Truths physical have an origin as divine as truths religious.
~Sir David BrewsterThe 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. On Dec 5, 1610 Benedetto wrote:
"If the position of Copernicus, that Venus revolves around the sun, is true (as I believe), it is clear that it would necessarily sometimes be seen by us horned and sometimes not, even though the planet maintains the same position relative to the sun. ... Now I want to know from you if you, with the help of your marvellous glasses, have observed such a phenomenon, which will be, beyond doubt, a sure means to convince even the most obstinate mind. I also suspect a similar thing with Mars near the quadrature with the sun; I don't mean a horned or non-horned shape, but only a semicircular and a more full one."
By the 11th, Galileo had discovered that Venus did indeed appear as a crescent for on that day he wrote to Giuliano d'Medici expressing the discovery in the cipher.
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| Horned Venus |
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
"New Englanders hadn’t seen much of the Northern Lights up until then. There had been a dearth of solar activity for about a century, though the Northern Lights weren’t completely unknown. During the 17th century, Gov. John Winthrop and Chief Justice Samuel Sewall had described in their journals borealis-like phenomena.
Still, the Northern Lights were so uncommon that their unexpected appearance in December 1719 alarmed the citizenry. The 1836 Regents Report of the State of New York reported that the Northern Lights caused such terror there was a suspension of 'all business, all amusements and even sleep.'
Cotton Mather, the influential Puritan minister, didn’t really know. He wrote a pamphlet called A Voice From Heaven – An Account of a Late Uncommon Appearance in the Heavens. Though Mather did much to promote scientific thought, he couldn’t shake the feeling that the Northern Lights were a bad omen.
'When we see a Pillar of Smoke and a Flame ascending in Heaven,' he wrote, 'We must conclude, That Evil is upon us.' " *New England Historical Soc.
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| *New England Historical Soc. |
1769 To Benjamin Franklin from Nevil Maskelyne (The letter is so badly mutilated that even the gist of some passages cannot be conjectured, hence a summery).
Illustration of possible parallax in transition path by viewers due to location on Earth
1860 Charles Dodgson and Alice Liddle met Queen Victoria. (at Christ Church Deanery, Oxford ) *VFR
Many people believe the oft told tale that at this meeting, "Queen Victoria, charmed by "Alice in Wonderland," expressed a desire to receive the author's next work, and was presented, in due course, with a loyally inscribed copy of "An Elementary Treatise on Determinants."
The author denied that anything of the sort ever happened.
There is a true story that the Queen's eighth child, Prince Leopold met Alice and had a fierce crush on her after their meeting at Christ Church, Oxford where her father was the dean (and Dodgeson\Lewis Caroll was a mathematics don). It is also true that she asked him to be the godfather of her first child, which he gladly did. She also named the second of her sons after the Prince.
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| Prince Leopold, Duke of Albany |
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
Hilbert met Minkowski here and the two developed a lifelong friendship.
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
Maxwell's demon is a thought experiment that would hypothetically violate the second law of thermodynamics. It was proposed by the physicist James Clerk Maxwell in 1867. In his first letter, Maxwell referred to the entity as a "finite being" or a "being who can play a game of skill with the molecules". Lord Kelvin would later call it a "demon". ( in the journal Nature in 1874, and implied that he intended the Greek mythology interpretation of a daemon, a supernatural being working in the background, rather than a malevolent being. the journal Nature in 1874, and implied that he intended the Greek mythology interpretation of a daemon, a supernatural being working in the background, rather than a malevolent being.)
In the thought experiment, a demon controls a small massless door between two chambers of gas. As individual gas molecules (or atoms) approach the door, the demon quickly opens and closes the door to allow only fast-moving molecules to pass through in one direction, and only slow-moving molecules to pass through in the other. Because the kinetic temperature of a gas depends on the velocities of its constituent molecules, the demon's actions cause one chamber to warm up and the other to cool down. This would decrease the total entropy of the system, without applying any work, thereby violating the second law of thermodynamics.
A young Maxwell at Trinity College, Cambridge, holding one of his colour wheels
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
1930 Einstein visited America for the second time, originally intended as a two-month working visit as a research fellow at the California Institute of Technology. After the national attention he received during his first trip to the US, he and his arrangers aimed to protect his privacy. Although swamped with telegrams and invitations to receive awards or speak publicly, he declined them all.*Wik
Einstein and his wife arriving by boat in New York on Dec. 11, 1930.*@AlbertEinstein
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
Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge to provide a general algorithm that, for any given Diophantine equation (a polynomial equation with integer coefficients and a finite number of unknowns), can decide whether the equation has a solution with all unknowns taking integer values. *Wik
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| *Wik |
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
Caenorhabditis elegans is a free-living transparent nematode about 1 mm in length that lives in temperate soil environments. It is the type species of its genus.
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.
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| *Linda Hall Org |
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
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| *Linda Hall Org |
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
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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
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| *Geogebra |
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
One of the best books on optics is Principles of Optics, colloquially known as Born and Wolf, is an optics textbook written by Max Born and Emil Wolf that was initially published in 1959 by Pergamon Press. After going through six editions with Pergamon Press, the book was transferred to Cambridge University Press who issued an expanded seventh edition in 1999. A 60th anniversary edition was published in 2019 with a foreword by Sir Peter Knight. It is considered a classic science book and one of the most influential optics books of the twentieth century. *Wik
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
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| *SAU |
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
On 1 July, 1770 Lexell's Comet is seen closer to the Earth than any other comet in recorded history, approaching to a distance of 0.0146 astronomical units (2,180,000 km). It was discovered by French astronomer Charles Messier though later named after Anders Johan Lexell.
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.
Mannheim was fortunate both in having his rule made by a firm of national reputation, and its adoption by the French Artillery. Mannheim's rule had two major modifications that made it easier to use than previous general-purpose slide rules. Such rules had four basic scales, A, B, C, and D, and D was the only single-decade logarithmic scale; C had two decades, like A and B. Most operations were done on the A and B scales; D was only used for finding squares and square roots.
Mannheim changed the C scale to a single-decade scale and performed most operations with C and D instead of A and B. Because the C and D scales were single-decade, they could be read more precisely, so the rule's results could be more accurate. The change also made it easier to include squares and square roots as part of a larger calculation. Mannheim's rule also had a cursor, unlike almost all preceding rules, so any of the scales could be easily and accurately compared across the rule width. The "Mannheim rule" became the standard slide rule arrangement for the later 19th century and remained a common standard throughout the slide-rule era.
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
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
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| *Wik |
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, he 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
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| *Natl Air and Space Museum |
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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