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
I would add that \(18^3 + 18^2 + 18 =6174, the Kaprekar's constant, and 6 + 1 + 7 + 4 =18.
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,
EVENTS
1664 Jan. 18, 1664, King Charles II of England officially established the Lucasian Chair of Mathematics at Cambridge University. Henry Lucas, member of Parliament from Cambridge (1640-48), of whom we have no portrait, died on July 6, 1663 (so family tradition has the date), and he left his library of 4000 books to Trinity College, Cambridge, and also bequeathed land to the university that yielded £100 per annum to fund a professorship of mathematics. We don't know enough about Lucas to know why he specified mathematics for his newly inaugurated chair. But the bequest was accepted, and in 1664, Isaac Barrow was appointed as the first Lucasian Professor of Mathematics at Cambridge. *Linda Hall Org
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.
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
On this day in 1711, James Stirling matriculated at Balliol College Oxford. His Jacobite sympathies did not allow him to swear an oath of loyalty to the crown and so ultimately he was unable to graduate.
The Stirling numbers, Stirling permutations, and Stirling's approximation are named after him. He also proved the correctness of Isaac Newton's classification of cubic plane curves.
In mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate results even for small values of n. It is named after James Stirling, though a related but less precise result was first stated by Abraham de Moivre
Comparison of Stirling's approximation with the factorial
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 beneficent life. This monument was erected by his two daughters, Eliza Cadogan and Sarah Stanley".*Wik
It was on a trip to Jamaica as the personal physician to the new Governor, Duke of Abermarle, that Hans encountered cocoa. Locals drank the bean with water but Sloane found it too bitter and took to mixing it with milk and sugar – the birth of milk chocolate.
On his return to England, Sloane introduced the mixture to society. It was taken up by apothecaries and sold as medicine but in the 19th century the mixture inspired the Cadbury brothers. Their use of the cocoa and milk mixture brought us chocolate as we know it in Britain today.
1761 the Royal Society agreed to send Nevil Maskelyne to the island of St Helena to observe a transit of Venus which would take place on 6 June 1761. Maskelyne had earlier proposed that the same expedition should try to measure the parallax of the star Sirius.
This Venus transit was important since accurate measurements would allow the distance from the Earth to the Sun to be accurately measured and the scale of the solar system determined. He set sail on the ship Prince Henry on 18 January 1761. During the voyage he experimented with the lunar position method of determining longitude using the lunar tables produced by Tobias Mayer. He arrived in St Helena on 6 April 1761 in plenty of time to find a good site for observing and to set up his instruments. Sadly, the 6 June was cloudy and he was unable to make measurements of the transit. He spent several months on St Helena trying to compute the parallax of Sirius but eventually decided that his instruments were faulty. Disappointed, Maskelyne set sail for England on the ship Warwick in February 1762. Reaching Plymouth on 15 May, he went back to Chipping Barnet, where he was a curate, and worked on publishing a book. He published the lunar distance method for determining longitude in The British Mariner's Guide (1763) where he also included Tobias Mayer's tables.
1799 Joseph Dixon, an American inventor and manufacturer, was born on Jan. 18, 1799.
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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. ...*The Letters of Thomas Jefferson, http://www.let.rug.nl/
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.
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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
A similar craze swept through England, "The interest in X-rays spread through public exhibitions and lectures, where volunteers from the audience could have their hands or purses X-rayed. The fluoroscope, invented in 1896, allowed an object placed between an X-ray coil and a screen to have its insides viewed in real time. People could also buy or build their own X-ray apparatus at home."
"The X-ray craze died as quickly as it was born. Within a few years, X-rays were mostly confined to medical settings. (Though, in one odd exception, shoe stores introduced coin-operated “Foot-o-Scopes”—fluoroscopes for fitting shoes—in 1920, and many continued using them until well after World War II.)" *dailyJstor
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
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.
An n-pancake graph is a graph whose vertices are the permutations of n symbols from 1 to n and its edges are given between permutations transitive by prefix reversals. It is a regular graph with n! vertices, its degree is n−1. The pancake sorting problem and the problem to obtain the diameter of the pancake graph is equivalent
The pancake graph P3
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." )
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
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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
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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 More about him here
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
Paul Ehrenfest (right) with Pieter Zeeman (left) and Albert Einstein, in the lab at the Leiden Institute, photograph, ca 1920 (Wikimedia commons)
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
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
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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
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