## Saturday 18 January 2020

### On This Day in Math - January 18

Sooner or later every one of us breathes an atom that has been breathed before by anyone you can think of who has lived before us - Michelangelo or George Washington or Moses.
~Jacob Bronowski

The 18th day of the year; there is only one number (289=172) for which the sum of its proper divisors is 18. (can you figure out which numbers can never appear as the sum of the proper divisors?)

183=(5+8+3+2)3=5832*jim wilder ‏@wilderlab

And speaking of powers of 18, 18^3 = 5832 and 18^4 = 104976, together they use all ten decimal digits once each. Smallest (only?) such number.*Ben Vitale

Chris Maslanka@ChrisMaslanka pointed out that 18 is involved in another "smallest" number,
378 = 2 X 3 X 3 X 3 X 7; sum of these prime factors = 18; sum of the digits of 378 is also 18. The smallest multidigit number for which sum of digits = sum of prime factors.

EVENTS

1663/4 King Charles II’s letter which conﬁrmed the Lucasian statutes forbade the Professor to take any but a Fellow-commoner as his pupil, and Newton was never that. Thus Newton was NEVER Barrow’s pupil. This myth began after Newton’s death with Conduitt’s anecdote of Barrow examining Newton in Euclid as an undergraduate and ﬁnding him wanting. Newton did attend Barrow’s lectures in 1665 but would not allow that they were helpful to him; Newton was self-taught in mathematics. [Whiteside, Notes and Records of the Royal Society of London, 19(1964), p. 61; Westfall, p. 99] *VFR

1753 Hans Sloane, whose collection formed the Basis of the British Museum, was buried at Chelsea Old Church with the following memorial:
"In memory of Sir Hans Sloane, Bart, President of the Royal Society and of the College of Physicians, who died in the year of our Lord 1752, the ninety-second year of his age, without least pain of body, and with a conscious serenity of mind ended a virtuous and beneficient life. This monument was erected by his two daughters, Eliza Cadogan and Sarah Stanley".
*Wik

1800 Thomas Jefferson writes to Joseph Priestley to tell him about the proposed formation of a new college in Virginia, and to seek his input:
" We wish to establish in the upper & healthier country, & more centrally for the state, an University on a plan so broad & liberal & modern, as to be worth patronizing with the public support, and be a temptation to the youth of other states to come and drink of the cup of knowledge & fraternize with us. ...
It has been the subject of consultation among the ablest and highest characters of our State, who only wait for a plan to make a joint & I hope successful effort to get the thing carried into effect. They will receive your ideas with the greatest deference & thankfulness.
*The Letters of Thomas Jefferson, http://www.let.rug.nl/

1802 Gauss read in the newspaper that Olbers had rediscovered Ceres. Gauss wrote to get the observations and a long friendship ensued. Gauss was such an avid newspaper reader that students nicknamed him the “newspaper bear” because of his habits in the library reading room. If someone was reading the paper he wanted he would sit glumly nearby and stare at them until they gave up the paper. *VFR

1844 John Thomas Graves communicated to Sir William Hamilton his theorem respecting sums of eight squares. This is the basis of his work on Octonions. *SAU

1887 The Great Southern Comet of 1887 was officially discovered by astronomer John Macon Thome at Córdoba, Argentina, on Jan 19 at which point it was located in the constellation Grus. However, correspondence from William Henry Finlay suggests that it may also have been seen from Blauwberg, South Africa, on January 18. At the time of discovery the comet had already passed perihelion a week earlier, and its closest approach to Earth had been a month earlier. A curious feature of the comet was the fact that few, if any observations were made of a cometary head or nucleus. As a result, some older astronomical texts refer to it as the "Headless Wonder". *Wik *David Dickinson ‏@Astroguyz

1895, James Dewar demonstrated the intimate connection between phosphorescence and photographic action of the electric light on bodies cooled to the temperature of boiling liquid air. Presented at the Royal Institution, these experiments were reported as "very remarkable." *TIS

1896, The first x-ray machine is exhibited in the U.S. at Casino Chambers, New York City. For an admission charge of 25 cents, patrons could view the "Parisian sensation" *TIS

1897 The famous Indiana Pi Bill, to change the value of pi to 3 (and several other numbers it seems) was first introduced in the House. See more of this story here.

1916 This 611 gram stone, reported to have struck a house near the town of Baxter, Missouri in 1916.
The meteorite Fell around 9AM, on January 18th, 1916, and was heard and seen by J.W. Jackson, as it hit his house near the town of Baxter. The meteorite broke through the roof, hitting a log beam, and was found in the attic by the homeowners.
The circumstances of the fall were published in a local newspaper, and the Jacksons kept the meteorite until the late 1930s. It was purchased for the Nininger meteorite collection after it came to the attention of H.H. Nininger in 1938. *Center for Meteorite Studies ASU

1938 J.W. Bryce writes a memorandum formalizing IBM's development of a computing machine for Harvard:the Harvard Mark I, completed in 1944. The Harvard Mark I was the first fully automatic machine to be completed and computed three additions or subtractions a second; its memory stored 72 numbers.(I can see my students trying to comprehend this. They laugh out loud when I tell them that my first computer had 4k of memory, embarrassment for me and sure that I MUST have meant 4 meg) Several of J.W. Bryce's major inventions—high-speed multiplying, dividing, cross adding, the read-out, and the emitter—were utilized in the Harvard Mark I. *CHM

1969, pulsars were first identified by University of Arizona astronomers. *TIS

1978 Harvard Sophomore Bill Gates best solution to date of Pancake Sorting Problem is received by Discrete Mathematics Journal, BOUNDS FOR SORTING BY PREFIX REVERSAL William H. GATES , Christos H. PAPADIMITRIOU. The classical solution is two flips per pancake. Gates solution required only 5/3 flips per pancake. *Wik This solution has only recently(2008) been improved. It would be revised in the fall and published in 1979.

1982 Guyana (on the Northeast coast of South America) issued a series of postage stamps celebrating their conversion to the metric system. Can you name two countries that have not yet adopted the metric system? *VFR (The usage of the metric system varies around the world. According to the American Central Intelligence Agency's Factbook, the International System of Units is the official system of measurement for all nations in the world except for Burma, Liberia and the United States... other sources say Liberia has adopted metric system. Russ Rowlett opines that "The U.S. adopted the metric system in 1866. What the U.S. has failed to do is to restrict or prohibit the use of traditional units in areas touching the ordinary citizen: construction, real estate transactions, retail trade, and education." )

BIRTHS

1825 Sir Edward Frankland (18 Jan 1825; 9 Aug 1899) English chemist who was one of the first investigators in the field of structural chemistry, invented the chemical bond, and became known as the father of valency. He studied organometallic compounds - hybrid molecules of the familiar organic non-metallic elements (such as carbon, hydrogen, nitrogen, sulphur, phosphorus) with true metals. By 1850, he had prepared small organic molecules containing such metals as zinc. Subsequently, he devised the theory of valence (announced 10 May 1852), that each type of atom has a fixed capacity for combination with other atoms. For his investigations on water purification and for his services to the government as water analyst, Frankland was knighted in 1897.
*TIS

1856 Luigi Bianchi (18 Jan 1856 in Parma, Italy - 6 June 1928 in Pisa, Italy) made important contributions to differential geometry.*SAU In 1898, Bianchi worked out the Bianchi classification of nine possible isometry classes of three-dimensional Lie groups of isometries of a (sufficiently symmetric) Riemannian manifold. As Bianchi knew, this is essentially the same thing as classifying, up to isomorphism, the three-dimensional real Lie algebras. This complements the earlier work of Lie himself, who had earlier classified the complex Lie algebras.*Wik

1879 Peter Mark Roget (18 Jan 1779; 12 Sep 1869). In 1852, at age 73, he published his famous Thesaurus of English Words and Phrases. He was also one of the founders of the Medical and Chirurgical Society of London. Of more mathematical interest, Roget also invented the log-log scale on slide rules, making exponentiation & roots much easier to calculate. *Wik

1880 Paul Ehrenfest (January 18, 1880 – September 25, 1933) was an Austrian and Dutch physicist, who made major contributions to the field of statistical mechanics and its relations with quantum mechanics, including the theory of phase transition and the Ehrenfest theorem. Among his students were Johannes Burgers, Hendrik Kramers, Dirk Coster, George Uhlenbeck and Samuel Goudsmit, who became famous for jointly proposing the concept of electron spin, Jan Tinbergen, Arend Rutgers, Hendrik Casimir, Gerhard Dieke, Dirk Struik, and Gerard Kuiper. His assistants included Yuri Krutkov, Viktor Trkal, Adriaan Fokker, Paul Epstein, and Gregory Breit. Other young foreign scientists who spent an extended period in his laboratory included Gunnar Nordström, Enrico Fermi, Igor Tamm, Oskar Klein, Robert Oppenheimer, Walter Elsasser, Ralph Kronig, Werner Heisenberg, Paul Dirac, and David Dennison.*Wik

1901 Ivan Georgievich Petrovsky (18 Jan 1901 in Sevsk, Orlov guberniya, Russia - 15 Jan 1973 in Moscow, USSR) Petrovsky's main mathematical work was on the theory of partial differential equations, the topology of algebraic curves and surfaces, and probability. Petrovsky also worked on the boundary value problem for the heat equation and this was applied to both probability theory and work of Kolmogorov.*SAU

1908 Jacob Bronowski (18 Jan 1908; 22 Aug 1974) Polish-British mathematician and science writer who eloquently presented the case for the humanistic aspects of science as the writer and presenter of the BBC television series, The Ascent of Man. Bronowski, who had a Ph.D. in algebraic geometry, spent WW II in Operations Research, and was an official observer of the after-effects of the Nagasaki and Hiroshima bombings. After this experience, he turned to biology, to better understand the nature of violence.*TIS

DEATHS

1707 Otto Mencke (22 March (OS) April 2, 1644– 18 Jan (OS) 29 Jan 1707) was a 17th-century German philosopher and scientist. He obtained his doctorate at the University of Leipzig in 1666 with a thesis entitled: Ex Theologia naturali — De Absoluta Dei Simplicitate, Micropolitiam, id est Rempublicam In Microcosmo Conspicuam.
He is notable as being the founder of the very first scientific journal in Germany, established 1682, entitled: Acta Eruditorum. *Wik

1873 Pierre Charles François Dupin (6 Oct 1784 in Varzy, France - 18 Jan 1873 in Paris, France) made contributions to differential geometry and in particular invented the 'Dupin indicatrix' which gives an indication of the local behavior of a surface up to the terms of degree two. His contributions to differential geometry include the introduction of conjugate and asymptotic lines on a surface. *SAU

1963 Edward Charles Titchmarsh (1 Jun 1899, 18 Jan 1963) English mathematician whose contributions to analysis placed him in the forefront of his profession. His contributions helped resolve the differences between the general theory of quantum mechanics and the methods used to solve particular problems in quantum theory. All Titchmarsh's work is in analysis. His early studies were on Fourier series, Fourier integrals, functions of a complex variable, integral equations and the Riemann zeta function. From 1939, Titchmarsh concentrated on the theory of series expansions of eigenfunctions of differential equations, work which helped to resolve problems in quantum mechanics. His work on this topic occupied him for the last 25 years of his life. *TIS

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