## Sunday, 9 February 2020

### On This Day in Math - February 9

 da Vinci's Stellated Dodecahedron from divina proportione

To argue with a man who has renounced the use of authority of reason is like administering medicine to the dead.
~Thomas Paine, American Patriot, and a pretty good bridge builder, perhaps pointing out something still very relevant to today's political discussions.

The 40th day of the year; in English forty is the only number whose letters are in alphabetical order.

There are 40 solutions on for the 7 queens problem.  placing seven chess queens on a 7x7 chessboard so that no two queens threaten each other.

-40 is the temperature at which the Fahrenheit and Celsius scales correspond; that is, −40 °F = −40 °C.

Euler first noticed (in 1772) that the quadratic polynomial P(n) = n2 + n + 41 is prime for all non-negative numbers less than 40.
Paul Halcke noted in 1719 that the product of the aliquot parts of 40 is equal to 40 cubed. 1*2*4*5*8*10*20 = 64000 = 403. He found the same is true for 24.

And.... forty is the highest number ever counted to on Sesame Street.

The expanded collection of Number Factoids for Day 1-60  are available here

EVENTS

1498 Luca Pacioli was professor at Milan. He was inspired to start his Divina Proportione on 9 Feb 1498 and completed it on 14 Dec 1498, though it was not published (in an expanded form) until 1509 He was a good friend of Leonardo da Vinci. It was Leonardo who drew the pictures for Pacioli's book. Pacioli may have advised Leonardo on the perspective for the painting of The Last Supper. Certainly Pacioli stimulated Leonardo's interest in perspective and it is possible that Leonardo's famous drawing of the proportions of the human body was inspired by Pacioli's comment on classical architecture; "For in the human body they found the two main figures ..., namely the perfect circle and the square." Pacioli seems to have made models of the polyhedra illustrated in his book, though we don't know if Leonardo used these for his drawings. A set was probably given to Pacioli's earlier patron, the Duke of Urbino, in 1494. Another set was paid for by Florence in 1504. *Unknown Internet Source
I was just reminded by a tweet from @IanMegaw that Pacioli also published the first description of double-entry bookkeeping. (thanks Ian)

1849 After the death of Lord Kelvin’s Father, James Thompson, his replacement was the subject of a letter from William Hopkins to discuss the merits of G.G. Stokes and Hugh Blackburn for the position, “if you determine … to elect a man who is sure to hereafter to dignify his postion by the highest scientific distinction, Stokes is unquestionably your man.” * The correspondence between Sir George Gabriel Stokes and Sir William Thomson, pg 59

In 1870, the U.S. Weather Bureau (later named the Weather Service) was authorized by Congress, and placed under the direction of the Signal Service. Cleveland Abbe had inaugurated a private weather reporting and warning service at Cincinnati and had been issuing weather reports or bulletins since 1 Sep 1869. Hence, Abbe was the only person in the country who was already experienced in drawing weather maps from telegraphic reports and forecasting from them. Naturally, he was offered an important position in this new service which he accepted, beginning 3 Jan 1871, and was often the official forecaster of the weather. He was the first U.S. metereologist, and known as the "father of the U.S. Weather Bureau."*TIS

1883 The very ﬁrst issue of Science is published. The ﬁrst item in the “Weekly summary of the progess of science” contains a report by Thomas Craig that “Lindemann gave a proof of the fact that π cannot be a root of an equation of any degree with rational co-eﬁcients. This is a most remarkable paper, as it thus contains the ﬁrst direct, absolute proof that has ever been given of the impossability of the quadrature of the circle. ... Lindemann has certainly done a splendid piece of work in thus absolutely proving the impossibility of ‘squaring the circle’; and it is only to be regretted that his work will not carry conviction to the minds of those mistaken individuals, the ‘circle-squarers.’ But it is hardly to be supposed that they will be convinced of the futility of their task, any more than the perpetual-motion inventors were convinced by the discovery and enunciation of the principles of the conservation of energy.” [p. 15] *VFR

1986 Halley’s comet last reached perihelion. The next return to perihelion will be on 28 July 2061. *Wik (I am still amazed that we can mathematically predict such an event with such precision.)

BIRTHS

1489 Georg Hartmann (sometimes spelled Hartman; February 9, 1489 – April 9, 1564) was a German engineer, instrument maker, author, printer, humanist, churchman, and astronomer. After finishing his studies, he travelled through Italy and finally settled in Nuremberg in 1518. There he constructed astrolabes, globes, sundials, and quadrants. In addition to these traditional scientific instruments Hartmann also made gunner's levels and sights. Hartmann was possibly the first to discover the inclination of Earth's magnetic field. He died in Nuremberg.
His two published works were Perspectiva Communis (Nuremberg, 1542), a reprint of John Peckham's 1292 book on optics and Directorium (Nuremberg, 1554), a book on astrology. He also left Collectanea mathematica praeprimis gnomonicam spectania, 151 f. MS Vienna, Österreichische Nationalbibliothek, Quarto, Saec. 16 (1527–1528), an unpublished work on sundials and astrolabes that was translated by John Lamprey and published under the title of Hartmann's Practika in 2002. *Wik

1775 Farkas Bolyai (9 Feb 1775, 20 Nov 1856) Hungarian mathematician, poet, and dramatist who spent a lifetime trying to prove Euclid's (fifth) postulate that parallel lines do not meet. While studying at the University of Göttingen, he met as a fellow student, the noted German mathematician Carl F. Gauss, with whom he corresponded as a life-long friend. Bolyai taught mathematics, physics and chemistry at Marosvásárhely all his life. He discouraged his son, János Bolyai, from studying the parallel axiom as he had, writing in a letter to him: "For God's sake, please give it up. Fear it no less than the sensual passion, because it, too, may take up all your time and deprive you of your health, peace of mind and happiness in life." *TIS (In 1804 he believed that he had a proof the Euclid's fifth postulate could be deduced from the other axims. He sent this proof to C. F. Gauss who found an error. His Son, Janos, would ignore his father's warnings and go on to discover a non-Euclidean Geometry. ).

1880 Lipót Fejér (9 Feb 1880, 15 Oct 1959) Fejér's main work was in harmonic analysis working on Fourier series and their singularities. Fejér collaborated to produce important papers with Carathéodory on entire functions and with Riesz on conformal mappings. *SAU In 1897 he won a prize in one of the ﬁrst mathematical competitions held in Hungary. *VFR

1907 Harold Scott MacDonald Coxeter (9 Feb 1907 in London, England - 31 March 2003 in Toronto, Canada) graduated from Cambridge and worked most of his life in Canada. His work was mainly in geometry. In particular he made contributions of major importance in the theory of polytopes, non-euclidean geometry, group theory and combinatorics. Among his most famous geometry books are The real projective plane (1955), Introduction to geometry (1961), Regular polytopes (1963), Non-euclidean geometry (1965) and, written jointly with S L Greitzer, Geometry revisited (1967). He also published a famous work on group presentations, which was written jointly with his first doctoral student W O J Moser, Generators and relations for discrete groups.
His 12 books and 167 published articles cover more than mathematical research. Coxeter met Escher in 1954 and the two became lifelong friends. Another friend, R Buckminister Fuller, used Coxeter's ideas in his architecture. In 1938 Coxeter revised and updated Rouse Ball's Mathematical recreations and essays, a book which Rouse Ball first published in 1892. *SAU

1908 Alexander Dinghas (February 9, 1908 – April 19, 1974) was a Turkish mathematician. He is known for his work in different areas of mathematics including differential equations, functions of a complex variable, functions of several complex variables, measure theory and differential geometry. His most important contribution was his work in function theory, in particular Nevanlinna theory and the growth of subharmonic functions.*Wik

1919 Irene Anne Stegun (February 9, 1919 – January 27, 2008) was a mathematician at the National Bureau of Standards who, with Milton Abramowitz, edited a classic book of mathematical tables called A Handbook of Mathematical Functions, widely known as Abramowitz and Stegun. When Abramowitz died of a heart attack in 1958, Stegun took over management of the project and finished the work by 1964, working under the direction of the NBS Chief of Numerical Analysis Philip J. Davis, who was also a contributor to the book. *Wik

1927 David John Wheeler FRS (9 February 1927–13 December 2004) the Inventor of the Wheeler Jump, is Born. In 1951, he introduced the concept of the subroutine to computer programming, is born. He concentrated his work on assembly programming language and invoked the subroutine in his Wheeler jump technique. For this work Wheeler received the IEEE Computer Society Pioneer Award. *CHM
He was born in Birmingham and gained a scholarship at Trinity College, Cambridge to read mathematics, graduating in 1948. He completed the world's first PhD in computer science in 1951. His contributions to the field included work on the EDSAC and the Burrows-Wheeler transform. Along with Maurice Wilkes and Stanley Gill he is credited with the invention of the subroutine (which they referred to as the closed subroutine), because of which a jump to subroutine instruction is often called Wheeler Jump. He was responsible for the implementation of the CAP computer, the first to be based on security capabilities. In cryptography, he was the designer of WAKE and the co-designer of the TEA and XTEA encryption algorithms together with Roger Needham. In 2003 he was a Computer History Museum Fellow Award recipient.
Wheeler is often quoted as saying "All problems in computer science can be solved by another level of indirection... Except for the problem of too many layers of indirection." *Wik

DEATHS

1734 Pierre Polinière (8 September 1671, Coulonces, France - 9 February 1734, Coulonces, France) was an early investigator of electricity and electrical phenomena, notably "barometric light", a form of gas-discharge light, which suggested the possibility of electric lighting. He also helped to introduce the scientific method in French universities. *Wik

1811 Nevil Maskelyne (6 Oct 1732, 9 Feb 1811) (SAU gives 5 Oct for birhtdate)
British astronomer noted for his contribution to the science of navigation. In 1761 the Royal Society sent Maskelyne to the island of St Helena to make accurate measurements of a transit of Venus. This in turn gives the distance from the Earth to the Sun, and the scale of the solar system. During the voyage he also experimented with the lunar position method of determining longitude. In 1764 he went on a voyage to Barbados to carry out trials of Harrison's timepiece, followed by appointment as Astronomer Royal (1765). In 1774, he carried out an experiment on a Scottish mountain with the use of a plumb line to determine the Earth's density. He found it was approximately 4.5 times that of water. *TIS (the current scientific value of the Earht's density is about 5.2 times that of water.) He was the fifth English Astronomer Royal. He held the office from 1765 to 1811.*Wik

1865 James Melville Gilliss (6 Sep 1811; 9 Feb 1865) U.S. naval officer and astronomer who founded the Naval Observatory in Washington, D.C., the first U.S. observatory devoted entirely to research. Gilliss joined the Navy as a midshipman at the age of 15. He taught himself astronomy, at a time when there was no fixed astronomical observatory in the U.S., and very little formal instruction. In 1838, when Charles Wilkes left on the famous South Seas Exploring Expedition, Gilliss became officer-in-charge of the Depot of Charts and Instruments, forerunner of the U. S. Naval Observatory. Gilliss's astronomical observations made during this time in connection with determining longitude differences with the Wilkes Expedition, resulted in the first star catalogue published in the United States. *TIS

1883 Henry John Stephen Smith (2 Nov 1826 in Dublin, Ireland, 9 Feb 1883 in Oxford, England) was an Irish mathematician whose most important contributions are in number theory where he worked on elementary divisors. He proved that any integer can be expressed as the sum of 5 squares and as the sum of 7 squares, showing in how many ways this could occur. In addition to solving these cases explicitly, he gave a method which would yield the number of ways that an integer can be expressed as the sum of k squares for any fixed k. He published his results in The orders and genera of quadratic forms containing more than three indeterminates published in the Proceedings of the Royal Society in 1867. Eisenstein had earlier proved the result for 3 squares and Jacobi for 2, 4 and 6 squares. Smith also extended Gauss's theorem on real quadratic forms to complex quadratic forms. *SAU He posthumously received the Grand Prix des Sciences Mathematiques of the Paris Academy of Science for his proof that every positive integer is the sum of ﬁve squares. He shared the prize with the eighteen year old Hermann Minkowski.*VFR The prize was awarded on April 2, less than two months after his death.

1937 Francis Sowerby Macaulay FRS (11 February 1862 – 9 February 1937) was an English mathematician who made significant contributions to algebraic geometry. He is most famous for his 1916 book, The Algebraic Theory of Modular Systems, which greatly influenced the later course of algebraic geometry. Both Cohen-Macaulay rings and the Macaulay resultant are named for Macaulay.
Macaulay was educated at Kingswood School and graduated with distinction from St John's College, Cambridge. He taught top mathematics class in St Paul's School in London from 1885 to 1911. His students included J. E. Littlewood and G. N. Watson.*Wik Littlewood consulted the examinations record and wrote, "In the 25 years from [Macaulay's] appointment to St Paul's in 1885 to his resignation in 1911 there were 41 scholarships (34 at Cambridge) and 11 exhibitions; and in the 20 years available there were 4 senior wranglers, one second, and one fourth among his former pupils." *SAU

1970 Leo Moser (April 11, 1921, Vienna—February 9, 1970, Edmonton) was an Austrian-Canadian mathematician, best known for his polygon notation.
A native of Vienna, Leo Moser immigrated with his parents to Canada at the age of three. He received his Bachelor of Science degree from the University of Manitoba in 1943, and a Master of Science from the University of Toronto in 1945. After two years of teaching he went to the University of North Carolina to complete a Ph.D., supervised by Alfred Brauer.[1] There, in 1950, he began suffering recurrent heart problems. He took a position at Texas Technical College for one year, and joined the faculty of the University of Alberta in 1951, where he remained until his death at the age of 48. *Wik In mathematics, Steinhaus–Moser notation is a means of expressing certain extremely large numbers. It is an extension of Steinhaus’s polygon notation.
a number n in a triangle means nn.
a number n in a square is equivalent with "the number n inside n triangles, which are all nested."
a number n in a pentagon is equivalent with "the number n inside n squares, which are all nested."
*Wik

1988 Israel Nathan Herstein (March 28, 1923, Lublin, Poland – February 9, 1988, Chicago, Illinois) was a mathematician, appointed as professor at the University of Chicago in 1951. He worked on a variety of areas of algebra, including ring theory, with over 100 research papers and over a dozen books.
He is known for his lucid style of writing, as exemplified by the classic and widely influential Topics in Algebra, an undergraduate introduction to abstract algebra that was published in 1964, which dominated the field for 20 years. A more advanced classic text is his Noncommutative Rings in the Carus Mathematical Monographs series. His primary interest was in noncommutative ring theory, but he also wrote papers on finite groups, linear algebra, and mathematical economics.*Wik

2001 Herbert Alexander Simon (15 Jun 1916, 9 Feb 2001 at age 84) American social scientist who was a pioneer of the development of computer artificial intelligence. In 1956, with his long-time colleague Allen Newell, Simon produced the computer program, The Logic Theorist, a computer program that could discover proofs of geometric theorems. It was the first computer program capable of thinking, and marked the beginning of what would become known as artificial intelligence. It proved many of the theorems of symbolic logic in Whitehead and Russell's Principia Mathematica. He is further known for his contributions in fields including psychology, mathematics, statistics, and operations research, all of which he synthesized in a key theory for which he won the 1978 Nobel Prize for economics. *TIS

2003 Masatoşi Gündüz İkeda (25 February 1926, Tokyo. - 9 February 2003, Ankara), was a Turkish mathematician of Japanese ancestry, known for his contributions to the field of algebraic number theory. *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