Monday 26 December 2022

On This Day in Math - December 26


A young man passes from our public schools to the universities, ignorant almost of the elements of every branch of useful knowledge.
~Charles Babbage

The 360th day of the year; Bryant Tuckerman found the Mersenne prime M19937 (which has 6000 digits) using an IBM360. *Prime Curios

360 is also the number of degrees in a full circle, and there is a (rather new) word for two angles that sum to 360 degrees.  They are called "explementary" .

360  also figures in another "almost integer, Fib(360)/Fib (216) is approx.  1242282009792667284144565908481.99999999999999999999999999999...
Students, Compare to Fib(5k)/Fib(2k),,,  

360 is a highly composite number, it has 24 divisors, more than any other number of the year, in fact any number that is below twice its size.

It is the smallest number that is divisible by nine of the ten numbers 1-10 (not divisible by 7) What is next, students?

The sum of the digits of the 360th Fibonacci number is 360. It is the 13th year day for which the digits of the nth Fibonacci number sum to n.

There are 360 possible rook moves on a 6x6 chess board.*Derek Orr

360 is centered on the 360th digit of pi (Also from Derek)[However 360 does occur once earlier centered at position 286.]

1638  Fermat, in a letter to Mersenne, stated that he had a method of solving any questions on aliquot parts. Frenicle would respond through Mersenne by challenging Fermat to find a perfect number of 20 or 21 digits, under the then common belief that a perfect number existed between any two consecutive powers of ten.  Fermat's answer, in March was to say that there are none.  *L E Dickson, History of the Theory of Numbers

1837 Charles Babbage completed his “Calculating Engine” manuscript. *VFR

1843 John Graves write to William Rowan Hamilton that he has invented an eight-dimension normed division algebra he called "Octaves" Within a few months, Hamilton would realize that the octonions were not associative. This would lead to the first use of the term "associative" by Hamilton in 1844. (Except for matrices, which were not generally considered as "numbers", there were no common non-associative systems at that time) *Joan Baez Rankin Lecture of September 17, 2008 Glascow
The complete Volume Two of the Proceedings of the Royal Irish Academy were released in 1844, but the paper had been read on November 13, 1843; over a full month before Grave's letter. Hamilton created the phrase in explaining that although the Quaterninons maintained the distributive property, "yet the commutative character is lost," and then adds, "another important property of the old multiplication is preserved ... which may be called the associative character of the operation."

1864 The official seal of MIT was adopted on December 26, 1864. The craftsman at the anvil and the scholar with a book on the seal of the Massachusetts Institute of Technology embody the educational philosophy of William Barton Rogers and other incorporators of MIT as stated in their 1860 proposal Objects and Plan of an Institute of Technology. *MIT History

1898 Radium discovered by Pierre and Marie Curie. *VFR Actually, it seems this was the date of their announcement of the discovery(which must have occurred a few days earlier. They created the name radium for their element. This was their second discovery in the first year of her research on her thesis. They had also discovered Polonium earlier in the year.

 In 1906, the world's first full-length feature film, the 70-min Story of the Kelly Gang was presented in the Town Hall at Melbourne, Australia, where it had been filmed at a cost of £450. It preceded D.W. Griffith's The Birth of a Nation by nine years. The subject of the Australian movie was Ned Kelly, a bandit who lived 1855 to 1880. The film toured through Australia for over 20 years, and abroad in New Zealand and Britain. Since some people, including politicians and police viewed the content of the film as glorifying the criminals, the movie was banned (1907) in Benalla and Wangaratta and also in Victoria (1912). Only fragments totalling about 10 minutes of the original nitrate film have survived to the present.*TIS

1951 Kurt Godel delivered the Gibbs Lecture, “Some Basic Theorems on the Foundations of Mathematics and their Philosophical Implications,” to the annual AMS meeting at Brown University. *VFR

1982 TIME Names a Non-Human “Man of the Year”
TIME magazine's editors selected the Personal Computer for “Machine of the Year,” in lieu of their well-known “Man of the Year” award. The computer beat out U.S. President Ronald Reagan, U.K. prime minister Margaret Thatcher and Prime Minister of Israel​, Menachem Begin. The planet Earth became the second non-human recipient for the award in 1988. The awards have been given since 1927. The magazine's essay reported that in 1982, 80% of Americans expected that "in the fairly near future, home computers will be as commonplace as television sets or dishwashers.” In 1980, 724,000 personal computers were sold in the United States, according to Time. The following year, that number doubled to 1.4 million. *CHM

1992  6141 Durda, provisional designation 1992 YC3 is a stony Hungaria asteroid, classified as slow rotator and Mars-crosser from the innermost region of the asteroid belt, approximately 3.2 kilometers in diameter. It was discovered on 26 December 1992, by Spacewatch at Kitt Peak National Observatory in Arizona, United States. 

Dan is a principal scientist in the Department of Space Studies at Southwest Research Institute (SwRI) in Boulder Colorado. He has more than 20 years experience researching the collisional and dynamical evolution of main-belt and near-Earth asteroids, Vulcanoids, Kuiper belt comets, and interplanetary dust. Dan is an active pilot, with time logged in over a dozen types of aircraft including the F/A-18 Hornet and the F-104 Starfighter, and was a 2004 NASA astronaut selection finalist. He is also a Board Member of the B612 Foundation for research into near-earth asteroids.  
 Daniel Durda is also an artist of astronomical paintings. In 2015, he was awarded the Carl Sagan Medal for "communicating the wonder of planetary science through visual artistry".
Not to be overlooked, Dan was my student in my early years of teaching at Standish Sterling HS in Michigan.  He was an outstanding student, and made me his fan for life.
I have a poster of the Hale-Bopp image in my Dining Room in the Michigan House.

2017 On the day after Christmas in the Germantown Church of Christ, in a suburb just Southeast of Memphis, a miracle, of sorts, happened. A computer began running a program that had been installed years before by a 20 year Deacon of the Church, John Pace, discovered the largest known prime number. The new "largest" prime was 23,249,425 digits long. The number is one less than the product of 77,232,917 twos multiplied together, and thus has the name M77232917. The computer then did one thing it was programmed to do; it forwarded the number to the Gimps (Great Internet Mersenne Prime Search) Project home computer. It failed to do the second thing it was supposed to do, notify the deacon that his computer had succeeded in finding a candidate for the largest known Mersenne Prime. He had to learn the news from a congratulatory email from the founder of the GIMPS project. The public was informed of the new largest prime on Jan 3 of 2018.  *NY TIMES

1532 Wilhelm Xylander (born Wilhelm Holtzman, graecized to Xylander) (December 26, 1532 – February 10, 1576) was a German classical scholar and humanist.
Xylander was the author of a number of important works. He translated the first six books of Euclid into German with notes, the Arithmetica of Diophantus, and the De quattuor mathematicis scientiis of Michael Psellus into Latin. *Wik

1780 Mary Fairfax Greig Somerville (26 Dec 1780 in Jedburgh, Roxburghshire, Scotland - 29 Nov 1872 in Naples, Italy) Somerville wrote many works which influenced Maxwell. Her discussion of a hypothetical planet perturbing Uranus led Adams to his investigation. Somerville College in Oxford was named after her.*SAU   
She studied mathematics and astronomy, and in 1835 she and Caroline Herschel were elected as the first female Honorary Members of the Royal Astronomical Society.
Page 157 from Mechanism of the Heavens, Somerville discusses the law of universal gravity and Kepler's laws of planetary motion.

1791 Charles Babbage born. *VFR (26 Dec 1791; 18 Oct 1871) English mathematician and pioneer of mechanical computation, which he pursued to eliminate inaccuracies in mathematical tables. By 1822, he had a small calculating machine able to compute squares. He produced prototypes of portions of a larger Difference Engine. (Georg and Edvard Schuetz later constructed the first working devices to the same design which were successful in limited applications.) In 1833 he began his programmable Analytical Machine, a forerunner of modern computers. His other inventions include the cowcatcher, dynamometer, standard railroad gauge, uniform postal rates, occulting lights for lighthouses, Greenwich time signals, heliograph opthalmoscope. He also had an interest in cyphers and lock-picking.*TIS

1861 Frederick Engle born in Germany. He became the closest student of the Norwegian mathe¬matician Sophus Lie. Engle was also the first to translate Lobachevsky’s work into a Western language (German). *VFR

1900 Antoni Zygmund (26 Dec 1900; 30 May 1992) Polish-born mathematician who created a major analysis research centre at Chicago, and recognized in 1986 for this with the National Medal for Science. In 1940, he escaped with his wife and son from German controlled Poland to the USA. He did much work in harmonic analysis, a statistical method for determining the amplitude and period of certain harmonic or wave components in a set of data with the aid of Fourier series. Such technique can be applied in various fields of science and technology, including natural phenomena such as sea tides. He also did major work in Fourier analysis and its application to partial differential equations. Zygmund's book Trigonometric Series (1935) is a classic, definitive work on the subject*TIS

1903 Lancelot Stephen Bosanquet (26 Dec 1903 in St. Stephen's-by-Saltash, Cornwall, England - 10 Jan 1984 in Cambridge, Cambridgeshire, England) Bosanquet wrote many papers on the convergence and summability of Fourier series. He also wrote on the convergence and summability of Dirichlet series and studied specific kinds of summability such as summability factors for Cesàro means. His later work on integrals include two major papers on the Laplace-Stieltjes integral published in 1953 and 1961. Other topics he studied included inequalities, mean-value theorems, Tauberian theorems, and convexity theorems. *SAU

1937 John Horton Conway (born 26 December 1937, ) is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of the cellular automaton called the Game of Life.
Conway is currently Professor of Mathematics and John Von Neumann Professor in Applied and Computational Mathematics at Princeton University. He studied at Cambridge, where he started research under Harold Davenport. He received the Berwick Prize (1971),[1] was elected a Fellow of the Royal Society (1981),[2] was the first recipient of the Pólya Prize (LMS) (1987),[1] won the Nemmers Prize in Mathematics (1998) and received the Leroy P. Steele Prize for Mathematical Exposition (2000) of the American Mathematical Society. He has an Erdős number of one.*Wik Conway is known for his sense of humor, and the last proof in his "On Numbers and Games" is this:
Theorem 100; This is the last Theorem in this book.
The Proof is Obvious.
In April of 2020, Conway was exposed to the corona virus and took a fever around the 8th of April.  He had suffered from ill health for an extended time, and in three days, on April 11, 2020 he died at his home in New Jersey.

I really enjoyed Siobhan Roberts biography of Conway.  You may, too.


1624 Simon Marius (10 Jan 1573, 26 Dec 1624) (Also known as Simon Mayr) German astronomer, pupil of Tycho Brahe, one of the earliest users of the telescope and the first in print to make mention the Andromeda nebula (1612). He studied and named the four largest moons of Jupiter as then known: Io, Europa, Ganymede and Callisto (1609) after mythological figures closely involved in love with Jupiter. Although he may have made his discovery independently of Galileo, when Marius claimed to have discovered these satellites of Jupiter (1609), in a dispute over priority, it was Galileo who was credited by other astronomers. However, Marius was the first to prepare tables of the mean periodic motions of these moons. He also observed sunspots in 1611 *TIS You can find a nice blog about the conflict with Galileo by the Renaissance Mathematicus.

1931 Melvil Dewey (10 Dec 1851, 26 Dec 1931) American librarian who developed library science in the U.S., especially with his system of classification, the Dewey Decimal Classification (1876), for library cataloging. His system of classification (1876) uses numbers from 000 to 999 to cover the general fields of knowledge and designating more specific subjects by the use of decimal points. He was an activist in the spelling reform and metric system movements. Dewey invented the vertical office file, winning a gold medal at the 1893 World's Fair. It was essentially an enlarged version of a card catalogue, where paper documents hung vertically in long drawers. *TIS

2006 Martin David Kruskal (September 28, 1925 – December 26, 2006) was an American mathematician and physicist. He made fundamental contributions in many areas of mathematics and science, ranging from plasma physics to general relativity and from nonlinear analysis to asymptotic analysis. His single most celebrated contribution was the discovery and theory of solitons. His Ph.D. dissertation, written under the direction of Richard Courant and Bernard Friedman at New York University, was on the topic "The Bridge Theorem For Minimal Surfaces." He received his Ph.D. in 1952.
In the 1950s and early 1960s, he worked largely on plasma physics, developing many ideas that are now fundamental in the field. His theory of adiabatic invariants was important in fusion research. Important concepts of plasma physics that bear his name include the Kruskal–Shafranov instability and the Bernstein–Greene–Kruskal (BGK) modes. With I. B. Bernstein, E. A. Frieman, and R. M. Kulsrud, he developed the MHD (or magnetohydrodynamic) Energy Principle. His interests extended to plasma astrophysics as well as laboratory plasmas. Martin Kruskal's work in plasma physics is considered by some to be his most outstanding.
In 1960, Kruskal discovered the full classical spacetime structure of the simplest type of black hole in General Relativity. A spherically symmetric black hole can be described by the Schwarzschild solution, which was discovered in the early days of General Relativity. However, in its original form, this solution only describes the region exterior to the horizon of the black hole. Kruskal (in parallel with George Szekeres) discovered the maximal analytic continuation of the Schwarzschild solution, which he exhibited elegantly using what are now called Kruskal–Szekeres coordinates.
This led Kruskal to the astonishing discovery that the interior of the black hole looks like a "wormhole" connecting two identical, asymptotically flat universes. This was the first real example of a wormhole solution in General Relativity. The wormhole collapses to a singularity before any observer or signal can travel from one universe to the other. This is now believed to be the general fate of wormholes in General Relativity.
Martin Kruskal was married to Laura Kruskal, his wife of 56 years. Laura is well known as a lecturer and writer about origami and originator of many new models. Martin, who had a great love of games, puzzles, and word play of all kinds, also invented several quite unusual origami models including an envelope for sending secret messages (anyone who unfolded the envelope to read the message would have great difficulty refolding it to conceal the deed).
His Mother, Lillian Rose Vorhaus Kruskal Oppenheimer was an American origami pioneer. She popularized origami in the West starting in the 1950s, and is credited with popularizing the Japanese term origami in English-speaking circles, which gradually supplanted the literal translation paper folding that had been used earlier. In the 1960s she co-wrote several popular books on origami with Shari Lewis.*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 

No comments: