September 10, 1861 - December 25, 1941) was a Baltic-German mathematician. He was born in Riga, Latvia, which at that time was a part of Russian Empire. Molien studied associative algebras and polynomial invariants of finite groups.*Wik Emmy Noether, referring to Molien's paper Über Systeme höherer complexer Zahlen (1893), wrote "The most general theorems about algebras go back to Molien. " *SAU

1863 Charles E. Spearman, FRS, (10 September 1863 - 17 September 1945)British psychologist and behavioral scientist perhaps best known for his work in statistics, especially in factor analysis, where he led its use is psych and in some circles is considered its inventor. Spearman was strongly influenced by the work of Galton, who developed correlation, which became the main statistical tool used by Spearman. Spearman developed rank correlation in 1904, a nonparametric version of conventional Pearson [APStat] correlation. The well-known Spearman's rank-correlation coefficient formula,1 - 6 SUM d^2 /[n(n^2 - 1)], is simply Pearson's product-moment-correlation coefficient, cov(x,y)/(sxsy), applied to ranks. (Not so surprisingly, Pearson did not appreciate Spearman's stat work, and there was a long feud between them.)*David Bee

1892 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 After WWII, Compton became Chancellor of Washington University in St. Louis. During his time as Chancellor, the university formally desegregated its undergraduate divisions, named its first female full professor, and enrolled a record number of students as wartime veterans returned to the United States. Compton's brother, Karl, was the President of MIT and a prominent American physicist. *Wik

1897 William Greaves (10 September 1897 – 24 December 1955) graduated from Cambridge and then worked at the Royal Observatory Greenwich. He became Professor of Astronomy in Edinburgh. He worked on both theoretical and practical astronomy. *SAU

1903 Georges de Rham (10 September 1903 – 9 October 1990) was a Swiss mathematician, known for his contributions to differential topology.
He studied at the University of Lausanne and then in Paris for a doctorate, becoming a lecturer in Lausanne in 1931; where he held positions until retirement in 1971; he held positions in Geneva in parallel.
In 1931 he proved de Rham's theorem, identifying the de Rham cohomology groups as topological invariants. *Wik

1919 Robert B. Leighton (September 10, 1919–March 9, 1997) was a prominent American experimental physicist who spent his professional career at the California Institute of Technology (Caltech). Leighton was known as a remarkably ingenious physicist and astrophysicist during his 58 years at Caltech. He found no instrumentation problem too difficult, especially if it might open a new part of the electromagnetic spectrum to observation. His subject matter evolved from physics to astrophysics as he helped astronomy take on its modern shape. *Wik Suring the only total eclipse he tried to observe (Hawaii 1991), he was clouded out. But, using the 60-ft. solar tower at Mt. Wilson (California) more than 30 years earlier, he had discovered
the 5-min. and 15-min. oscillations of the Sun, thereby creating the field of helioseismology, which occupies several dozen scientists around the world today. *NSEC

1930 Anatoliy Volodymyrovych Skorokhod (September 10, 1930 – January 3, 2011) was a Soviet and Ukrainian mathematician, and an academician of the National Academy of Sciences of Ukraine from 1985 to his death.
In 1956–1964 he worked at Kyiv University. From 1964 until 2002, he was at the Institute of Mathematics of the National Academy of Sciences of Ukraine. At the same time, he was a professor at Kyiv University. Since 1993, he had been a professor at Michigan State University, U.S., and a member of the American Academy of Arts and Sciences.
His scientific works are on the theory of stochastic differential equations, limit theorems of random processes, distributions in infinite-dimensional spaces, statistics of random processes and Markov processes.
Skorokhod is the author of more than 450 scientific works, including more than 40 monographs and books. *Wik

1941 Stephen Jay Gould (10 Sep 1941; 20 May 2002) American paleontologist, evolutionary biologist, and science writer who grew up in New York City. He graduated from Antioch College and received his Ph.D. from Columbia University in 1967. Since then he has been Professor of Geology and Zoology at Harvard University. He considers himself primarily a palaeontologist and an evolutionary biologist, though he teaches geology and the history of science as well. A frequent and popular speaker on the sciences, his published work includes both scholarly study and many prize-winning popular collections of essays.*TIS

1948 Charles Simonyi, (September 10, 1948, )whose work as chief architect of Microsoft Word is born in Budapest, Hungary. After moving to the United States for study at the University of California, Berkeley. Simonyi took a job at the Xerox PARC in Palo Alto, developing the first WYSIWYG (What You See Is What You Get) word-processing editor. Later, at Microsoft, he integrated such theories into Word and Multiplan, the predecessor of the Microsoft Excel spreadsheet.*CHM

DEATHS
1635 Johann Faulhaber (5 May 1580; Ulm, Germany – 10 September 1635; Ulm, Germany) was a German mathematician.
Born in Ulm, Faulhaber was trained as a weaver. However he was taught mathematics in Ulm and showed such promise that the City appointed him city mathematician and surveyor. He opened his own school in Ulm in 1600 but he was in great demand because of his skill in fortification work. He collaborated with Johannes Kepler and Ludolph van Ceulen. Besides his work on the fortifications of cities (notably Basel and Frankfurt), Faulhaber built water wheels in his home town and geometrical instruments for the military. Faulhaber made the first publication of Henry Briggs's Logarithm in Germany.
Faulhaber's major contribution was in calculating the sums of powers of integers, what is now called Faulhaber's formula. Jacob Bernoulli makes references to Faulhaber in his Ars Conjectandi and the Bernouli numbers arise in solving coefficients of Faulhaber's formula.
In Academia Algebra Faulhaber gives ∑ nk as a polynomial in N, for k = 1, 3, 5, ... ,17. He also gives the corresponding polynomials in n. Faulhaber states that such polynomials in N exist for all k, but gave no proof. This was first proved by Jacobi in 1834. It is not known how much Jacobi was influenced by Faulhaber's work, but we do know that Jacobi owned Academia Algebra since his copy of it is now in the University of Cambridge.
At the end of Academia Algebra Faulhaber states that he has calculated polynomials for ∑ nk as far as k = 25. He gives the formulae in the form of a secret code, which was common practice at the time. Donald Knuth suggests he is the first to crack the code: (the task [of cracking the code] is relatively easy with modern computers) and shows that Faulhaber had the correct formulae up to k = 23, but his formulae for k = 24 and k = 25 appear to be wrong.
A nice example of how to calculate sum of powers using Pascal's arithmetic triangle is given at Theorem of the Day.
*SAU *Wik

1749 Emilie du Chˆatelet died of childbed fever (Voltaire was her lover then, but not the father of the child). Ten years later her annotated translation of Newton’s Principia was published. It is still the only French translation (is this true?). *VFR She took to mathematics and the sciences, being exposed to distinguished guests of her aristocratic parents. Emilie was interested in the philosophies of Newton and Leibniz, and dressed as a man to enter the cafes where the scientific discussions of the time were carried on. Châtelet's major work was a translation of Newton's Principia, begun in 1745. Voltaire wrote the preface. The complete work appeared in 1759 and was for many years the only translation of the Principia into French.

1915 John Howard Van Amringe (3 April 1835 in Philadelphia, Pennsylvania, USA - 10 Sept 1915 in Morristown, New Jersey, USA) was a U.S. educator and mathematician. He was born in Philadelphia, and graduated from Columbia in 1860. Thereafter, he taught mathematics at Columbia, holding a professorship from 1865 to 1910 when he retired. Van Amringe was also the first Dean of Columbia College, the university's undergraduate school of arts and sciences, which he defended from dismemberment and incorporation into the larger university. During his long presence at the school, he made many addresses and enjoyed unrivaled popularity. He is memorialized with a bust enshrined in a column-supported cupola on "Van Am Quad" in the southeastern portion of the campus, surrounded by three College dormitories (John Jay Hall, Hartley Hall, and Wallach Hall) and by the main College academic building, Hamilton Hall. He is buried in Greenwood Cemetery in Brooklyn.
Van Amringe served as the first president of the American Mathematical Society between 1888 and 1890.
In honor of Van Amringe, Columbia University's Department of Mathematics has presented a "Van Amringe Mathematical Prize" each year (since 1911) to the best freshman or sophomore mathematics student, based on a very challenging examination. *Wik

1931 Dimitri Fjodorowitsch Jegorow (egorov) died (December 10,(Julian)/ December 22 1869 (greg) in Moscow - 10 September 1931 in Kazan). Egorov worked on triply orthogonal systems and potential surfaces, making a major contribution to differential geometry. Some of Egorov's work was presented by Darboux in his famous four volume work Leçons sur la théorie général des surfaces et les applications géométriques du calcul infinitésimal.
Egorov also worked on integral equations and a theorem in the theory of functions of a real variable is named after him. Luzin was Egorov's first student and became a member of the school Egorov created in Moscow dealing with functions of a real variable. Some time later he was arrested as a "religious sectarian" and put in prison. The Moscow Mathematical Society continued to support Egorov, refusing to expel him, and those who presented papers at the next meeting, including Kurosh, were to be expelled by an "Initiative group" who took over the Society in November 1930. They expelled Egorov denouncing him as a reactionary and a churchman.
Egorov went on a hunger strike in prison and eventually, by this time close to death, he was taken to the prison hospital in Kazan. Chebotaryov's wife was working as a doctor in the prison hospital and, although it sounds rather unlikely, it is reported that Egorov died at Chebotaryov's home. *SAU

1946 John Carruthers Beattie (21 Nov 1866, 10 Sept 1946) graduated from Edinburgh University and studied at Munich, Vienna, Berlin and Glasgow. He became Professor of Applied Mathematics and Experimental Physics at the University of Cape Town and was later Vice Chancellor and Principal of the University. He was knighted in 1920. *SAU

1948 Walther Mayer, the Austrian born mathematician who collaborated with Einstein on the theory of relativity, died in Princeton NJ at the age of 61.

1956 Robert Julius Trumpler (2 Oct 1886, 10 Sep 1956) Swiss-American astronomer who moved to the US in 1915 and worked at the Lick Observatory. In 1922, by observing a solar eclipse, he was able to confirm Einstein's theory of relativity. He made extensive studies of galactic star clusters, and demonstrated (1930) the presence throughout the galactic plane of a tenuous haze of interstellar material that absorbs light generally that dims and reddens the light from of distant clusters. The presence of this obscuring haze revealed how the size of spiral galaxies had been over-estimated. Whereas Harlow Shapley, in 1918, determined the distance to the centre of the Milky Way to be 50,000 light-years away, Trumpler's work reduced this to 30,000 light-years.*TIS

1975 Sir George Paget Thomson (3 May 1892, 10 Sep 1975)English physicist who shared (with Clinton J. Davisson of the U.S.) the Nobel Prize for Physics in 1937 for demonstrating that electrons undergo diffraction, a behavior peculiar to waves that is widely exploited in determining the atomic structure of solids and liquids. He was the son of Sir J.J. Thomson who discovered the electron as a particle.*TIS

1983 Felix Bloch (23 Oct 1905, 10 Sep 1983)Swiss-born American physicist who shared (with independent discoverer, E.M. Purcell) the Nobel Prize for Physics in 1952 for developing the nuclear magnetic resonance (NMR) method of measuring the magnetic field of atomic nuclei. He obtained his PhD under Werner Heisenberg in 1928, then taught briefly in Germany, but as a Jew, when Hitler came to power, he left Europe for the USA. Bloch's concept of magnetic neutron polarization (1934) enabled him, in conjunction with L. Alvarez, to measure the neutron's magnetic moment. During WW II he worked on the atomic bomb. Thereafter, Bloch and co-workers developed NMR, now widely used technique in chemistry, biochemistry, and medicine. In 1954 he became the first director of CERN. *TIS

1985 Ernest Julius Öpik (23 Oct 1893, 10 Sep 1985) Estonian astronomer best known for his studies of meteors and meteorites, and whose life work was devoted to understanding the structure and evolution of the cosmos. When Soviet occupation of Estonia was imminent, he moved to Hamburg, then to Armagh Observatory, Northern Ireland (1948-81). Among his many pioneering discoveries were: (1) the first computation of the density of a degenerate body, namely the white dwarf 40 Eri B, in 1915; (2) the first accurate determination of the distance of an extragalactic object (Andromeda Nebula) in 1922; (3) the prediction of the existence of a cloud of cometary bodies encircling the Solar System (1932), later known as the Oort Cloud''; (4) the first composite theoretical models of dwarf stars like the Sun which showed how they evolve into giants (1938); (5) a new theory of the origin of the Ice Ages (1952).*TIS

2005 Sir Hermann Bondi (1 Nov 1919, 10 Sep 2005) Austrian-born British mathematician and cosmologist who, with Fred Hoyle and Thomas Gold, formulated the steady-state theory of the universe (1948). Their theory addressed a crucial problem: "How do the stars continually recede without disappearing altogether?" Their explanation was that the universe is ever-expanding, without a beginning and without an end. Further, they said, since the universe must be expanding, new matter must be continually created in order to keep the density constant, by the interchange of matter and energy. The theory was eclipsed in 1965, when Arno Penzias and Robert Wilson discovered a radiation background in microwaves giving convincing support to the "big bang" theory of creation now accepted.*TIS

===============================================================================================================

PIZZA : The maximum number p of pieces that can be created with a given number of cuts n, where n ≥ 0, is given by the formula
$p = \frac{n^2+n+2}{2}.$
Using binomial coefficients, the formula can be expressed as
$p = {\tbinom {n + 1} 2} + 1 = {\tbinom n 2}+{\tbinom n 1}+{\tbinom n 0}.$
=======================================================================================================

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