Wednesday, 2 December 2020

On This Day in Math - December 2

The saddest aspect of life right now is that science gathers knowledge faster than society gathers wisdom.
~Isaac Asimov

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

1697 St Paul's Cathedral, reconstructed after the Great Fire of 1666 as redesigned by Christopher Wren, was officially opened on December 2nd, 1697. *History Today

In 1895, James Dewar exhibited his new apparatus for the production of liquid air at the Royal Institution.*TIS

In 1934, the molten glass was poured in the Corning, N.Y. for the first 200-inch diameter telescope mirror. Pyrex glass at 2,700 degrees Fahrenheit was poured into a ceramic mold. The mold had been constructed over a period of several months. The temperature of the glass was lowered during 11 months, a degree or two a day. It was then allowed to cool to room temperature. The 20-ton disk was shipped 26 Mar 1936 for grinding and polishing at the California Institute of Technology, which spanned 11 years, completed on 3 Oct 1947. It was installed in a telescope at the Mount Palomar Observatory on Palomar Mountain, San Diego County, California, which was named the Hale telescope in honour of Dr George Hale who had conceived and promoted it.*TIS

1942 At 3:36 p.m. in a squash court (Actually it was a Racketball court *James Zug Squash, A History of the Game pgs. 135–136.) under the West Stands of Stagg Field (the abandoned football stadium) at the University of Chicago, the ﬁrst self-sustaining nuclear (ﬁssion) reaction took place. Enrico Fermi (1901–1954) was leader of the Manhattan Project. [DSB 4, 582]. *VFR This first run of the nuclear pile produced a single watt of power, Just enough to show that the process was feasible. One of the “about 40” people who watched was Leo Szilard who had conceived the idea of a chain reaction leading to power while stopped at a red light on Southampton Row in London only four years before. *Frederik Pohl, Chasing Science, Pg 20
One of Fermi's assistants ran from the test to the telephone to notify Openheimer, "The Italian navigator has just landed in the New World." *Brody & Brody, The Science Class You Wished You Had

1954 The U.S. Navy dedicates its Naval Ordnance Research Calculator (NORC) at the Naval Surface Weapons Center in Dahlgren, Virginia. John von Neumann was the keynote speaker. The machine was built at the Watson Scientific Computing Laboratory under the direction of Wallace Eckert.
This computer was in demand by many organizations, including two different Navy facilities and Lawrence Livermore National Laboratory in California. Physicist Edward Teller had been trying to receive NORC arguing that the LLNL's nuclear calculations were more important than Dahlgren's ballistic calculations. The Navy won and NORC was delivered to Dahlgren, following the Mark II (1948) and the Mark III (1951).*CHM

1967 Italy issued a postage stamp to commemorate the 25th anniversary of the ﬁrst atomic chain reaction. Pictured is Enrico Fermi at Los Alamos and a model of the ﬁrst Atomic Reactor. *VFR

1978 Science News reports, p. 390, that 221,701 − 1 is prime.

BIRTHS

1831 Paul David Gustav du Bois-Reymond (2 Dec 1831 in Berlin, Germany - 7 April 1889 in Freiburg, Germany) Du Bois-Reymond's work is almost exclusively on calculus, in particular partial differential equations and functions of a real variable. The standard technique to solve partial differential equations used Fourier series but Cauchy, Abel and Dirichlet had all pointed out problems associated with the convergence of the Fourier series of an arbitrary function. In 1873 du Bois-Reymond was the first person to give an example of a continuous function whose Fourier series diverges at a point. Perhaps what was even more surprising, the Fourier series of du Bois-Reymond function diverged at a dense set of points. The important work Eine neue Theorie der Convergenz und Divergenz von Reihen mit positiven Gliedern ("A new theory of convergence and divergence of series with positive terms") led to an increasing understanding of the whole concept of a function.
Du Bois-Reymond published an example of a continuous function which is nowhere differentiable in 1875. It was inspired by a similar function found by Weierstrass in 1872 but not published by him until much later. This example contradicted most mathematicians' intuition, for it was generally believed that a continuous function was differentiable everywhere except in special points. *SAU

1865 Niels Nielsen (2 Dec 1865 in Orslev, Denmark - 16 Sept 1931 in Copenhagen, Denmark) was a Danish mathematician who worked on special functions and number theory. *SAU

1901 Dom George Frederick James Temple​ FRS(born 2 December 1901, London; died 30 January 1992, Isle of Wight) was an English mathematician, recipient of the Sylvester Medal in 1969. He was President of the London Mathematical Society in the years 1951-1953.[2]
Temple took his first degree as an evening student at Birkbeck College, London, between 1918 and 1922, and also worked there as a research assistant. In 1924 he moved to Imperial College as a demonstrator, where he worked with Professor Sydney Chapman. After a period spent with Eddington at Cambridge, he returned to Imperial as reader in mathematics. He was appointed professor of mathematics at King's College London in 1932, where he returned after war service with the Royal Aircraft Establishment at Farnborough. In 1953 he was appointed Sedleian Professor of Natural Philosophy at the University of Oxford, a chair which he held until 1968, and in which he succeeded Chapman. He was also an honorary Fellow of Queen's College, Oxford.
After the death of his wife in 1980, Temple, a devout Christian, took monastic vows in the Benedictine order and entered Quarr Abbey on the Isle of Wight, where he remained until his death. *Wik

1914 Robert Palmer Dilworth (December 2, 1914 – October 29, 1993) was an American mathematician. His primary research area was lattice theory; his biography at the MacTutor History of Mathematics archive states "it would not be an exaggeration to say that he was one of the main factors in the subject moving from being merely a tool of other disciplines to an important subject in its own right". He is best known for Dilworth's theorem (Dilworth 1950) relating chains and antichains in partial orders; he was also the first to study antimatroids (Dilworth 1940). Dilworth advised 17 Ph.D. students and as of 2010 has 373 academic descendants listed at the Mathematics Genealogy Project, many through his student Juris Hartmanis, a noted complexity theorist.*Wik

DEATHS

1594 Gerardus Mercator (5 Mar 1512- 2 Dec 1594) Flemish cartographer whose most important innovation was a map, embodying what was later known as the Mercator projection, on which parallels and meridians are rendered as straight lines spaced so as to produce at any point an accurate ratio of latitude to longitude. He also introduced the term atlas for a collection of maps. *TIS

1873 Karl Gräffe Gräffe (7 Nov 1799 in Brunswick, Germany - 2 Dec 1873 in Zurich, Switzerland) is best remembered for his method of numerical solution of algebraic equations, developed to answer a prize question of the Berlin Academy of Sciences. It is particularly suitable for methods developed for using computers to solve mathematical problems. This method is today called the Dandelin-Gräffe method after the two mathematicians who independently investigated it. The history of the Dandelin-Gräffe method is discussed in and . Lobachevsky is also credited with the independent discovery of the method which appears in his little-known book on algebra.*SAU

1966 L(uitzen) E(gbertus) J(an) Brouwer (27 Feb 1881, 2 Dec 1966) was a Dutch mathematician who founded mathematical Intuitionism (a doctrine that views the nature of mathematics as mental constructions governed by self-evident laws). He founded modern topology by establishing, for example, the topological invariance of dimension and the fixpoint theorem. (Topology is the study of the most basic properties of geometric surfaces and configurations.) The Brouwer fixed point theorem is named in his honor. He proved the simplicial approximation theorem in the foundations of algebraic topology, which justifies the reduction to combinatorial terms, after sufficient subdivision of simplicial complexes, the treatment of general continuous mappings. *TIS

1982 Geoffrey Timms studied at Leeds and Cambridge and then took up a post at St Andrews. During World War II he served at Bletchley Park and Cheltenham and joined the Foreign Office afterwards. He became President of the EMS in 1941.*SAU

2006 Dikran "Dick" Tahta (7 August 1928 – 2 December 2006) was a British-Armenian mathematician, teacher and author.
Dikran Tahta is a descendant of an Ottoman Armenian family who settled in Manchester after the First World War. Much of his childhood, and the influence of his Armenian religious upbringing, is reflected upon in his penultimate book Ararat Associations, in which he notes how his parents were keen for their children to have an English education, yet made sure that they spoke Armenian at home. He was christened by Bishop Tourian in the Armenian Church in Manchester, and his name Dikran was shortened to Dick, but he never forgot his Armenian roots.
From Rossall School, in Fleetwood, Lancashire, he gained a scholarship to Christ Church, Oxford, in 1946. His main subject was Mathematics, but he also read widely in English literature, philosophy and history.
In the 1970s he was involved in the ATV television programme of mathematics for schools entitled 'Leapfrogs' (produced and directed by Paul Martin) and promoted visual approaches to mathematics. His paper "On Geometry" argued that geometrical approaches to mathematics could not be reduced to algebraic approaches. In line with this thinking, he produced the ATM book Geometric Images, and co-authored Images of Infinity with Ray Hemmings. The Leapfrogs group of Tahta and Hemmings, together with David Sturgess, Leo Rogers and Derick Last also produced hands-on teaching materials including workbooks for the polycube. He also drew upon insights into pedagogy in the writings of Mary Boole on mathematics education.
After retirement, he went to teach in the United States and South Africa, and became a tutor for the Open University.
His last book was The Fifteen Schoolgirls about Thomas Kirkman, known for the Kirkman's schoolgirl problem, a problem in combinatorics, which also delved into the byways of Victorian amateur mathematics.
In his obituary, The Guardian newspaper described Dick as "one of the outstanding mathematics teachers of his generation", who was notable for having inspired physicist Stephen Hawking. The Guardian commented on his death that "He was a wise and generous man who inspired love and an increase of intellectual energy in everyone who came within his ambit." *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