The British Mathematical Colloquium consists of three days of mathematics
with no dogs and no wives.
~Henry WhiteheadThe 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 * @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.
EVENTS1572 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 NatureThis dream is often cited as a pivotal moment in his philosophical and scientific development, solidifying his belief in the power of reason and mathematical logic to unravel the mysteries of nature. *Google AI
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 |
| *Wik |
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
The work, titled "The Diffraction of Short Electromagnetic Waves by a Crystal," was subsequently published in the Proceedings of the Cambridge Philosophical Society in 1913.
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 |
| Millikan's original oil-drop apparatus, circa 1909–1910, *Wik |
1930 Albert Einstein and his colleague Leo Szilard designed a refrigerator that avoided the need for seals that could go bad. Instead of the mechanical pumps used in existing commercial refrigerators, the Einstein-Szilard refrigerator used an electromagnetic pump that required no moving parts. The two were motivated by contemporary newspaper reports of a Berlin family who had been killed when a seal in their refrigerator failed and leaked toxic fumes into their home. Einstein and Szilard received a US patent on November 11, 1930, for their invention.
Einstein had other patents such as an expandable blouse, an electrical sound system for hearing aids, and a self-focusing camera.
A much more interesting telling of this story, and many more, can be found in the book, Beer and thew Nobel Prize by Thomas M. Annesley, Professor of Clinical Chemistry at The University of Michigan Medical School.
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.
*http://pubs.acs.org
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
A little over two decades later I ran across the smallest slide rule I have ever seen in an Antique shop in Cadiz, Ky. It was a sterling silver tie clip with a working center bar and slide, two inches long.
And on a tip from Ted Courant, I found these even smaller cuff link working slide rules, 1.125" long
1997 Proof by John Friedlander and Henryk Iwaniec that there are infinitely many prime numbers of the form m
2 + n
4, 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 Jingrun 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 approximately 17 (10
1872344071119348) *HT to John Cook
BIRTHS
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."
1905 Sigekatu Kuroda (黒田 成勝, Kuroda Shigekatsu, 11 November 1905 – 3 November 1972) was a Japanese mathematician who worked in number theory and mathematical logic.
In 1942 he became a professor at the newly founded Nagoya Imperial University, where he stayed for over twenty years. He was responsible for much of the effort in setting up its Department of Mathematics.
He was married to the renowned number theorist Teiji Takagi's daughter Yakeo. The couple had three sons, all of whom became mathematicians, including S.-Y. Kuroda, who was a professor of linguistics at the University of California, San Diego.
He published a text on the foundations of algebraic number theory with Tomio Kubota in 1963.
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.
DEATHS
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)
He is the father of L. R. Ford Jr, who specializes in network flow problems.
1997 Menahem Max Schiffer (24 September 1911, Berlin – 11 November 1997)) was a German-born American mathematician who worked in complex analysis, partial differential equations, and mathematical physics.Menachem Max Schiffer studied physics from 1930 at the University of Bonn and then at the Humboldt University of Berlin with Max von Laue, Erwin Schrödinger, Walter Nernst, Erhard Schmidt, Issai Schur and Ludwig Bieberbach. In Berlin he worked closely with Issai Schur. In 1934, after being forced by the Nazis to leave the academic world, he immigrated to Mandatory Palestine.
On the basis of his prior mathematical publications, Schiffer received a master's degree from the Hebrew University of Jerusalem. In 1938, he received his doctorate under the supervision of Michael Fekete. In his dissertation on Conformal representation and univalent functions he introduced the "Schiffer variation", a method for handling geometric problems in complex analysis.
In September 1952, he began to teach at Stanford University, along with George Pólya, Charles Loewner, Stefan Bergman, and Gábor Szegő.
With Paul Garabedian, Schiffer worked on the Bieberbach conjecture with a proof in 1955 of the special case n=4. He was a speaker at the International Congress of Mathematicians (ICM) in 1950 at Cambridge, Massachusetts, and was a plenary speaker at the ICM in 1958 at Edinburgh with plenary address Extremum Problems and Variational Methods in Conformal Mapping. In 1970 he was elected to the United States National Academy of Sciences. He retired from Stanford University as professor emeritus in 1977. *Wik
2003 Andrei Andreevich Bolibrukh (30 January 1950 – 11 November 2003) was a Soviet and Russian mathematician. He was known for his work on ordinary differential equations especially Hilbert's twenty-first problem (Riemann–Hilbert problem). Bolibrukh was the author of about a hundred research articles on theory of ordinary differential equations including Riemann–Hilbert problem and Fuchsian system.
After receiving his mathematical education at the Lomonosov Moscow State University, with Mikhail Mikhailovich Postnikov and Alexey Chernavskii as thesis advisers, he started working on the proof of the existence of linear differential equations having a prescribed monodromic group. He applied modern methods of complex analytic geometry to classical problems about ordinary differential equations and was an expert on Hilbert's twenty-first problem. In 1989, Bolibrukh produced his famous counterexamples which invalidated the Josip Plemelj's 1908 solution of Hilbert's twenty-first problem. Bolibrukh dedicated much of his efforts to the Riemann-Hilbert problem in order to find full necessary and sufficient conditions for given monodromy data to be those of a Fuchsian system.
During his short career he served as Deputy Director of the Steklov Institute of Mathematics and professor at the Moscow Institute of Physics and Technology. *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
This image is also from the U Regina site mentioned above.Another nice thing about this relation is that when you set up the rather fearsome looking integral for the surface area, it reduces through simple algebra to a constant.
The unexpected constant here is that for any radius sphere you start with, the volume of the bead depends only on the height. And perhaps even less expected, is that the volume is the same as the volume of an un-drilled sphere with the same height (i.e., when 2r = h).
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