Friday 11 November 2022

On This Day in Math - November 11


The British Mathematical Colloquium consists of three days of mathematics
with no dogs and no wives.
~Henry Whitehead

The 315th day of the year; 3152 can be written as the sum of the cubes of five consecutive integers. Find them. (Students may also wish to find the smallest square that can be expressed as the sum of the cubes of two or more consecutive integers.)

315 = 3^2 x 5 x 7  (or 5 x 7 x 9)  In a variation of use of Vandermonde's (and others since) "rising factorials" and "falling factorials" I have adopted the symbol \(9!_(2}\)  for 9x7x5x3x1; and \(9!_(2,3}\) for 9 x 7 x 5.  stopping after three terms.   

315 is a (barely)deficient number, the sum of it's proper divisors is only 309 ...309/315 is about .9809 *Derek Orr @Derektionary  pointed out to me that 256 is the closet to one of any (non-perfect) year day, (255/256 = .996), and for non-powers of two, 136 with a ratio of 134/136 = .985 is the best.

1572 Tycho Brahe first observed a supernova in the constellation Cassiopeia. Cornelius Gemma, the son of Gemma Frisius, made the first recorded observation of it on 9 November. Cornelius, Tycho, and others all observed the nova and determined it to be superlunary, thereby signalling a change in the superlunar sphere contradicting Aristotelian cosmology. *RMAT
(Brahe was at the beginning of his career in 1572, and it was this supernova that inspired him to devote his lifetime to making accurate measurements of the positions of the stars and planets.) For two weeks it was brighter than any other star in the sky and visible in daytime. By month's end, it began to fade but it remained visible to the naked eye for about 16 months until Mar 1574. *TIS  

1619 During the night, while living in Neuberg on the Danube, Descartes had a dream that he was visited by the Angel of Truth who revealed to him that mathematics was the sole key needed to unlock the secrets of nature. *Sheldrake, The Presence of the Past: Morphic Resonance and the Habits of Nature

1675 In a manuscript Leibniz struggled with the product and quotient rules for differentiation. At first he thought d(uv)= du dv.  *VFR  It would not be until the 21st that he completes the product rule. *F Cajori, History of Mathematics, (pg 208) Leibniz had previously used d twelve days earlier in the denominator, but in the margin he explains that dx is the same as his previous x/d, the difference of two neighboring x's.  Within a fortnight he had created the two basic symbols of calculus that have lasted for almost 350 years.

1744 in a letter of November 11, 1744, Cramer gave Euler a complete description of his rule for solving systems of linear equations. This is noteworthy, because Cramer's Rule would not appear in print until six years later, where it was an appendix in his very influential book “Introduction to the analysis of algebraic curves”.  Even more interesting is that the passage in Cramer's letter is virtually identical, word for word, to a three-page passage in the Introduction [Cramer 1750, pp. 657-659]. *VFR

1844 Both the terms vector and scalar were introduced by William Rowan Hamilton (1805-1865). Both terms appear in "On quaternions" a paper presented by Hamilton at a meeting of the Royal Irish Academy on November 11, 1844. This paper adopts the convention of denoting a vector by a single (Greek) letter, and concludes with a discussion of formulae for applying rotations to vectors by conjugating with unit quaternions. *Jeff Miller, Earliest Known Uses of Some of the Words of Mathematics
The term vector, and radius vector had been used much earlier. OED gives the earliest use of "vector" in Astronomy, from a technical dictionary of 1704: J. Harris Lexicon Technicum I. s.v., "A Line supposed to be drawn from any Planet moving round a Center, or the Focus of an Ellipsis, to that Center or Focus, is by some Writers of the New Astronomy, called the Vector; because 'tis that Line by which the Planet seems to be carried round its Center." The term is drawn from the Latin for "to carry".

1912 Bragg's law was first presented by Lawrence Bragg to the Cambridge Philosophical Society. Bragg's law confirmed the existence of real particles at the atomic scale, as well as providing a powerful new tool for studying crystals in the form of X-ray and neutron diffraction. Lawrence Bragg and his father, William Henry Bragg, were awarded the Nobel Prize in physics in 1915 for their work in determining crystal structures beginning with NaCl, ZnS, and diamond. They are the only father-son team to jointly win. Lawrence Bragg was 25 years old, making him the youngest physics Nobel laureate. *Wik 
Bragg’s original notebook where he first wrote down his law for diffraction of X-rays. *

Prof Stuart Mangles@plasmaStu

1918 Armistice Day. At the eleventh hour of the eleventh day of the eleventh month World War I ended.*VFR

In 1925, the discovery of cosmic rays was announced in Madison, Wisconsin by Robert A. Millikan who coined their name.*TIS  After the discovery of radioactivity by Henri Becquerel in 1896, it was generally believed that atmospheric electricity, ionization of the air, was caused only by radiation from radioactive elements in the ground or the radioactive gases or isotopes of radon they produce. In 1909 Theodor Wulf developed an electrometer, a device to measure the rate of ion production inside a hermetically sealed container, and used it to show higher levels of radiation at the top of the Eiffel Tower than at its base. However, his paper published in Physikalische Zeitschrift was not widely accepted. In 1911 Domenico Pacini observed simultaneous variations of the rate of ionization over a lake, over the sea, and at a depth of 3 meters from the surface. Pacini concluded from the decrease of radioactivity underwater that a certain part of the ionization must be due to sources other than the radioactivity of the Earth. *Wik

1945, Glenn T. Seaborg appeared as a guest on "Quiz Kids." One of the children on the show, Richard Williams, asked Seaborg if any new elements, in addition to plutonium and neptunium, had been discovered at the Metallurgical Laboratory in Chicago during the war. Since the discovery information had already been declassified for announcement at the forthcoming ACS national meeting on Nov. 16, Seaborg shared the news that two new elements (americium and curium) with atomic numbers 95 and 96 had been discovered.
Seaborg then told Williams, "So now you'll have to tell your teachers to change the 92 elements in your schoolbook to 96 elements." Seaborg later recalled in his 1979 Priestley Medal address that many kids did, in fact, tell their teachers to change the number of elements. "Judging from some of the letters I received from such youngsters, they were not entirely successful in convincing their teachers," he said.

1954 Algeria issued a stamp honoring Saint Augustine of Hippo (354–430). He is best remembered for his quote about mathematicians being in league with the devil. [Scott #261] *VFR  (The Quote, "Quapropter bono christiano, sive mathematici, sive quilibet impie divinantium, maxime dicentes vera, cavendi sunt, ne consortio daemoniorum animam deceptam, pacto quodam societatis irretiant." has been translated to "The good Christian should beware the mathematician and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of hell." Some suggest this is a mistranslation. The Latin word 'mathematici' derives from the Greek meaning of 'something learned' and refers mainly to astrologers. This was the chief branch of mathematics at the time but has been replaced in modern times by a plethora of other branches. According to the Shorter Oxford English Dictionary, 3rd edition, the word "mathematician" still meant astrologer as late as 1710.) *Wik

1979 Greg Maggs and Robert Kolstad complete the world’s longest slide rule. It is 323 feet long and 9.5 inches wide and is located in the University of Illinois College of Law building, Champaign.  The previous record, 320 feet 11.1 inches in length completed in March, 1979, by students of Alvirne High School, Hudson, New Hampshire. *Guinness  This record was broken in 2001 with a 350 feet 6.6 inch model. To my knowledge, this is currently the World's Longest documented Slide Rule, called The Texas Magnum by Skip Solberg and Jay Francis. It was demonstrated on February 28, 2001 in the Lockeed-Martin Aircraft Assembly Facility at Air Force Plant 4 in Fort Worth, Texas. The Texas Magnum was designed as a traditional Mannheim style slide rule. The A, C, D and L scales are included. *International Slide Rule Museum

1997 Proof by John Friedlander and Henryk Iwaniec that there are infinitely many prime numbers of the form m2 + n4, for positive integers m and n submitted to Proceedings of the National Academy of Sciences (USA) "Using a parity-sensitive sieve to count prime values of a polynomial." *Theorem of the Day

2015 In 1966 Chen Jigrun made a giant step toward a proof of Goldbach's conjecture when he stated Chen's Theorem: Every sufficiently large even number can be written as the sum of two primes, or a prime and a semi-prime. On November 11, 2015;  Tomohiro Yamada gave an explicit value for "sufficiently large" when he proved that Chen's theorem is true for all numbers greater than ee6(36) or approximately 17 (101872344071119348) *HT to John Cook

2019 Mark your calendars; the next Transit of Mercury occurs on November 11th, 2019 *2019 David Dickinson ‏@Astroguyz

1729 Birthdate of Louis Antoine de Bougainville. Although he began as a mathematician (under d’Alembert’s influence he wrote the first textbook on the integral calculus in 1752), he became famous as an explorer. He was the first Frenchman to sail around the world. But he was no great navigator, in spite of his mathematical ability. *VFR (The largest of the Solomon Islands is named after him, as is the colorful tropical climbing plant bougainvillaea. (see image at top))

1851 Adolphe-Louis Jacques Bertillon (11 Nov 1851 in Paris, France - 7 July 1922 in Valmondois, near Paris, France) Bertillon was a French statistician who applied statistics to social sciences. *SAU

1875 Vesto Melvin Slipher (11 Nov 1875; died 8 Nov 1969) American astronomer whose systematic observations (1912-25) of the extraordinary radial velocities of spiral galaxies provided the first evidence supporting the expanding-universe theory. Slipher spectroscopically measured the displacement of their spectral lines by the Doppler effect by which the wavelength of light from an object moving away from an observer will shifted toward the red end of the spectrum. Earlier, Slipher had determined the rotation periods of some of the planets by spectroscopic means. With Lowell (1912), he found Uranus had a  rotation period of  10.8 hours. He also produced comparable data for Venus, Mars, Jupiter, and Saturn and showed that Venus's period was much longer than expected. *TIS

1904 John Henry Constantine Whitehead (11 November 1904–8 May 1960), known as Henry, was a British mathematician and was one of the founders of homotopy theory. He was born in Chennai (then known as Madras), in India, and died in Princeton, New Jersey, in 1960. *Wik
Whitehead's work in differential geometry culminated in the paper "On the Covering of a Complete Space by the Geodesics Through a Point" (1935), containing pioneering contributions to this area of mathematics. He always retained his interest in geometry but soon focused on topology. He made substantial contributions to combinatorial homotopy and Stiefel manifolds and set up a school of topology at Oxford. *TIS One of his better quotes was, "It is the snobbishness of the young to suppose that a theorem is trivial because the proof is trivial."

1911 Caleb Gattegno (November 11, 1911; Alexandria, Egypt- July 28, 1988, Paris, France) was born in Alexandria, Egypt. He is best known for his innovative approaches to teaching and learning mathematics (Visible & Tangible Math). Creator of the Geoboard, and founder of the Cuisenaire Company which manufactures educational manipulatives. *Wik

1930 Hugh Everett III (November 11, 1930 – July 19, 1982) was an American physicist who first proposed the many-worlds interpretation (MWI) of quantum physics, which he termed his "relative state" formulation.
Discouraged by the scorn of other physicists for MWI, Everett ended his physics career after completing his Ph.D. Afterwards, he developed the use of generalized Lagrange multipliers for operations research and applied this commercially as a defense analyst and a consultant. He was married to Nancy Everett née Gore. They had two children: Elizabeth Everett and Mark Oliver Everett, who became frontman of the musical band Eels.

1938 Typhoid Mary (Mary Mallon) , (23 Sep 1869, 11 Nov 1938) famous typhoid carrier in the New York City area in the early 20th century. Fifty-one original cases of typhoid and three deaths were directly attributed to her (countless more were indirectly attributed), although she herself was immune to the typhoid bacillus (Salmonella typhi). The outbreak of Typhus in Oyster Bay, Long Island, in 1904 puzzled the scientists of the time because they thought they had wiped out the deadly disease. Mallon's case showed that a person could be a carrier without showing any outward signs of being sick, and it led to most of the Health Code laws on the books today. She died not from typhoid but from the effects of a paralytic stroke dating back to 25 Dec 1932. *TIS

1954 Horatio Carslaw (12 February 1870, Helensburgh, Dumbartonshire, Scotland – 11 November 1954, Burradoo, New South Wales, Australia) studied at Glasgow and Cambridge. He lectured at the University of Glasgow before moving to a professorship in Sydney, Australia. He worked on a variety of topics in both pure and applied mathematics. He co-authored  Conduction of Heat in Solids, which remains a classic in the field. *SAU

1967 Lester Randolph Ford, Sr. (October 25, 1886 – 11 November 1967) was an American mathematician, editor of the American Mathematical Monthly from 1942 to 1946, and President of the Mathematical Association of America from 1947 to 1948.
Ford circles are named after him.*Wik (Students, if you are not familiar with Ford Circles, and their rich beautiful history and interesting algebraic and geometric relations, look them up for an interesting exploration.  Start here)

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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