## Friday 9 December 2022

### On This Day in Math - December 9

Gravestone of Poincar'e

One geometry cannot be more true than another; it can only be more convenient.
~Henri Poincar´e

The 343rd day of the year, a Friedman number (named after Erich Friedman, as of 2013 an Associate Professor of Mathematics and ex-chairman of the Mathematics and Computer Science Department at Stetson University, located in DeLand, Florida *Wik), since it can be made up of arithmetical operations of its digits, (3+4)3 = 343.  There will be one more Friedman number this year; can you find it?

Interestingly, the speed of sound in dry air at 20 °C (68 °F) is 343 m/s.

343 is the smallest cube ending in 3. It is also the last cube of the year. As a perfect cube, it is also a perfect number of the second kind, the product of its aliquot parts is equal to the number itself. In 1879, E. Lionett defined a perfect number of the second kind as a number for which the product of the aliquot parts is equal to the number itself. So 343 is the 7th perfect number of the second kind. The only values that can be perfect numbers of the second kind are values in the form P*Q for primes P, Q, and P3Lagrange's theorem tells us that each positive integer can be written as a sum of four squares (perhaps including zero), but many can be written as the sum of only one or two non-zero squares.  The smallest examples of numbers that need at least four are 7, 15, and 23. If you take any number in this sequence, and raise it to an odd positive power, you get another number in the sequence, so now you know that 73 = 343 is also not expressible as the sum of less than four non-zero squares.
*Prime Curios

EVENTS

1571  Adriaan Adriaanszoon, now known as Adriaan Metius, a Dutch mathematician and astronomer, was born Dec. 9. 1571, He is little known today, and would probably be totally forgotten today were it not for one odd historical happenstance.
Adrianne's father, Adriaan Anthoniszoon, was a Dutch mathematician, surveyor, cartographer, and military engineer.  Along the way, he (re)discovered a rational number approximation for pi (not called that for another 130 yrs,) of 355/113.  Rediscovered, because now that we are more aware of the mathematical developments in the east, some folks call that number Zu's ratio,  found by Chinese mathematician and astronomer Zu Chongzhi in the 5th century.
But Adrianne (the papa) told sonny boy and Adriaan Metius later published his father's results, and the value in the west is sometimes referred to as Metius' number'. (Mostly it is not referred to by either, because nearly no one knows either story)

So jump ahead about 100 years to when a young (mid thirties) painter named Jan Vermeer decided to paint a picture called The Astronomer.
Can you find the book on the table?  I should mention that it is Institutiones Astronomicae et Geographicae. It is opened to Book III, where "inspiration from God" is recommended for astronomical research along with knowledge of geometry and the aid of mechanical instruments.  Oh by the way, that is the book by son Adrianne which has papa's ratio for pi inside.
While we are dropping names, the guy in the portrait, he seems to show up in several of Vermeer's paintings.  He's never identified, but best bet,  although far from certain, was Antonie van Leeuwenhoek, the famous Dutch scientist who lived a few blocks from Vermeer in Delft.  And the celestial globe?  It is not the one recommended by son Adrianne's book, but Jodocus Hondius Hondius' globe, a very worthy substitute.
If you ever saw the show, you have to imagine you just revisited an episode of Connections with James Burke.

========================================================
1675  Newton writes to Leibniz to comment on the response to his theory that light was corpuscular, "I was so persecuted with discussions arising from the publication of my theory of light, that I blamed my own imprudence for parting with so substantial a blessing as my quiet, to run after a shadow.” *A history of physics in its elementary branches By Florian Cajori  After criticism of his theories on light, Newton withdrew from publishing much at all, became very aloof to the Royal Society,  and waited for Hooke, one of the critics of his theory, to die before he published his Opticks.

1679  The missing letter of Robert Hooke to Newton in their discussion about the motion of the Earth resurfaced in at a Sothebys auction in April of 1918.  What it revealed, to many scholars, was that Newton had lied about never having heard Hooke's work on the motion of  planets, and particularly his denial that Hooke had influenced his use of the "double proportional".  Westfall writes that "Newtons papers reveal no similar understanding of circular motion before this letter. Every time he had considered it, he had spoken of a tendency to recede from the center, what Huygens had called centrifugal force. * Robert Korye, An Unpublished Letter of Robert Hooke to Isaac Newton

1741 Euler sets out on the trail of his most beautiful theorem. Euler to Goldbach: Berlin Dec 9, 1741 ([1], p. 91) “I have lately also found a remarkable paradox. Namely that the value of the expression (2i+2-i)/2 {Euler wrote sqrt of -1 instead of the imaginary constant} is approximately equal to 10/13 and that this fraction differs only in parts per million from the truth. The true value of this expression however is the cosine of the arc .6931471805599 (ln(2)) or the arc of 39 degrees 42 min. 51 sec. 52 tenths of sec. and 9 hundredths of sec. in a circle of radius one. “ (from An English translation of portions of seven correspondences between Euler and Goldbach on Euler’s complex exponential paradox and special values of cosine by Elizabeth Volz)
--------------------------------------------------------------------------------------------------------------------------
1817  The Chinese Puzzle later called a Tangram arrived in Europe in the first months of 1817.  By December, the first edition of "The New and Fashionable Chinese Puzzle," was published and advertised in New York City by Andrew T Goodrich. By the end of the year he had two books on the puzzle with wooden tiles.  By 1822 he offered sets in wood, mother of pearl and ivory.  *The Tangram Book, Jerry Slocum
-------------------------------------------------------------------------------------------------
1878  The cartoon is from the pen of George du Maurier, printed in the Punch Almanack for 1879. Although titled "Edison's Telephonoscope" it is not, in fact, a creation of Thomas Edison's at all (either realised or proposed) but rather an imagining by Maurier of what the great inventor might come up with next: a machine which, for all intents and purposes, amounts to some kind of Victorian Zoom. A mother and father — the "Pater- and Materfamilias" — sit at home and converse with, while also viewing, their children at play across the other side of the world.
The telectroscope (also referred to as 'electroscope') was the first conceptual model of a television or videophone system. The term was used in the 19th century to describe science-based systems of distant seeing.
The name and its concept came into being not long after the telephone was patented in 1876, and its original concept evolved from that of remote facsimile reproductions onto paper, into the live viewing of remote images

1906 New York Times Headlines, "Life on Mars"!

1911 Henri Poincar´e wrote the editor of a mathematical journal to ask if, contrary to custom, an unﬁnished piece of work could be published. He explained that at his age he may not be able to ﬁnish it, but that his work might provide ideas for another. The paper was published and not long after this “unﬁnished symphony,” George David Birkhoﬀ (1884–1944) completed the solution. Poincar´e died suddenly on 17 July 1912. [Eves, Squared, 173◦; Bell, Men of Mathematics,
p. 553]. *VFR

1960 Sperry Rand Corporation of St. Paul, Minnesota, announced the ﬁrst electronic computer to employ thin-ﬁlm memory, the UNIVAC 1107. Its operational speed was measured in billionths
of a second (nanoseconds), compared to speeds in most other computers of millionths of a second (microseconds). Memory could be accessed more than a million times a second.*VFR

1965 The Kecksburg UFO incident occurred on December 9, 1965, at Kecksburg, Pennsylvania, USA. A large, brilliant fireball was seen by thousands in at least six U.S. states and Ontario, Canada. It streaked over the Detroit, Michigan/Windsor, Ontario area, reportedly dropped hot metal debris over Michigan and northern Ohio, starting some grass fires and caused sonic booms in Western Pennsylvania. It was generally assumed and reported by the press to be a meteor after authorities discounted other proposed explanations such as a plane crash, errant missile test, or reentering satellite debris.
However, eyewitnesses in the small village of Kecksburg, about 30 miles southeast of Pittsburgh, claimed something crashed in the woods. A boy said he saw the object land; his mother saw a wisp of blue smoke arising from the woods and alerted authorities. Another reported feeling a vibration and "a thump" about the time the object reportedly landed. Others from Kecksburg, including local volunteer fire department members, reported finding an object in the shape of an acorn and about as large as a Volkswagen Beetle. Writing resembling Egyptian hieroglyphics was also said to be in a band around the base of the object. Witnesses further reported that intense military presence, most notably the United States Army, secured the area, ordered civilians out, and then removed the object on a flatbed truck. At the time, however, the military claimed they searched the woods and found "absolutely nothing.
 A model of the crashed object, originally created for the show Unsolved Mysteries, and put on display near the Kecksburg fire station.*Wik

In 1968
, the first demonstration of the use of a computer mouse was given at the American Federation of Information Processing Societies' Fall Joint Computer Conference at Stanford University, California. The mouse's inventor, Doug Engelbart and a small team of researchers from the Stanford Research Institute stunned the computing world with an extraordinary demonstration at a San Francisco computer conference. They debuted the computer mouse, graphical user interface, display editing and integrated text and graphics, hyper-documents, and two-way video-conferencing with shared work spaces. These concepts and technologies were to become the cornerstones of modern interactive computing.*TIS Patent was over a year later.

BIRTHS

1667 William Whiston (born 9 Dec 1667, 22 Aug 1752)English Anglican priest and mathematician who sought to harmonize religion and science, and who is remembered for reviving in England the heretical views of Arianism. He attended Newton's lectures while at Cambridge and showed great promise in mathematics. Ordained in 1693. While chaplain to the bishop of Norwich (1694-98), he wrote A New Theory of the Earth (1696), in which he claimed that the biblical stories of the creation, flood and final conflagration could be explained scientifically as descriptions of events with historical bases. The Flood, he believed, was caused by a comet passing close to the Earth on 28 Nov 2349 BC. This put stress on the Earth's crust, causing it to crack and allow the water to escape and flood the Earth. After serving as vicar of Lowestoft (1698–1701), he returned to his alma mater, Cambridge University to become assistant to the mathematician Sir Isaac Newton, whom he succeeded in the Lucasian chair in 1703. *TIS ( His translation of the works of Flavius Josephus may have contained a version of the famous Josephus Problem, and in 1702 Whiston's Euclid discusses the classic problem of the Rope Round the Earth, (if one foot of additional length is added, how high will the rope be). I am not sure of the dimensions in Whiston's problem, and would welcome input, I have searched the book and can not find the problem in it, but David Singmaster has said it is there, and he is not a easy source to reject. It is said that Ludwig Wittgenstein was fascinated by the problem and used to pose it to students regularly. )
In 1701, Newton arranged for Whiston to succeed him as Lucasian professor. In 1710 he was deprived of the chair and driven from Cambridge for his unorthodox religious views (it is not acceptable to be a unitarian at the College of the Whole and Undivided Trinity).*VFR
Whiston was expelled from his chair on 30 October 1710; at the appeal of the heads of colleges. Comets were also part of this disaster in his life. He had become famous for his studies that stated that the Biblical flood had been caused by a comet, and gave support for other geological impacts of comets on the Earth. Whiston was removed from his position at Cambridge, and denied membership in the Royal Society for his “heretical” views. He took the “wrong” side in the battle between Arianism and the Trinitarian view, but his brilliance still made the public attend to his proclamations. When he predicted the end of the world by a collision with a comet in October 16th of 1736 the Archbishop of Canterbury had to issue a denial to calm the panic.

1837 Nils Dalén (30 Nov 1869; 9 Dec 1837)Swedish engineer who won the Nobel Prize for Physics in 1912 for his invention of the automatic sun valve, or Solventil, which regulates a gaslight source by the action of sunlight, turning it off at dawn and on at dusk or at other periods of darkness. It rapidly came into worldwide use for buoys and unmanned lighthouses. While recovering from an accident, convalescing at home, he noticed how much time his wife spent caring for their wood-burning stove. He decided to invent a more efficient and cost-effective stove. In 1922, Dalen's Amalgamated Gas Accumulator Co. patented his design and put the first AGA stoves into production. These stoves produced a radiant heat that kept the kitchen warm. The AGA remains popular today.*TIS (My wife's favorite entry. Her first experience with an AGA was to turn materials for a pie into pure carbonized dust.)

1839 Gustav Roch (9 Dec 1839 in Dresden, Germany - 21 Nov 1866 in Venice, Italy)was a German mathematician known for the Riemann-Roch theorem which relates the genus of a topological surface to algebraic properties of the surface. Sadly, however, he died of consumption in Venice in November at the age of 26 years. *SAU

1883 Nikolai Nikolaevich Luzin, (also spelled Lusin) (9 December 1883, Irkutsk – 28 January 1950, Moscow), was a Soviet/Russian mathematician known for his work in descriptive set theory and aspects of mathematical analysis with strong connections to point-set topology. He was the eponym of Luzitania, a loose group of young Moscow mathematicians of the first half of the 1920s. They adopted his set-theoretic orientation, and went on to apply it in other areas of mathematics.*Wik

1900 (Noël) Joseph (Terence Montgomery) Needham (9 Dec 1900, 24 Mar 1995 at age 94)was an English biochemist, embryologist, and historian of science who wrote and edited the landmark history Science and Civilization in China, a remarkable multivolume study of nearly every branch of Chinese medicine, science, and technology over some 25 centuries. As head of the British Scientific Mission in China (1942-46) he worked to assure adequate liaison between Chinese scientists and technologists and their colleagues in the West. As an historian of science and technology he wanted to break through the parochial, Europe-centred views of most of his colleagues by disclosing the achievements of traditional China and the contributions made by China leading up to the scientific revolution. *TIS

1906 Grace Murray Hopper (9 Dec 1906; 1 Jan 1992), one of the first women to work on the computer, is born in New York City. Hopper, a rear admiral in U.S. Navy, did significant work on the Harvard Mark II, where she discovered the first computer bug -- a moth -- and coined the term to mean a problem with a program. Hopper went on to develop the first compiler, A-0, and the programming language COBOL. Grace Hopper was honored by having the most modern ship in the U.S. Navy named after her, the U.S.S. Hopper, launched in mid-1997. *CHM
Her ideas contributed to the first commercial electronic computer, Univac I, and naval applications for COBOL (co-mmon b-usiness o- riented l-anguage). With a Ph.D. in Mathematics from Yale University (1934), she taught mathematics (Vassar, 1931-43), before she joined the Naval Reserve. In 1944, she was commissioned as a Lieutenant (Junior Grade) 1944, assigned to the Bureau of Ordnance where she became involved in the early development of the electronic computer. For more than four decades, she was a leader in computer applications and programming languages. *TIS (See Sep 9, 1945 for more on "BUG")

1907 Max Deuring (9 December 1907, Göttingen, Germany – 20 December 1984, Göttingen, Germany) was a mathematician. He is known for his work in arithmetic geometry, in particular on elliptic curves in characteristic p. He worked also in analytic number theory.
Deuring graduated from the University of Göttingen in 1930, then began working with Emmy Noether, who noted his mathematical acumen even as an undergraduate. When she was forced to leave Germany in 1933, she urged that the university offer her position to Deuring. In 1935 he published a report entitled Algebren ("Algebras"), which established his notability in the world of mathematics. He went on to serve as Ordinarius at Marburg and Hamburg, then took a position as ordentlicher Lehrstuhl at Göttingen, where he remained until his retirement.*Wik

1916 Irving John Jack Good, Cryptologist and Statistician, is born in London, England. He obtained a PhD in mathematics from Cambridge under the supervision of G. H. Hardy in 1938. During W.W.II he worked on both the Enigma and Teleprinter encrypting machines with Alan Turing at Bletchley *CHM

1917 Leo James Rainwater (9 Dec 1917; 31 May 1986) was an American physicist who won a share of the Nobel Prize for Physics in 1975 for his part in determining the asymmetrical shapes of certain atomic nuclei. During WW II, Rainwater worked on the Manhattan Project to develop the atomic bomb. In 1949 he began formulating a theory that not all atomic nuclei are spherical, as was then generally believed. The theory was tested experimentally and confirmed by Danish physicists Aage N. Bohr and Ben R. Mottelson. For their work the three scientists were awarded jointly the 1975 Nobel Prize for Physics. He also conducted valuable research on X rays and took part in Atomic Energy Commission and naval research projects. *TIS

1917 Sergei Vasilyevich Fomin (9 December 1917 – 17 August 1975) was a Soviet mathematician who was co-author with Kolmogorov of Introductory real analysis, and co-author with I.M. Gelfand of Calculus of Variations (1963), both books that are widely read in Russian and in English.
Fomin entered Moscow State University at the age of 16. His first paper was published at 19 on infinite abelian groups. After his graduation he worked with Kolmogorov. He was drafted during World War II, after which he returned to Moscow. When the war ended Fomin returned to Moscow University and joined Tikhonov's department. In 1951 he was awarded his habilitation for a dissertation on dynamical systems with invariant measure. Two years later he was appointed a professor. Later in life, he became involved with mathematical aspects of biology. *Wik

1926 Henry Way Kendall (9 Dec 1926; 15 Feb 1999)American nuclear physicist who shared the 1990 Nobel Prize for Physics with Jerome Isaac Friedman and Richard E. Taylor for obtaining experimental evidence for the existence of the subatomic particles known as quarks. To study the internal structure of the proton, they worked with the 3-km linear accelerator recently opened at Stanford (SLAC). Electrons were accelerated to an energy of 20,000 million electronvolts and directed against a target of liquid hydrogen. In 1969 Kendall helped found the Union of Concerned Scientists. In 1997, in connection with the Kyoto Climate Summit, he helped produce a statement signed by 2,000 scientists calling for action on global warming.*TIS

DEATHS

1866 James P. Pierpont (June 16, 1866 – December 9, 1938) was a Connecticut-born American mathematician. He did undergraduate studies at Worcester Polytechnic Institute, initially in mechanical engineering, but turned to mathematics. He went to Europe after graduating in 1886. He studied in Berlin, and later in Vienna. He prepared his PhD at the University of Vienna under Leopold Gegenbauer and Gustav Ritter von Escherich. His thesis, defended in 1894, is entitled Zur Geschichte der Gleichung fünften Grades bis zum Jahre 1858. After his defense, he returned to New Haven and was appointed as a lecturer at Yale University, where he spent most of his career. In 1898, he became professor. Initially, his research dealt with Galois theory of equations. After 1900, he worked in real and complex analysis.
In his textbooks of real analysis, he introduced a definition of the integral analogous to Lebesgue integration. His definition was later criticized by Maurice Fréchet. Finally, in the 1920s, his interest turned to non-Euclidean geometry. *Wik

1958 John Jackson (11 Feb 1887 in Paisley, Renfrewshire, Scotland - 9 Dec 1958 in London, England) graduated from Glasgow and Cambridge. He went to the Royal Observatory at Greenwich but his career there was interrupted by World War I. He was then appointed HM Astronomer at the University of Cape Town. *SAU

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell