**Truths physical have an origin as divine as truths religious.**

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

1610 Galileo composed the cipher “The mother of love emulates the ﬁgures of Cynthia” to “copyright” his claim that Venus had phases like the moon. This idea, which may have been cribbed from a student, provided the ﬁrst hard evidence that the earth revolved around the sun. *Science News, Nov. 26, 1983, p. 347. (The student in question was surely Benedetto Castelli, See Dec 5, 1610)

1719 The ﬁrst aurora borealis display recorded in America took place in New England: “This evening, about eight o’clock, there arose a bright and red light in the E.N.E. like the light which arises from a house on ﬁre (as I am told by several credible people who saw it, when it ﬁrst arose) which soon spread itself through the heavens from east to west, reaching about 43 or 44 degrees in height, and was equally broad.” *VFR

1860 Charles Dodgson and Alice Liddle met Queen Victoria. (at Christ Church Deanery, Oxford ) *VFR

1884 David Hilbert passed his Ph.D. orals at the University of Konigsberg, where he would teach for nearly ten years before moving to the University of Gottingen where he spent the rest of his illustrious career. *MathDL

1867 James Clerk Maxwell wrote to Peter Guthrie Tait with a thought experiment for violating the Second Law of Thermodynamics that came to be known as Maxwell's Demon. It was Lord Kelvin who would coin the term for the idea in 1874 *Wik

1902 The University of Texas ﬁred George Bruce Halsted. When asked why Halsted was ﬁred, an Austin lawyer responded: “Well, Halsted just had more intelligence than the remainder of the faculty, taken together, and they just couldn’t stand it.” See D. Reginald Traylor, Creative Teaching: Heritage of R. L. Moore (1972), pp. 34-37. *VFR

In 1911, at Stockholm, Sweden, Marie Curie became the first person to be awarded a second Nobel prize. She had isolated radium by electrolyzing molten radium chloride. At the negative electrode the radium formed an amalgam with mercury. Heating the amalgam in a silica tube filled with nitrogen at low pressure boiled away the mercury, leaving pure white deposits of radium. This second prize was for her individual achievements in Chemistry, whereas her first prize (1903) was a collaborative effort with her husband, Pierre, and Henri Becquerel in Physics for her contributions in the discovery of radium and polonium.*TIS

1946 Frederick Williams Receives Patent for Memory Device The patent is issued for a device for random-access memory. The Williams tube was a modified cathode-ray tube that painted dots and dashes of phosphorescent electrical charge on a screen representing binary ones and zeros. It became the primary memory for vacuum tube machines such as the IBM 701. Williams developed his device at Manchester University. *CHM

1969 Yuri Matiyasevich reads journal article by Julia Robinson that will lead him to proof of Hilbert's 10th problem. Having been frustrated by the problem, he had given up hope of solving it. Asked to review an article by Robinson, he was inspired by the novelty of her approach and went back to work on H10. By Jan 3, 1970 he had a proof. He would present the proof on January 29, 1970

In 1972, Apollo XVII astronauts Gene Cernan and Harrison Schmitt landed on the moon for a three-day exploration, which would be the final Apollo mission to the moon.

In 1998, scientists announced in the Dec 11 issue of the journal Science that they have deciphered the entire genetic blueprint of an animal - the tiny nematode worm, Caenorhabditis elegans. This is the first time genetic instructions have been spelt out for an animal that, like humans, has a nervous system, digests food, and has sex. The worm's genetic code is spelled out by 97 million genetic letters corresponding to 20,000 genes. This work is a milestone in global efforts to unravel the entire human genetic code - or genome - which is expected to be completed in 2003. The research grew into a collaboration between 1,500 scientists in 250 laboratories worldwide. The efforts were led by John Sulston, in England and Dr Bob Waterston in the U.S.*TIS

BIRTHS

1712 Francesco Algarotti (11 Dec 1712; 3 May 1764) Italian connoisseur of the arts and sciences, recognized for his wide knowledge and elegant presentation of advanced ideas. At age 21, he wrote Il Newtonianismo per le dame (1737; "Newtonianism for Ladies"), a popular exposition of Newtonian optics. He also wrote upon architecture, opera and painting. *TIS

1781 Sir David Brewster (11 Dec 1781; 10 Feb 1868) Scottish physicist noted for his experimental work in optics and polarized light (light in which all waves lie in the same plane.) He is known for Brewster's Law, which relates the refractive index of a material to its polarizing angle (which is the incident angle at which reflected light becomes completely polarized. He patented the kaleidoscope in 1817. Later, he used lenses to improve three-dimensional images viewed with a stereoscope. Brewster also recommended the use of the lightweight, flat Fresnel lens in lighthouses.*TIS A nice blog about Brewster is here.

1863 Annie Jump Cannon (11 Dec 1863; 13 Apr 1941) American, deaf astronomer who specialized in the classification of stellar spectra. In 1896 she was hired at the Harvard College Observatory, remaining there for her entire career. The Harvard spectral classification system had been first developed by Edward C. Pickering, Director of the Observatory, around the turn of the century using objective prism spectra taken on improved photographic plates. In conjunction with Pickering Cannon was to further develop, refine, and implement the Harvard system. She reorganized the classification of stars in terms of surface temperature in spectral classes O, B, A, F, G, K, M, and cataloged over 225,000 stars for the monumental Henry Draper Catalog of stellar spectra, (1918-24).*TIS

1840 Carl Johannes Thomae (11 December 1840, Laucha an der Unstrut – 1 April 1921, Jena) (sometimes called "Johannes Thomae", "Karl Johannes Thomae", or "Johannes Karl Thomae") was a German mathematician. Carl Johannes Thomae's research was concerned with function theory and with what German-speaking mathematicians often call "Epsilontik", the precise development of analysis, differential geometry, and topology using epsilon-neighborhoods in the style of Weierstrass. The Thomae function, the Thomae transformation formula (aka, Thomae's transformation and Thomae's theorem), the Thomae formula for hyperelliptic curves, and the Sears–Thomae transformation formula are named after him. He called himself Riemann's student, although he never attended a lecture by Riemann. *TIS

1845 Vaclav Jerabek (11 Dec 1845 in Kolodeje, Pardubice, Czech Republic - 20 Dec 1931 in Telc, Czech Republic) a member of the Royal Bohemian Society of Sciences, the Moravian Society of Natural Sciences, and a honorary member of the Union of Czech Mathematicians.

His main research interest was in constructive geometry. He is best remembered by mathematicians for the Jerabek hyperbola. Given a triangle, the isogonal-conjugate images of lines are conics passing through the vertices of the triangle. The Jerabek hyperbola is the isogonal-conjugate image of the Euler line. It is a rectangular hyperbola, passing through the orthocenter and the circumcenter and many other interesting points of the triangle. The center of the Jerabek hyperbola lies on the nine-point circle.

Jerabek wrote over 50 papers, published mostly in Casopis pro pestovani matematiky a fysiky, some of them in the Belgian journal Mathesis. He donated his extensive library to the University of Brno.*SAU

1870 George Lidstone (11 Dec 1870 in London, England - 12 May 1952 in Edinburgh, Scotland) was an actuary who worked for various Edinburgh insurance companies. He wrote papers on various numerical and statistical topics. *SAU

1882 Max Born (11 Dec 1882; 5 Jan 1970) German physicist who shared the Nobel Prize for Physics in 1954 (with Walther Bothe), for his statistical formulation of the behavior of subatomic particles. Born's studies of the wave function led to the replacement of the original quantum theory, which regarded electrons as particles, with a mathematical description. *TIS

1873 Josip Plemelj (December 11, 1873 – May 22, 1967) was a Slovene mathematician, whose main contributions were to the theory of analytic functions and the application of integral equations to potential theory.*Wik

1884 Otto Szász (11 December 1884, Hungary – 19 December 1952, Cincinnati, Ohio) was a Hungarian mathematician who worked on real analysis, in particular on Fourier series. He proved the Müntz–Szász theorem and introduced the Szász–Mirakyan operator. The Hungarian Mathematical and Physical Society awarded him the Julius König prize in 1939. *Wik

1906 Samarendra Nath Roy or S. N. Roy (11 December 1906 – 23 July 1964) was an Indian-born American mathematician and an applied statistician. He was well known for his pioneering contribution to multivariate statistical analysis, mainly that of the Jacobians of complicated transformations for various exact distributions, rectangular coordinates and the Bartlett decomposition. *Wik

DEATHS

1748 E(wald) Georg von Kleist (c. 1700, 11 Dec 1748) German physicist, was dean of the Cathedral of Kamin. Kleist experimented to store electric charge efficiently, and discovered (1745) the Leyden jar, a fundamental electric circuit element for storing electricity, now usually referred to as a capacitor. The first Leyden jar was a stoppered glass jar partially filled with water with a wire or nail extending through the cork into the water. While holding the jar in one hand, the jar was charged by placing the end of the wire into contact with a static electricity producer, then removed. When Kleist touched the wire with his other hand, a discharge took place, giving himself a violent shock. The device was more thoroughly investigated by Pieter van Musschenbroek (1946).*TIS

1784 Anders Johan Lexell (24 Dec 1740 in Äbo, Sweden (now Turku, Finland) - 11 Dec 1784 in St Petersburg, Russia) Lexell's work in mathematics is mainly in the area of analysis and geometry. Lexell made a detailed investigation of exact equations differential equations. His work here extended a necessary condition which had been discovered earlier by Condorcet and Euler. He also gave a proof which was not based on using the calculus of variations. In addition Lexell developed a theory of integrating factors for differential equations at the same time as Euler but, although it has often been thought that he learned of the technique, some state that he independently discovered original methods to solve problems investigated by Euler.

Lexell did work in analysis on topics other than differential equations, for example he suggested a classification of elliptic integrals and he worked on the Lagrange series. He was also the first to develop a general system of polygonometry. This is a study of polygons similar to earlier work on triangles. It involves the solution of polygons given certain sides and angles between them, their mensuration, division by diagonals, circumscribing polygons around circles and inscribing polygons in circles.

Lexell made major contributions to spherical geometry and trigonometry. In fact trigonometry was the main tool used by Lexell in his work on polygonometry. Spherical geometry was a major tool in his astronomical studies. *SAU

1796 Johann Daniel Titius (2 Jan 1729, 11 Dec 1796) Prussian astronomer, physicist, and biologist whose formula (1766) expressing the distances between the planets and the Sun was confirmed by J.E. Bode in 1772, when it was called Bode's Law. Titius suggested that the mean distances of the planets from the sun very nearly fit a simple relationship of A=4+(3x2n) giving the series 4, 7, 10, 16, 28*, 52, 100, corresponding to the relative distance of the six known planets, up to Saturn, and an unassigned value (*) between Mars and Jupiter. Olbers searched for a planetary object at this empty position, thus discovering the asteroid belt. However, since the discovery of Neptune, which did not fit the pattern, the "law" is regarded as a coincidence with no scientific significance.*TIS

1906 Victor Mayer Amédée Mannheim (17 July 1831 in Paris, France - 11 Dec 1906 in Paris, France) Amédée Mannheim entered the École Polytechnique in Paris in 1848 at the age of 17. Two years later he went to Metz where he attended the École d'Application. Although slide rules existed before Mannheim's time, invented by Oughtred and Gunter and others, it was Mannheim who standardised the modern version of the slide rule which was in common use until pocket calculators took over a few years ago. It was while he was a student at Metz that the ideas for this slide rule came to Mannheim.

Koppelman writes, "He was a dedicated and popular teacher, strongly devoted to the École Polytechnique, and was one of the founders of the Société Amicale des Anciens Elèves de l'École. "

Mannheim retired from his army post in 1890, having attained the rank of colonel in the engineering corps. He continued teaching at the École Polytechnique until he retired in 1901 at the age of 70.

He made numerous contributions to geometry and for his outstanding contributions to the subject he was awarded the Poncelet Prize of the Académie des Sciences in 1872. He studied the polar reciprocal transformation introduced by Chasles and applied his results to kinetic geometry. Mannheim's own definition of kinetic geometry considered it to be the study of motion of a figure without reference to any forces, time or other properties external to the figure.

He also studied surfaces, in particular Fresnel's wave surfaces. The paper [5] studies this topic of his work in detail. *SAU

1910 Jules Tannery (March 24, 1848 – December 11, 1910) was a French mathematician who notably studied under Charles Hermite and was the PhD advisor of Jacques Hadamard.

He discovered a surface of the fourth order of which all the geodesic lines are algebraic. He was not an inventor, however, but essentially a critic and methodologist. He once remarked, "Mathematicians are so used to their symbols and have so much fun playing with them, that it is sometimes necessary to take their toys away from them in order to oblige them to think."

He notably influenced Paul Painlevé, Jules Drach, and Émile Borel to take up science.

His efforts were mainly directed to the study of the mathematical foundations and of the philosophical ideas implied in mathematical thinking.*Wik

1941 (Charles-) Émile Picard (24 Jul 1856, 11 Dec 1941) was a French mathematician whose theories did much to advance research into analysis, algebraic geometry, and mechanics. He made his most important contributions in the field of analysis and analytic geometry. He used methods of successive approximation to show the existence of solutions of ordinary differential equations. Picard also applied analysis to the study of elasticity, heat and electricity. *TIS

1945 Charles Fabry (11 Jun 1867, 11 Dec 1945) French physicist who specialized in optics, devising methods for the accurate measurement of interference effects. He worked with Alfred Pérot, during 1896-1906, on the design and uses of a device known as the Fabry-Pérot interferometer, specifically for high-resolution spectroscopy, composed of two thinly silvered glass plates placed in parallel, producing interference due to multiple reflections. In 1913, Fabry demonstrated that ozone is plentiful in the upper atmosphere and is responsible for filtering out ultraviolet radiation from the Sun, protecting life on the surface of Earth from most of its harmful effects. *TIS

1950 Hantaro Nagaoka (Born 15 Aug 1865; died 11 Dec 1950)Japanese physicist who was influential in advancing physics in Japan in the early twentieth century. In 1904, he published his Saturnian model of the atom, inspired by the rings around the planet Saturn. He placed discrete, negatively charged electrons of the same tiny mass, spaced in a ring revolving around a central huge positive spherical mass at its centre. Considering the electrostatic forces, hee made a mathematical analogy to Maxwell's model of the stability of the motion of Saturn's rings in a huge central gravitational field. However, Nagaoka's theory failed in other ways, and he sidelined it in 1908. *TIS

1950 Astronomer Leslie John Comrie, died (Born Aug 15 1893) …“showed how to ‘program’ commercial machines for scientiﬁc computation; developed impeccable interpolation techniques; produced mathematical tables of the highest standards of accuracy and presentation; and, in eﬀect, created computational science.” For this work he was elected F. R. S. a few months before his death on this date. *VFR He was a New Zealand astronomer and pioneer in the application of punched-card machinery to astronomical calculations. He joined HM Nautical Almanac Office (1926-36), where he replaced the use of logarithm tables with desk calculators and punched card machines for the production of astronomical and mathematical tables. This made scientific use of these machines, made originally for only business uses. In 1938, he founded the Scientific Computing Service Ltd., the first commercial calculating service in Great Britain, to further his ideas of mechanical computation for the preparation of mathematical tables. His use of card processing systems prepared the way for electronic computers.*TIS

1984 Krafft Arnold Ehricke (24 Mar 1917, 11 Dec 1984) German-born American physicist; rocketry engineer and space-travel theorist. During WW II, he was a key member of the famed Peenemunde Rocket Development team, specializing in the propulsion system for the German V-2 rocket (1942-45). He moved to the U.S. with Wernher Von Braun's rocket team in 1945. Entering the U.S. private industry in 1953, he helping develop the Atlas missile at General Dynamics. Subsequently, he invented the first liquid hydrogen propelled upper stage launch vehicle, the Centaur which enabled the U.S. to explore the solar system by launching planetary probes. A vial of his cremated remains accompany those of Star Trek creator Gene Roddenberry and others in space orbit, launched 20 Apr 1997. *TIS

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