**Some proofs command assent. Others woo and charm the intellect.**

**They evoke delight and an overpowering desire to say, 'Amen, Amen'.**

The 316th day of the year; 316 can be written as the sum of 3 consecutive triangular numbers.

316 is also a centered triangular number (these two definitions turn out to be identical, all sums of 3 consecutive triangular numbers are centered triangular numbers, and vice-versa) The nth Centered triangle number has a single point at the center (the first centered triangular number) , and triangles surrounding it with 2,3,..., n dots on a side. The fourth centered triangular, 19 =3+6+10, number is shown

Students often enjoy finding cycles in the "sort then add" sequence. 316 is the only year date that does not reach a sorted number to terminate(at least we haven't found it yet) . [If a number is not sorted, then add n to sorted n, for example 21 is not sorted, so f(21)= 21+12=33 (a sorted number) 65 is not sorted, so f(65)= 65+56 = 121, still not sorted so do 121+112= 233, a sorted number so f(65) terminates in 233]

**EVENTS**

**1673**Christopher Wren is appointed architect of the new St. Paul’s by Royal Warrant. Wren had been one asked for an opinion on the renovation needed on Old St Paul's in 1663 and had recommended foundation work and a facelift. In a few years it would need a lot more. *Lisa Jardine, Ingenious Pursuits pg 71

**1680**Leeuwenhoek writes to Hooke suggesting that all reproduction is sexual

But in my opinion we can now be assured sufficiently that no animals, however small they may be, take their origin in putrefaction, but exclusively in procreation... For seeing that animals, from the largest down to the little despised animal, the flea, have animalcules in their semen, seeing also that some of the vessels of the lungs of horses and cows consist of rings and that these rings can occur on the flea's veins, why cannot we come to the conclusion that as well as the male sperm of that large animal the horse and similar animals, and of all manner of little animals, the flea included, is furnished with animalcules (and other intestines, for I have often been astonished when I beheld the numerous vessels in a flea), why, I say should not the male sperm of the smallest animals, smaller than a flea may even the very smallest animalcules have the perfection that we find in a flea.— Antonie van Leeuwenhoek * The Collected Letters of Antoni van Leeuwenhoek (1957), Vol. 3,

**1733**Abraham DeMoivre privately presented to some friends the normal distribution curve. *School Science and Mathematics, vol. 62, p. 172

**1792**After subscriptions to his Universal Tontine Association failed to meet expectations, Samual Blodgett met with the investors in the scheme and adopted articles of association forming the Insurance Company of North America (INA), the oldest stock insurance company in the United States, giving the company the ability to write fire, life, or marine insurance. Other fire insurance companies existed in Philadelphia, but INA was the first to include protection of the contents rather than just the building. The first policy was issued to Nesbitt's mercantile firm, Conyngham, Nesbitt & Co., for the ship America on its voyage from Philadelphia to Londonderry.

The Universal Tontine was a sort of early annuity fund that also acted as a lottery for the members who survived beyond the 21 year limit, when they would share the remains.*Wik

**In 1799**, Andrew Ellicott wrote the first known record of a meteor shower observed in the U.S. He viewed the display from a ship off the coast of Florida Keys at full moon. He wrote: "In every instant the meteors were as numerous as the stars," and that the "whole heaven appeared as if illuminated with sky rockets, flying in an infinity of directions, and I was in constant expectation of some of them falling on the vessel. They continued until put out by the light of the sun after day break." His account was read to the American Philosophical Society on 16 Jan 1801. The Leonids meteor shower is an annual event that is greatly enhanced every 33 years when accompanied by the appearance of the comet Tempel-Tuttle. *TIS *History of Astronomy @hist_astro

Image from The midnight sky, notes on the stars and planets By Edwin Dunkin

**1802**The United States Military Philosophical Socienty was founded at West Point. Jonathan Williams, nephew of Benjamin Franklin and superintendent of the Academy was the ﬁrst presi¬dent. Members received an attractive certiﬁcate bearing a scene of the destruction of the Roman ﬂeet at Syracuse by means of Archimedes’ mirror and the motto “Scientia in bello pax” (The use of science in war leads to peace). *VFR

**In 1833**, the great shower of the Leonid Meteors was recorded. Many observers

clearly reported that the meteors seemed to radiate from a spot in Leo and that, as the constellation moved slowly westward during the night, the radiant point moved with it. Within weeks a Yale mathematician, Denison Olmsted, showed that this radiant point was simply an effect of perspective. The millions of meteors that fell that night had in fact been moving along parallel paths. They appeared to diverge from a point in Leo for the same reason that parallel lines on the ground (such as railroad tracks), appear to diverge from a point on the horizon. Following this realization, the meteors were given the Latin family name for their apparent place of origin: the Leonids.*TIS According to some sources, the 1934 jazz standard, "

**Stars Fell on Alabama**", composed by Frank Perkins with lyrics by Mitchell Parish, refers to this occurrence of the Leonids. As reported by the Florence

*Gazette*: "[There were] thousands of luminous bodies shooting across the firmament in every direction. There was little wind and not a trace of clouds, and the meteors succeeded each other in quick succession." *Wik

**In 1901,**the first Nobel Prize for Physics was awarded to Wilhelm Roentgen for his discovery of X-rays.*TIS

**1906**Alberto Santos-Dumont, Brazilian aviation pioneer, flew his 14-BIS airplane a distance of 220 meters, height of 6 m. and speed of 37 km/h. to win the "Archdecon Prize." In 1909, he produced his famous "Demoiselle" or "Grasshopper" monoplanes, the forerunners of the modern light plane. *Wik

**1906**“The unique strength of Cambridge, as a place of experimental research, and as a leader in the advancement of Science generally, has depended greatly on the mathematical foundations given a large portion of all the undergraduates by the mathematical Tripos.” So wrote William Thomson, by then Lord Kelvin. See H. W. Becher, “William Whewell and Cambridge Mathematics,” HSPS, 11(1980), p. 15. *VFR

Kelvin was very confident of his own mathematical ability and the story is told that on the day of the examination results were released he sent his servant to find out, "Who is second wrangler?" He was devasted when the servant returned to answer, "You, Sir.". *Walter Gratzer, Eurekas and Euphorias, pg 21

**1937**Alan Turing’s paper entitled On Computable Numbers with an Application to the Entscheidungs-problem appeared on November 12, 1937, somewhat contemporaneously with Konrad Zuse’s work on the first of the Z machines in Germany, John Vincent Atanasoff ‘s work on the ABC, George Stibitz’s work on the Bell Telephony relay machine, and Howard Aiken’s on the Automatic Sequence Controlled Calculator.

Later renamed the Turing Machine, this abstract engine provided the fundamental concepts of computers that the other inventors would realize independently. So Turing provided the abstraction that would form the basic theory of computability for several decades, while others provided the pragmatic means of computation.*CHM

**In 1980**, the space probe Voyager I traveled under the rings and within 77,000 miles of Saturn.*TIS

**2002**Grigori Perelman posts the first of a series of eprints to the arXiv, in which he proves the century old Poincaré conjecture. On 22 December 2006, the journal Science recognized Perelman's proof of the Poincaré conjecture as the scientific "Breakthrough of the Year", the first such recognition in the area of mathematics. *Wik

**BIRTHS**

**1746 Jacques-Alexandre-César Charles**(12 Nov 1746; 7 Apr 1823) French mathematician, physicist, and inventor. When Benjamin Franklin visited France in 1779, Charles was inspired to study physics. He soon became an eloquent speaker to non-scientific audiences. His lectures and demonstrations attracted notable patrons and helped popularize Franklin's theory of electricity and other new scientific concepts. With Nicolas and Anne-Jean Robert, he made several balloon ascents, and was the first to use hydrogen for balloon inflation (1783). Charles invented most of the equipment that is still used in today's balloons. About 1787 he developed

**Charles's law**concerning the thermal expansion of gases that for a gas at constant pressure, its volume is directly proportional to its absolute temperature. *TIS

**1825 Mikhail Vashchenko-Zakharchenko**worked on the theory of linear differential equations, the theory of probability and non-euclidean geometry.*SAU

**1835Hugues Charles Robert Méray**(November 12, 1835, Chalon-sur-Saône, Saône-et-Loire - February 2, 1911, Dijon) was a French mathematician. He is noted as the first to publish an arithmetical theory of irrational numbers. His work did not have much of a role in the history of mathematics because France, at that time, was less interested in such matters than Germany.*Wik

**1842 John William Strutt,**3rd Baron of Rayleigh (of Terling Place) (12 Nov 1842; 30 Jun 1919) was an English physical scientist who made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He received the Nobel Prize for Physics in 1904 for his investigations into the densities of the most important gases and his successful isolation of argon, an inert atmospheric gas. *TIS

**1891 Seth Barnes Nicholson**(12 Nov 1891; 2 Jul 1963) was an American astronomer best known for discovering four satellites of Jupiter. As a graduate student at the University of California, while photographing the recently-discovered 8th moon of Jupiter with the 36-inch Crossley reflector, he discovered a 9th (1914). During his life career at Mt.Wilson Observatory, he discovered two more Jovian satellites (1938) and the 12th (1951), as well as a Trojan asteroid, and computed orbits of several comets and of Pluto. His main assignment at Mt. Wilson was observing the sun with the 150-foot solar tower telescope, and he produced annual reports on sunspot activity and magnetism for decades. With Edison Pettit, he measured the temperatures of the moon, planets, sunspots, and stars in the early 1920s. *TIS

**1910 Hua Luogeng**(12 November 1910 – 12 June 1985) was a Chinese mathematician born in Jintan, Jiangsu. He was the founder and pioneer in many fields in mathematical research. He wrote more than 200 papers and monographs, many of which became classics. Since his sudden death while delivering a lecture at the University of Tokyo, Japan, many mathematics secondary education programs have been named after him. His book on additive prime number theory influenced many subsequent number theorists in China, including the renowned Chen Jingrun who obtained the best result so far towards the binary Goldbach conjecture.*Wik

**1923 Irving Stoy Reed**(November 12, 1923 in Seattle, Washington- September 11, 2012) is a mathematician and engineer. He is best known for co-inventing a class of algebraic error-correcting and error-detecting codes known as Reed-Solomon codes in collaboration with Gustave Solomon. He also co-invented the Reed-Muller code.

Reed has made many contributions to areas of electrical engineering including radar, signal processing, and image processing. He was part of the team that built the MADDIDA, guidance system for Northrop's Snark cruise missile - one of the first digital computers. He developed and introduced the now-standard Register Transfer Language to the computer community while at M.I.T. Lincoln Laboratory. He had been a faculty member of the Electrical Engineering-Systems Department of the University of Southern California from 1962 to 1993. *Wik

**1927 Yutaka Taniyama**(November 12, 1927, Kisai near Tokyo – November 17, 1958, Tokyo) was a Japanese mathematician known for the Taniyama-Shimura conjecture.

Taniyama was best known for conjecturing, in modern language, automorphic properties of L-functions of elliptic curves over any number field. A partial and refined case of this conjecture for elliptic curves over rationals is called the Taniyama-Shimura conjecture or the modularity theorem whose statement he subsequently refined in collaboration with Goro Shimura. The names Taniyama, Shimura and Weil have all been attached to this conjecture, but the idea is essentially due to Taniyama.

In 1986 Ribet proved that if the Taniyama-Shimura conjecture held, then so would Fermat's last theorem, which inspired Andrew Wiles to work for a number of years in secrecy on it, and to prove enough of it to prove Fermat's Last Theorem. Due to the pioneering contribution of Wiles and the efforts of a number of mathematicians the Taniyama-Shimura conjecture was finally proven in 1999. The original Taniyama conjecture for elliptic curves over arbitrary number fields remains open, and the method of Wiles and others cannot be extended to provide its proof.*Wik

**DEATHS**

**1793 Jean-Sylvain Bailly**(15 Sep 1736, 12 Nov 1793) French astronomer, first Mayor of Paris (1789-91), was guillotined in Paris during the French Revolution. Noted for his computation of an orbit for Halley's Comet (1759) and for his studies of the four satellites of Jupiter then known. *TIS

**1916 Percival Lowell**(13 Mar 1855, 12 Nov 1916) American astronomer who predicted the existence of the planet Pluto and initiated the search that ended in its discovery. Lowell was also passionately committed to finding proof of intelligent life on Mars. In 1894, he founded the Lowell Observatory, atop Mars Hill, at Flagstaff as Arizona's first astronomical observatory. Studying Mars, Lowell drew in intricate detail, the network of several hundred fine, straight lines and their intersection in a number of "oases." Lowell concluded that the bright areas were deserts and the dark ones were patches of vegetation. He believed further, that water from the melting polar cap flowed down the canals toward the equatorial region to revive the

**vegetation. *TIS**

**1944 George David Birkhoff**(21 Mar 1884, 12 Nov 1944) American mathematician, foremost of the early 20th century, who formulated the ergodic theorem. As the first American dynamicist, Birkhoff picked up where Poincaré left off, gaining distinction in 1913 with his proof of Poincaré's Last Geometric Theorem, a special case of the 3-body problem. Although primarily a geometer, he discovered new symbolic methods. He saw beyond the theory of oscillations, created a rigorous theory of ergodic behavior, and foresaw dynamical models for chaos. His ergodic theorem transformed the Maxwell- Boltzmann ergodic hypothesis of the kinetic theory of gases (to which exceptions are known) into a rigorous principle through use of the Lebesgue measure theory. He also produced a mathematical model of gravity. *TIS

1974 Seishi Kikuchi (August 25, 1902 – November 12, 1974) was a Japanese physicist, known for his explanation of the Kikuchi lines that show up in diffraction patterns of diffusely scattered electrons. *Wik

**2000 Jacob Willem "Wim" Cohen**(27 August 1923 Leeuwarden – 12 November 2000) was a Dutch mathematician, well known for over hundred scientific publications and several books in queueing theory. *Wik

*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