Tuesday 10 April 2018

On This Day in Math - April 10

The Cyclopedia of Puzzles

The true business of the philosopher(scientist), though not flattering to his vanity, is merely to ascertain, arrange and condense the facts.
~Sir John Leslie

The 100th day of the year; The first 3 primes add to 10 and the first 32 primes add to 102 = 100 *Prime Curios

And 100=1+2+3+4+5+6+7+(8•9) *jim wilder ‏@wilderlab or 123 + 4 - 5 + 67 - 89 = 100 *Alexander Bogomolny ‏@CutTheKnotMath There are many more of these, find your own. Using only + or - there is only one way using exactly 7 +/- signs. This classic old problem is generally credited to Henry Ernest Dudeney whose birthday is today (see below) .

The last proof in John Horton Conway's "On Numbers and Games" is: Theorem 100; "This is the last Theorem in this book.The Proof is Obvious."

How many legs does a centipede have? Although the name is derived from cent(100) and ped (foot) the answer is NOT 100! In fact, it seems that all centipedes have twice an odd number for the number of legs so they can't have 100. In "The Book of General Ignorance" it is said that one (or at lest one) variety of centipede had been found with 96 legs, this seems not to be supported by the folks who study the creatures. There are some types that seem to have 2*49 = 98 legs, but none have been found with 100 legs (and none are expected to be found)

West Virginia seems to have more communities with numerical names than anywhere else in the world. They have a  Six, and an Eight, and they even have the only town in the US named Hundred. Originally named "Old Hundred"  for a long lived early settler, Henry Church. The sign points out that Henry served for the British in the Revolutionary War, but doesn't include that he took up arms to fight against them in the War of 1812.  Before he arrived at his assignment, the war ended, so he returned to his home in Hundred.


In 1662, Robert Hooke read his first publication, a pamphlet on capillary action, to the Society for the Promoting of Physico-Mathematical Experimental Learning. The Society had been constituted, to promote experimental philosophy, by at a meeting of a dozen scientists in Gresham College on 28 Nov 1660. The Society subsequently petitioned King Charles II to recognize it and to make a royal grant of incorporation. The Royal Charter, which was passed by the Great Seal on 15 Jul 1662, created the Royal Society of London. On 5 Nov 1662, Hooke was appointed its Curator of Experiments.*TIS

1751 Euler writes to Clairaut after receiving a paper from Clairaut that explained his error in a theory of the motion of the moon (Euler had thought Newton's inverse square law failed to explain motion of the moon...below). He describes Clairaut's work as "the most important and most profound discovery that has ever been made in mathematics." *Thomas L. Hankins, Jean d'Alembert: science and the Englightenment; pg 35
(In 1747 at a public session in the French Academy of Sciences Clairaut stated that Newton's theory of gravity was wrong. Euler and d’Alembert had simultaneously came to the same conclusion as all had been working on the motion of the moon as a special case of the three body problem. Clairaut suggested that the strength of gravity was proportional not to 1/r^2 , but the more complicated 1/r^2 +c/r^4 for some constant c. Over large distances, the c/r^4 term would effectively disappear, accounting for the utility of the inverse square law over large distances. He then began trying to find a value of c which could account for the moon's motion. He would continue to pursue this idea until May 17, 1749, when he made an equally dramatic announcement in which he claimed that Newton was right after all.)

1755 Simpson introduced error distributions. *VFR Simpson is best remembered for his work on interpolation and numerical methods of integration. However the numerical method known today as "Simpson's rule", although it did appear in his work, was something he learned from Newton as Simpson himself acknowledged. By way of compensation, however, the Newton-Raphson method for solving the equation f (x) = 0 is, in its present form, due to Simpson. Newton described an algebraic process for solving polynomial equations which Raphson later improved. The method of approximating the roots did not use the differential calculus. The modern iterative form xn+1 = xn - f (xn) / f '(xn) is due to Simpson, who published it in 1740.
He also worked on probability theory and in 1740 published The Nature and Laws of Chance. Much of Simpson's work in this area was based on earlier work of De Moivre. In fact he was involved in a dispute with De Moivre over issues of priority on the topic of probability and annuities. He worked on the Theory of Errors and aimed to prove that the arithmetic mean was better than a single observation. His justification of this appeared in his 1757 memoir "An attempt to show the advantage arising by taking the mean of a number of observations in practical astronomy". *SAU

1790 First patent law enacted in the U.S. *VFR the first U.S. patent statute was signed into law by President Washington. Although a number of inventors were clamoring for patents and copyrights, the first session of the First Congress in 1789 acted on none of the petitions. On 8 Jan 1790, President Washington recommended in his State of the Union address that Congress give attention to the encouragement of new and useful inventions, and within the month, on 25 Jan 1790, the House appointed a committee to draft a patent statute. The bill was given a first reading to the House on 4 Mar 1790, and amendments reconciled with the Senate by 5 Apr 1790. The first patent issued under this statute was signed by George Washington on 31 Jul 1790 for Samuel Hopkins' process to make potash and pearl ash. *TIS

1793 Gaspard Monge was permitted to resign from the Ministry of the Navy and the Colonies of France in order to undertake the urgent task of supplying the French army with gunpowder. *VFR

1846 It was supposedly on this date that Charles Wheatstone, scheduled to speak at a Royal Society lecture, bolted from the stage in fright. Seemingly at ease in small gatherings, he had a phobia of public speaking. According to the myth, and his biographer, Brian Bowers suggests that the probably factual foundation of the event has been extended to mythic proportions. Speakers have sometimes said they were "lock-in" prior to their speeches to prevent them from doing a "Wheatstone." At the very least the date must be wrong (and thus part of the myth) since that day was Good Friday, and no lectures were planned. In the extended part of the myth, Faraday, who often delivered the timid Wheatstone's work to the Society, supposedly stepped in and gave a powerful lecture on the nature of light. *Sir Charles Wheatstone FRS: 1802-1875
By Brian Bowers

1882 The U.S. issued its first postage stamp honoring President James A. Garfield (1831–1881). His only claim to mathematical fame was a new proof of the Pythagorean Theorem.

1915 Emmy Noether would frequently discuss abstract algebra via postcard with Ernst Fisher. The one below was sent on this date in 1915. *Wik

1943 ENIAC" Project Underway:
Researchers at the University of Pennsylvania begin work on the Electronic Numerical Integrator and Computer (ENIAC), a machine capable of the then-remarkable speed of 5,000 additions per second. ENIAC was shrouded in wartime secrecy since its main purpose was to compute "firing tables" for artillery shells. Before ENIAC, this was done by women (called "computers") working in large groups at mechanical desktop calculators. ENIAC was not completed until after the war (February 1946) but a generation of computer designers learned from its design and from the summer course given by Eckert and Mauchly at the Moore School. ENIAC could solve a wide range of general purpose computing problems, however, and was booked for two years in 1948. The ENIAC becomes public upon its completion in February 1946, when project leaders John Mauchly and J. Presper Eckert proudly show off 1,000 square feet of plugs, switches, and lights that calculate 1,000 times faster than other machines at the time. *CHM

1971 Lebanon issued a stamp honoring Hassan Kamel al-Sabbah (1894–1935). [Scott #C622]
Hassan Kamel Al-Sabbah (August 16, 1895 - March 31, 1935) was born in Nabatieh, Lebanon. He was an electrical and electronics research engineer, mathematician and inventor par excellence. He studied at the American University of Beirut. He taught mathematics at Imperial College of Damascus, Syria, and at the American University of Beirut. He is seen as being the father of the solar cell. He died in an automobile accident at Lewis near Elizabeth Town, N.Y

Norway issues stamp commemorating the 200th anniversary of the birth of astronomer Christopher Hansteen.


1651 Ehrenfried Tschirnhaus (10 April 1651 – 11 October 1708) was a German mathematician who worked on the solution of equations and the study of curves. He is best known for the transformation which removes the term of degree n-1 from an equation of degree n. *SAU Together with Leibniz he studied the unpublished papers of Descartes, Pascal and Roberval. His algebra, which Newton hoped to publish in an annotated translation, contains one of the earliest statements of the quadratic formula in a form identical to what we use today. *VFR

1766 Sir John Leslie (10 Apr 1766; 3 Nov 1832 at age 66) Scottish physicist and mathematician who first created artificial ice. His practical scientific investigations led to his book Experimental Inquiry Into the Nature and Propagation of Heat (1804), dealing with the fundamental laws of heat radiation. Leslie gave the first correct description of capillary action (1802) and invented many instruments, most notably an accurate differential air thermometer, and also a hygrometer, a photometer, the pyroscope, atmometer and aethrioscope. In 1810, he devised a method of obtaining very low temperatures, by evaporating water in a receiver evacuated with an air-pump but containing a drying agent. His mathematical works include texts on geometry, trigonometry and The Philosophy of Arithmetic. *TIS

1838 Frank Stephen Baldwin (10 Apr 1838; 8 Apr 1925 at age 87) American inventor best-known for his development of the Monroe calculator. Baldwin began in 1870 to experiment with the design of mechanical calculators. The device was patented and marketed in 1875 (No. 159,244). The improved 1875 machine initiated the development of the second fundamental principle in rotary four-rules calculators which became known as “The Baldwin Principle.” Baldwin developed many more calculators during his life. His last model was the forerunner of the Monroe machine. The Monroe Calculator Company was formed in 1912 and was a pioneer in electric adding machines. The Monroe Calculator was used extensively in the 1930's.*TIS

1857 Henry Ernest Dudeney (pronounced with a long “u” and a strong accent on the first syllable, as in “scrutiny”). He was England’s greatest maker of puzzles of mathematical interest, publishing six books of puzzles. His first work appears under the pseudonym “sphinx.” Although he never met Sam Loyd, they were in frequent correspondence and informally exchanged ideas. For samples of his puzzles see 536 Puzzles & Curious Problems, by Henry Ernest Dudeney (Edited, 1967, by Martin Gardner). *VFR Although Dudeney spent his career in the Civil Service, he continued to devise various problems and puzzles. Dudeney's first puzzle contributions were submissions to newspapers and magazines, often under the pseudonym of "Sphinx." Much of this earlier work was a collaboration with American puzzlist Sam Loyd; in 1890, they published a series of articles in the English penny weekly Tit-Bits. Dudeney later contributed puzzles under his real name to publications such as The Weekly Dispatch, The Queen, Blighty, and Cassell's Magazine. For twenty years, he had a successful column, "Perplexities", in the magazine The Strand, edited by the former editor of Tit-Bits, George Newnes. Dudeney continued to exchange puzzles with fellow recreational mathematician Sam Loyd for a while, but broke off the correspondence and accused Loyd of stealing his puzzles and publishing them under his own name. Some of Dudeney's most famous innovations were his 1903 success at solving the Haberdasher's Puzzle (Cut an equilateral triangle into four pieces that can be rearranged to make a square) and publishing the first known crossnumber puzzle, in 1926. In addition, he has been credited with inventing verbal arithmetic and discovering new applications of digital roots.
\[The Kindle edition of his classic "Canterbury Puzzles" is/was available for FREE..from Amazon ]


1752 Joseph Louis Lagrange (25 Jan 1736, 10 Apr 1813 at age 77) He excelled in all fields of analysis and number theory and analytical and celestial mechanics. *SAU He made great contributions to the theory of numbers and to analytic and celestial mechanics. His most important book is Mécanique analytique (1788; "Analytic Mechanics"), the textbook on which all later work in this field is based. *TIS

1868 Giovanni Battista Amici (25 Mar 1786, 10 Apr 1868 at age 82) was an Italian physicist, microscopist, astronomer and optical instrument designer who is best known for his invention of the achromatic lens. He also introduced the Amici-Bertrand lens, a lens for the inspection of an objective's rear focal plane. The lens system he designed for a new type of microscope in 1837 improved the magnification, capable of up to 6000 times. In 1840, he also introduced an immersion system for microscopes; the lowermost lens was immersed in a drop of oil to reduce improve clarity. He improved the design of mirrors used in reflecting telescopes. As a biologist, he investigated the sexual function of flowers, in particular he clarified the mechanism of the pollination of orchids.*TIS

1914 Moritz Cantor, historian of mathematics, . *VFR best remembered for the four volume work Vorlesungen über Geschichte der Mathematik which traces the history of mathematics up to 1799. The first volume (published 1880) traces the general history of mathematics up to 1200. The second volume traces the history up to 1668 (the year Newton and Leibniz were just about to embark on their mathematicalresearches). The third volume continues up to 1758 (Lagrange's work began shortly after this date). Cantor then, at the age of 69, as editor-in-chief, organised a team with nine further contributors to collaborate on the fourth volume (published 1908), continuing to 1799, the year of Gauss's doctoral thesis. (TIS)

1911 Sam Loyd, Americas greatest puzzlist. His son edited several collections of the father’s puzzles, including the mammoth Cyclopedia of Puzzles, which he privately printed in 1914. It remains today the largest, most interesting collection of puzzles ever printed. For a selection see Mathematical Puzzles of Sam Loyd, edited by Martin Gardner, Dover 1959 [p. xiv]. *VFR You can visit the Sam Loyd puzzle site here.
or just play an online version of the classic fifteen puzzle here.

1930 William Edward Story (29 April 1850 in Boston, Massachusetts, USA - 10 April 1930 in Worcester, Massachusetts, USA) He taught at Johns Hopkins with Sylvester and then moved on to Clark University which was, during the early 1890’s, the strongest mathematics department in the country. In the 1890’s he edited the short lived Mathematical Reviews.*VFR

1967 Oscar Chisini (March 4, 1889 – April 10, 1967) was an Italian mathematician. He introduced the Chisini mean in 1929. In 1929 he founded the Institute of Mathematics (Istituto di Matematica) at the University of Milan, along with Gian Antonio Maggi and Giulio Vivanti. He then held the position of chairman of the Institute from the early 1930s until 1959.The Chisini conjecture in algebraic geometry is a uniqueness question for morphisms of generic smooth projective surfaces, branched on a cuspidal curve. A special case is the question of the uniqueness of the covering of the projective plane, branched over a generic curve of degree at least five. *Wik

1974 G Waldo Dunnington (January 15, 1906, Bowling Green, Missouri – April 10, 1974, Natchitoches, Louisiana) was a writer, historian and professor of German known for his writings on the famous German mathematician Carl Friedrich Gauss. Dunnington wrote several articles about Gauss and later a biography entitled Gauss: Titan of Science (ISBN 0-88385-547-X). He became interested in Gauss through one of his elementary school teachers, Minna Waldeck Gauss Reeves, who was a great-granddaughter of Gauss.
Dunnington was also a translator at the Nuremberg trials. He ended his teaching career at Northwestern State University which houses his collection of Gauss-related material, believed to be the largest collection of its kind in the world. He became Dean of International Students there near the end of his life. *Wik *The Dunnington-Gauss award is given annually at Northwestern State University to the outstanding student in mathematics.

1988 Annie Hutton Numbers (6 March 1897 in Edinburgh, Scotland - 10 April 1988 in High Wycombe, England) After a brief spell teaching she was appointed as Assistant Lecturer and Demonstrator at the Department of Chemistry at Edinburgh University. While on the staff of the University, Numbers undertook research towards the degree of Ph.D. which she took in 1926 for the thesis The influence of substituents on the optical rotatory power of compounds. She left her post at the Department after 1930 to become a teacher in Ipswich and then in High Wycombe, retiring in 1965. *SAU
Who wouldn't want to have a math teacher whose name was Ms. Numbers?

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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