## Saturday 10 December 2016

### On This Day in Math - December 10

Euclid, The Beautiful Fountain, Nuremburg, Germany

Gilbert shall live, till Load-stones cease to draw,
Or British Fleets the boundless Ocean awe.
~John Dryden
(wonder what percentage of HS science students could identify the "Gilbert" in the quote)

The 345th day of the year; 345 is the average number of squirts from a cow's udder needed to yield a US gallon of milk. *Archimedes-lab.org (I have not personally verified this, so the proof is left to the reader)

The numbers 345 and 184 form an unusual pair. Their sum is a square, the sum of their squares is a square, and the sum of their cubes is a square. $345+184=23^2, 345^2+184^2 = 391^2, 345^3+184^3 = 6877^2$ There are an infinite number of such pairs, but all the others are quite large.

Jim Wilder@wilderlab pointed out that the digits of 345 show up in two interesting equations, $3^2 + 4^2 = 5^2$   and $3^3 + 4^3 + 5^3 = 6^3$

EVENTS

1566 Tycho Brahe gets into an argument that will result in a famous nose job. "On December 10, 1566, Tycho and the Danish blue blood Manderup Parsbjerg were guests at an engagement party at Prof. Bachmeister in Rostock. The party included a ball, but the festive environment did not keep the two men from starting an argument that went on even over the Christmas period. On December 29, they finished the matter with a rapier duel. During the duel, which started at 7 p.m. in total darkness, a large portion of the nose of Brahe was cut off by his Opponent. It was the most famous cut in science, if not the unkindest." *Neatorama

1672 In a letter to Collins, Newton described a method of drawing tangents to curves whose equations are polynomials in x and y. If the curve is given by f(x, y) = 0 *VFR (according to the Penny Cyclopedia {vol 9-10, 1832}, the letter included an example, and was later sent to Leibniz)

1684 Halley at Royal Society meetings on December 10 reported that he’d seen Newton in Cambridge, who had “shewed him a curious treatise, De Motu, [De motu corporum in gyrum] which, upon Mr Halley’s desire, was, he said, promised to be sent to the Society to be entered upon their register.” This paper would develop into the three-book Philosophiae Naturalis Principia Mathematica over the next 18 months. *Kate Morant, halleyslog.wordpress.com
 *Bibliophilia @Libroantiguo

1687 Clashes between students of University of Jena and the night watchman . The students were arrested. *@ErhardWeigel

1701 Newton resigned his Lucasian professorship at Cambridge, having been at the mint since 1696. *VFR (Newton succeeded in getting the position awarded to William Whiston. Newton, who had used a minor clause in the description of the position to convince Charles II that he (Whiston) could not take Holy Orders, which was generally required of all Cambridge graduates. His successor was eventually removed from his position in 1710 for the zealousness of his religious practice. He explained, and often gave exact dates for many biblical events such as the great flood, as the effects of comets hitting or passing very near the Earth. He also predicted the Earth would be destroyed by a comet on Oct 10, 1736.)

1797 Napoleon, in a conversation with Laplace, Lagrange and other members of the French Academy, called attention to La geometria del compasso (Pavia, 1797) by Lorenzo Mascheroni (1750– 1800). In this book Mascheroni showed that all of the constructions of Euclidean geometry can be carried out with compass alone. This work had a practical origin: constructions made with a compass alone are more accurate than those which use a straightedge. The book is dedicated to Napoleon, who is praised as liberator of Northern Italy. *Rademacher and Toeplitz, The
Enjoyment of Mathematics, p. 203

1799 Delambre and Méchain measured the meridian from Dunkirk (qv in Section 7-B) to Barcelona (qv under Spain in Section 10), completing their work in 1799 and leading to the formal definition of the metre on 10 Dec 1799. In 1812, it was decreed that a hybrid 'systeme usuelle' could be used. The metric system became the only legal system on 1 Jan 1840.
Thony Christie has a nice post on the history, creation, and importance of Triangulation here.

In 1901, the first Nobel Prizes were awarded. The king of Sweden distributed the first Nobel Prizes, in accordance with the will of inventor Alfred Nobel. *TIS The Nobel Prizes were presented in the large hall of the Royal Swedish Academy of Music1 at Nybroviken. The unpretentious, rather boring hall had been richly decorated under the supervision of the much sought-after royal architect, Agi Lindegren. As one of the so-called student marshals, decked out in student cap and a broad silk blue-and-gold band over my left shoulder, I had an excellent view of everything from my seat in the gallery to the right of the podium. The large bandstand where the royal orchestra was to play was completely decorated with plants and pine boughs. Centered at the back of the stage, beneath a giant laurel wreath tied with blue-and-gold ribbon, was a large broad obelisk with a white bust of Alfred Nobel. At the front there was a lectern and four more obelisks with the inscriptions PHYSICS, CHEMISTRY, MEDICINE, LITERATURE. Just in front of the stage were three armchairs for royalty, and behind these was a semicircle of chairs for the prize winners, the presenters, and attendants. Back of the semicircle there were places for all the intellectuals, distinguished officials, and military officers from Stockholm and around the country.
The hall filled gradually with people dressed in festive attire. Then, the three current prize winners entered and sat down, without music or fanfare as now is customary. First came the stately German, Wilhelm Conrad von Röntgen, with his large dark professor's beard, then the smiling, blond, clean-shaven Dutchman, Jakobus Hendricus van t'Hoff, followed by the elegant German Nobel Laureate in Medicine, Emil Adolf von Behring. Last came the French minister, who was to receive the Nobel Prize in Literature for his countryman, the poet, Sully Prudhomme, who was ill. Finally, the royal family entered: in the middle, Crown Prince Gustaf--later to become King Gustaf V--standing in for King Oscar who had been forced to travel to Christiania because of the threatening break-up of the Swedish Norwegian union. With him, came the 19-year old Prince Gustaf Adolf (much later our Gustaf VI Adolf) together with Prince Eugen. The seating arrangement meant that the royalty sat more or less with their backs to the Nobel Laureates and presenters. *Nobel Org

1857 Arthur Cayley's A Memoir on the Theory of Matrices is received by the Royal Society. Cayley establishes rules of notation and operations for these newly emerging ideas in mathematics. This paper also contained the first formal statement of what we now call the Cayley-Hamilton Theorem. The paper would be read the following January 14. *Jacqueline Stedall, Mathematics Emerging

1903, the New York Times advised inventor Samuel Langley to stop experimenting with flying machines. “We hope that Professor Langley will not put his substantial greatness as a scientist in further peril by continuing to waste his time, and the money involved, in further airship experiments. Life is short, and he is capable of services to humanity incomparably greater than can be expected to result from trying to fly. … For students and investigators of the Langley type there are more useful employments.” *Greg Ross, Futility Closet, 2 Sep 2011 (Langley's machine had crashed on his two previous trials dipping the pilot, Manley, into the River. The last only two days before this article. Within the week the Wright Brothers would fly their controlled aircraft into history. Among the things Langley had achieved during his "substantial greatness as a scientist" were:Langley invented the bolometer, an instrument for measuring infrared radiation, and used it on astronomical objects. He made one of the first attempts to measure the surface temperature of the Moon, and his measurement of interference of the infrared radiation by carbon dioxide in Earth's atmosphere was used by Svante Arrhenius in 1896 to make the first calculation of how climate would change from a future doubling of carbon dioxide levels. *Wik

1928 The Netherlands issued a stamp with a portrait of Christiaan Huygens. [Scott #B36]. *VFR

1933 Paul Dirac receives Nobel Prize on this date. A short video w/o sound the day after his arrival is available from the *Nobel Prize committee.

1934 BOURBAKI began at 12 noon on 10 Dec 1934 when H. Cartan, Chevalley, Delsarte, Dieudonné, René de Possel and Weil met for lunch at the Café Capoulade. This group, with some variations, met regularly at the Café. The group was not named and officially announced until the following summer, so the earlier group has been called Proto-Bourbaki. *VFR

1947 Sir Edward Victor Appleton’s speech at the 1947 Nobel Banquet:
Ladies and gentlemen, you should not … overrate scientific methods, as you will learn from the story of a man who started an investigation to find out why people get drunk. I believe this tale might interest you here in Sweden. This man offered some of his friends one evening a drink consisting of a certain amount of whisky and a certain amount of soda water and in due course observed the results. The next evening he gave the same friends another drink, of brandy and soda water in the same proportion as the previous night. And so it went on for two more days, but with rum and soda water, and gin and soda water. The results were always the same.
He then applied scientific methods, used his sense of logic and drew the only possible conclusion — that the cause of the intoxication must have been the common substance: namely the soda water!
That’s from Ronald Clark, Sir Edward Appleton, 1971. Clark adds, “Appleton was pleased but a little surprised at the huge success of the story. Only later did he learn that the Crown Prince drank only soda water — ‘one of those unexpected bonuses which even the undeserving get from Providence from time to time,’ as he put it.” *Greg Ross, Futility Closet

In 1984, the National Science Foundation reported the discovery of the first planet outside our solar system, orbiting a star 21 million light years from Earth.*TIS

BIRTHS

1804 Karl Gustav Jacob Jacobi (10 Dec 1804; 18 Feb 1851) German mathematician who, with the independent work of Niels Henrik Abel of Norway, founded the theory of elliptic functions. He also worked on Abelian functions and discovered the hyperelliptic functions. Jacobi applied his work in elliptic functions to number theory. He also investigated mathematical analysis and geometry. Jacobi carried out important research in partial differential equations of the first order and applied them to the differential equations of dynamics. His work on determinants is important in dynamics and quantum mechanics and he studied the functional determinant now called the Jacobian. *TIS

1815 Countess Augusta Ada King Lovelace (10 Dec 1815, 27 Nov 1852) (countess of Lovelace) English mathematician, the legitimate daughter of Lord Byron​, was educated privately, studying mathematics and astronomy in addition to the more traditional topics. She seems to have developed an early ambition to be a famous scientist. After she met Charles Babbage​ in 1833, she began to assist in the development of his analytical engine and published notes on the work. She was one of the first to recognize the potential of computers and has been called the first computer programmer. (The programming language Ada is named after her.) Her other plans, such as a Calculus of the Nervous System, failed to mature - the obstacles in her way were simply too great. As a woman, for example, she was denied access to the Royal Society Library.*TIS (In 2009 and 2010, 24 March was commemorated by some as Ada Lovelace​ Day​, a day to celebrate the achievements of women in technology and science. The 2011 Ada Lovelace Day was on 7 October)
Ada's mother, Lady Byron​, had intentionally schooled Ada in the Sciences and Mathematics to counteract the "poetic tendencies" she might have inherited from her father. Ada knew Mary Somerville​ and Augustus de Morgan socially and received some math instruction from both. She died of cancer in the womb in November of 1852, only 36 years of age, and was buried beside Lord Byron, the father she never knew, in the parish church of St. Mary Magdalene, Hucknall in the UK. It may be of interest to students of mathematics and computer science that Ada Lovelace husband,also named William, was the Baron of Ockham (ancestor of 14th century William of Occam​, for whom Occam’s Razor is named) in the 19th century.

1851 Melvil Dewey (10 Dec 1851; 26 Dec 1931) American librarian who developed library science in the U.S., especially with his system of classification, the Dewey Decimal Classification (1876), for library cataloging. His system of classification (1876) uses numbers from 000 to 999 to cover the general fields of knowledge and designating more specific subjects by the use of decimal points. He was an activist in the spelling reform and metric system movements. Dewey invented the vertical office file, winning a gold medal at the 1893 World's Fair. It was essentially an enlarged version of a card catalogue, where paper documents hung vertically in long drawers.*TIS (In response to a question about what "decimal" means, once had student declare, "Its the name of the guy who invented it, Dewey Decimal." I thought a long time about whether he was that clever, or that dumb)

1906 Walter Henry Zinn (10 Dec 1906; 14 Feb 2000) Canadian-American nuclear physicist who contributed to the U.S. atomic bomb project during World War II and to the development of the nuclear reactor. He collaborated with Leo Szilard, investigating atomic fission. In 1939, they demonstrated that uranium underwent fission when bombarded with neutrons and that part of the mass was converted into energy (given by E = mc2). This work led him into research into the construction of the atomic bomb during WW II. After the war Zinn started the design of an atomic reactor and, in 1951, he built the first breeder reactor. In a breeder reactor, the core is surrounded by a "blanket" of uranium-238 and neutrons from the core convert this into plutonium-239, which can also be used as a fission fuel.*TIS

1920 Alfred Goldie (10 Dec 1920 in Coseley, Staffordshire, England - 8 Oct 2005 in Barrow in Furness, Cumbria, England) was an English mathematician who proved an important result in Ring Theory. Goldie published his results, now known as "Goldie's Theorem," in The structure of prime rings with maximum conditions (1958) and The structure of prime rings under ascending chain conditions (1958). A generalisation appears in Semi-prime rings with maximum condition (1960).*SAU

1961 Oded Schramm (December 10, 1961 – September 1, 2008) was an Israeli-American mathematician known for the invention of the Schramm–Loewner evolution (SLE) and for working at the intersection of conformal field theory and probability theory. *Wik

DEATHS

1198 Averroes (1126, 10 Dec 1198)Spanish-Arab philosopher, physician, and astronomer. He is known for his Kulliyat fi ab tb (Generalities on Medicine) produced between 1162-69 on topics ranging from organ anatomy and hygiene to the prevention, diagnosis, and treatment of diseases. In this work, which spread widely in translations, he attempted to logically codify the existing medical knowledge. He critized adherance to tradition and instead stressed the importance of empirical evidence. In astronomy, he believed that the motion of the planets had to be around a physical centre (the Earth) and rejected Ptolemy's system of epicycles. He was also the most famous of the medieval Islamic philosophers and a principal interpreter of Aristotle.*TIS

1603 William Gilbert (24 May 1544, 10 Dec 1603) English scientist, the "father of electrical studies" and a pioneer researcher into magnetism, who spent years investigating magnetic and electrical attractions. Gilbert coined the names of electric attraction, electric force, and magnetic pole. He became the most distinguished man of science in England during the reign of Queen Elizabeth I. Noting that a compass needle not only points north and south, but also dips downward, he thought the Earth acts like a bar magnet. Like Copernicus, he believed the Earth rotates on its axis, and that the fixed stars were not all at the same distance from the earth. Gilbert thought it was a form of magnetism that held planets in their orbits. *TIS

1626 Edmund Gunter (1581, 10 Dec 1626)English mathematician who invented many useful measuring devices, including a forerunner of the slide rule. Gunter published seven figure tables of logarithms of sines and tangents in 1620 in Canon Triangulorum, or Table of Artificial Sines and Tangents. The words cosine and cotangent are due to him. He made a mechanical device, Gunter's scale, to multiply numbers based on the logs using a single scale and a pair of dividers. He also invented Gunter's chain which was 22 yards long with 100 links. It was used for surveying and the unit of area called an acre is ten square chains. Gunter also did important work on navigation, publishing New Projection of the Sphere in 1623. He also studied magnetic declination and was the first to observe the secular variation. *TIS {The chain is now almost obsolete as a unit of measure but was once very common in laying out townships and mapping the US along the train routes in the 19th century. In America there was a federal law passed in 1785 that all official government surveys must be done with a Gunter Chain. It was also called the Surveyor's Chain. On a visit to Stratford on Avon while at Hall's croft, the home of Shakespeare's daughter Susanna and her husband, Dr John Hall, I came across an early map of the town and the only legend shown was in Gunter's Chains, then while watching an English Cricket match I realized that the length of the bowling area (between the two wickets) is one chain also.

1831 Thomas Johann Seebeck (9 Apr 1770, 10 Dec 1831) German physicist who discovered (1821) that an electric current flows between different conductive materials that are kept at different temperatures, known as the Seebeck effect. It is the basis of the thermocouple and is considered the most accurate measurement of temperature. It is also a key component of the semi-conductor, the foundation of the modern computer business. Seebeck's work was the basis of German physicist Georg Simon Ohm (1789-1854) discoveries in electricity and of French physicist Jean Charles Athanase Peltier (1785-1845), whose Peltier effect became well known as a way to use electricity to freeze water (air conditioning, refrigeration). *TIS

1896 Albert Nobel died. Nobel prizes are awarded on this date each year in Stockholm (except the Peace Prize which is awarded in Oslo). There is an unfounded anecdote that there is no prize in mathematics as Nobel feared Mittag-Leﬄer would win it. *VFR

1968 Clement Vavasor Durell (born 6 June 1882, Fulbourn, Cambridgeshire, died South Africa, 10 December 1968) was an English schoolmaster who wrote mathematical textbooks. In 1900 he joined the Mathematical Association and in the 1900s was contributing articles on teaching to its journal, The Mathematical Gazette. After the First World War, he found a substantial second career and income in writing textbooks.
After spending most of his career teaching and writing about mathematics at Winchester, Durell retired to East Preston, Sussex, wintering in Madeira and South Africa, where he died in 1968.
His estate at death amounted to £200,098, which in the 1960s was a large fortune for the son of a clergyman to amass as a schoolmaster. *Wik

1995 Sarvadaman D. S. Chowla (22 October 1907, London–10 December 1995, Laramie, Wyoming) was a prominent Indian mathematician, specializing in number theory. Among his contributions are a number of results which bear his name. These include the Bruck–Chowla–Ryser theorem, the Ankeny–Artin–Chowla congruence, the Chowla–Mordell theorem, and the Chowla–Selberg formula, and the Mian–Chowla sequence.*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