## Saturday 3 December 2022

### On This Day in Math - December 3

Symmetry, as wide or narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty, and perfection.
~Hermann Weyl

The 337th day of the year, 337 is a Pythagorean prime number, and when its digits are reversed, that is also prime. (A Pythagorean prime is a prime number of the form 4n + 1. Pythagorean primes are exactly the primes that are the sum of two squares (and from this derives the name in reference to the famous Pythagorean theorem.)

The mean of the first 337 square numbers is itself a square. This is the smallest number for which this is true.

The famous Fibonacci area paradox shows a 13x13 square converted to an 8x21 rectangle. The areas of the two figures, 13x13 + 8x21 = 337 (this illusion works with any Fibonacci number F(n) squared and a rectangle that is F(n-1) by F(n+1)  )  Students must be aware that 13 x 13 = 169 is NOT equal to 8 x 21 = 168, so where is the flaw.  Here is a post for a little history of these geometric vanishes.

EVENTS

1610 Galileo dedicates his Sidereus nuncius to Grandduke Cosmos II. *VFR I am not sure what event Professor Rickey is referring here. According to Albert Van Helden in his introduction to his translation, "The Dedicatory letter of Sidereus nuncius is dated 12 March 1610, and on the next day Galileo sent an advance, unbound copy, accompanied by a letter, to the Tuscan court."
Thony Christie sent this translation from page 33 of the same book, "Written in Padua on the fourth day before the Ides of March 1610. Your Highnesses's most loyal servant, Galileo Galilei."

1833 Oberlin College, the ﬁrst truly coeducational institution of higher education in the U.S., opens with 29 men, 15 women. *VFR
 *WIK Partial View Oberlin by H. Alonzo Pease, 1838

1836   Adolphe Quetelet presents the average number of meteors per hour.
The 1833 Leonid storm had galvanized interest in meteors, and the time was ripe. Adolphe Quetelet, a Belgian statistician and founder and director of the Brussels Observatory, had mentioned mid-August meteors very tentatively six months earlier. His attention had been called to meteors by François Arago of France, who dominated European science at the time with his skill in discerning important scientific problems and suggesting experiments to solve them. What, asked Arago in the wake of the 1833 display, constituted a shower of meteors, and what was the rate of the ordinary, every night drizzle?
The problem was ideal for Quetelet, whose passion was statistics. In a speech to the Royal Academy of Sciences and Arts of Brussels on December 3, 1836, Quetelet gave his answer: averaged over the night and year, a single observer should expect to see eight sporadic (nonshower) meteors per hour. That figure is still good today. After his speech Quetelet made a brief mention of unusual August meteors, and in his 1836 annual report of the Brussels Observatory he presented the idea timidly and almost in passing: "I thought I also noticed a greater frequency of these meteors in the month of August (from the 8th to the 15th)."
By the following year, Quetelet had accidentally found records in his observatory of exceptional meteor displays on August 10th of 1834 and 1835 to accompany the increase he had seen in 1836. He called for scientists at the March 4, 1837, session of the Royal Academy of Brussel to watch the sky on August 10, 1837. *Sky and Telescope

1880 The Railroad Gazette credits Ellis Holbrook with being the first to give an accurate description of the so-called track transition curve, a method of making the transition from a straight track to a circular curve without the sudden lateral "jerk" caused by the change in curvature.
Unknown to them, the curve had been described {in part} by James Bernoulli in 1694 and known then as the Cantilever problem., to find the curvature a beam must have in order to be straightened by a given weight.  Bernoulli gave the solution a = s^2 r where a is a constant r is the radius of curvature, thus the curvature was proportional to the arc length.
Euler, in the same year, 1744, extended the curve to the shape now called the Euler Spiral.
 *Wik

The curve emerged again in 1874 as the solution to a problem in diffraction, now known as the spiral of [Alfred] Cornu.
By 1886 the spiral attracted the attention of Italian Ernesto Cesaro, who thought the curve looked like the shape of thread wrapped on a spindle, and called the curve the clothoid, after Clotho, one of the three fates who was a spinner. HT to Julian Havel
Got a note about the demo at this site, *HT @mral@mastodon.sdf.org

1910 Modern neon lighting is first demonstrated by Georges Claude at the Paris Motor Show. *PainterFlynn

1958 Germany issued a stamp to commemorate  the 500th anniversary of the Cusanus Hospice at Kues, founded by Cardinal Nicolaus (1401-1464), Nicolaus Cusanus (Nickolaus Krebs). *VFR

1968 CDC Announces 7600 Supercomputer: Control Data Corporation announces its 7600 model, considered by some to be the first true supercomputer. The CDC 7600 calculated at a speed of nearly 40 megaflops. Seymour Cray designed this computer, as well as its predecessor, the 6600 that was popular with scientific researchers, and a successor, the 8600, which the company never marketed. *CHM

1992  a test engineer for Sema Group uses a personal computer to send the world's first text message via the Vodafone network to the phone of a colleague. *PainterFlynn

BIRTHS

1616 John Wallis (3 Dec 1616; 8 Nov 1703) English mathematician. Wallis was skilled in cryptography and decoded Royalist messages for the Parliamentarians during the Civil War. Wallis was part of a group interested in natural and experimental science who started to meet in London. This group became the Royal Society (1663), with Wallis as a founder member and one of its first Fellows. He contributed substantially to the origins of calculus and was the most influential English mathematician before Newton. Wallis introduced our symbol for infinity (1656), and exponents using negative or fractional numbers (such as 1/x2 = x-2 or square root of x = x-1/2). In 1668, he was the first to suggest the law of conservation of momentum for colliding bodies, the first of all-important conservation laws.*TIS

1903 Sydney Goldstein (3 Dec 1903 in Hull, England - 22 Jan 1989 in Belmont, Massachusetts, USA)  Goldstein's work in fluid dynamics is of major importance. He is described as, "... one of those who most influenced progress in fluid dynamics during the 20th century." He studied numerical solutions to steady-flow laminar boundary-layer equations in 1930. In 1935 he published work on the turbulent resistance to rotation of a disk in a fluid. His work was important in aerodynamics, a subject in which Goldstein was extremely knowledgeable. *SAU

1938 Cleveland Abbe (3 Dec 1838; 28 Oct 1916) U.S. astronomer and first meteorologist, born in New York City, the "father of the U.S. Weather Bureau," which was later renamed the National Weather Service. Abbe inaugurated a private weather reporting and warning service at Cincinnati. His weather reports or bulletins began to be issued on Sept. 1, 1869. The Weather Service of the United States was authorized by Congress on 9 Feb 1870, and placed under the direction of the Signal Service. 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.*TIS

1924 John Backus (3 Dec 1924; 28 Oct 1988) American computer scientist who invented the FORTRAN (FORmula TRANslation) programming language in the mid 1950s. He had previously developed an assembly language for IBM's 701 computer when he suggested the development of a compiler and higher level language for the IBM 704. As the first high-level computer programming language, FORTRAN was able to convert standard mathematical formulas and expressions into the binary code used by computers. Thus a non-specialist could write a program in familiar words and symbols, and different computers could use programs generated in the same language. This paved the way for other computer languages such as COBOL, ALGOL and BASIC. *TIS

1942 Joseph Ivor Silk FRS (3 December 1942-) was the Savilian Chair of Astronomy at the University of Oxford from 1999 to September 2011. He was educated at Tottenham County School (1954-1960) and went on to study Mathematics at the University of Cambridge (1960-1963). He gained his PhD in Astronomy from Harvard in 1968. Silk took up his first post at Berkeley in 1970, and the Chair in Astronomy in 1978. Following a career of nearly 30 years there, Silk returned to the UK in 1999 to take up the Savilian Chair at the University of Oxford. He is currently Professor of Physics at the Institut d’Astrophysique de Paris, Université Pierre et Marie Curie, and he joined Johns Hopkins University in 2010 as Homewood Professor of Physics and Astronomy.

He is an Emeritus Fellow of New College, Oxford and a Fellow of the Royal Society (elected May 1999). He was awarded the 2011 Balzan Prize for his works on the early Universe. Silk has given more than two hundred invited conference lectures, primarily on galaxy formation and cosmology.
In 2015 he was selected the Gresham Professor of Astronomy. *Wik

DEATHS

1882 James Challis (12 Dec 1803, 3 Dec 1882) British clergyman and astronomer, famous in the history of astronomy for his failure to discover the planet Neptune. Astronomer and mathematician John Couch Adams had studied the known deviations in the orbit of the planet Uranus which indicated a planet even further out. In 1845, Adams gave Astronomer Royal George Airy a calculated orbital path for the unknown planet. But Airy was more interested in the primary job of navigation and timekeeping observations. Airy informed Challis, who did not begin until July 1846, and actually sighted the new planet four times without recognizing it. On 23 Sep 1845, the new planet was instead discovered from Berlin Observatory. Challis admitted that Adam's prediction was within 2° of the planet's position.*TIS

1956 Felix Bernstein (24 Feb 1878 in Halle, Germany - 3 Dec 1956 in Zurich, Switzerland) established his famous theorem on the equivalence of sets while in Cantor's seminar at Halle in 1897. He also worked on transfinite ordinal numbers.Bernstein is best remembered by mathematicians for the Schröder-Bernstein Theorem. This theorem states:
If each of two sets A and B are equivalent to a subset of the other, then A is equivalent to B. *SAU

1983 Elliott Waters Montroll (May 4, 1916 in Pittsburgh, Pennsylvania, USA - December 3, 1983 in Chevy Chase, Maryland, USA) was an American scientist and mathematician.Montroll had an exceptionally varied career: was a Sterling Research Fellow at Yale University where his work on the Ising model of a ferromagnet led him to solve certain Markov chain problems. Following this he was a Research Associate at Cornell University in 1941-42 where he began his studies of the problem of finding the frequency spectrum of elastic vibrations in crystal lattices. He was elected to the National Academy of Sciences (United States) in 1969, and to the American Academy of Arts and Sciences in 1973. His work on traffic flow led to him winning (jointly) the Lanchester Prize of the Operations Research Society of America in 1959. *Wik

2004 Shiing-shen Chern (26 Oct 1911, 3 Dec 2004) Chinese-American mathematician and educator whose researches in differential geometry include the development of the Chern characteristic classes in fibre spaces, which play a major role in mathematics and in mathematical physics. "When Chern was working on differential geometry in the 1940s, this area of mathematics was at a low point. Global differential geometry was only beginning, even Morse theory was understood and used by a very small number of people. Today, differential geometry is a major subject in mathematics and a large share of the credit for this transformation goes to Professor Chern." *TIS

2008 Oliver Gordon Selfridge (May 10, 1926 – December 3, 2008), grandson of Harry Gordon Selfridge, the founder of Selfridges' department stores, was a pioneer of artificial intelligence. He has been called the "Father of Machine Perception."
Selfridge was born in England, educated at Malvern College and Middlesex School and then earned an S.B. from MIT in mathematics in 1945. He then became a graduate student of Norbert Wiener's at MIT, but did not write up his doctoral research and never earned a Ph.D. While at MIT, he acted as one of the earlier reviewers for Wiener's Cybernetics book in 1949. He was also technically a supervisor of Marvin Minsky, and helped organize the first ever public meeting on Artificial Intelligence (AI) with Minsky in 1955.
Selfridge wrote important early papers on neural networks and pattern recognition and machine learning, and his "Pandemonium" paper (1959) is generally recognized as a classic in artificial intelligence. In it, Selfridge introduced the notion of "demons" that record events as they occur, recognize patterns in those events, and may trigger subsequent events according to patterns they recognize. Over time, this idea gave rise to Aspect-oriented programming.
In 1968, in their formative paper "The Computer as a Communication Device", J. C. R. Licklider and Robert Taylor introduced a concept known as an OLIVER (Online Interactive Expediter and Responder) which was named in honor of Selfridge.
Selfridge spent his career at Lincoln Laboratory, MIT (where he was Associate Director of Project MAC), Bolt, Beranek and Newman, and GTE Laboratories where he became Chief Scientist. He served on the NSA Advisory Board for 20 years, chairing the Data Processing Panel. Selfridge retired in 1993.
Selfridge also authored four children's books, "Sticks", "Fingers Come In Fives", "All About Mud", and "Trouble With Dragons". *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