*varlikmuzik.com
Euclid might be an extra course for learned men, like Homer.
But Euclid for children is barbarous.
~Oliver Heaviside
The 34th day of the year; 34 is the smallest integer such that it and both its neighbors are the product of the same number of primes.
and another gem from Jim, Wilder that is .
For days 34 & 35:
3435 = 3³+4⁴+3³+5⁵
These are sometimes called Munchhausen numbers. 1 and 3435 are the only two below 5000
34 is the smallest number which can be expressed as the sum of two primes in four ways.*Prime Curios
The Budhist Sulve Sutras of the fourth or fifth century BC approximate \( \sqrt{2}\) as 17/12 (This same ratio is found many times on the Acropolis). The actual instructions given by Baudhayana was"Increase the side by its third part, and this third by its own fourth, decreased by its 34th". \( \sqrt{2}= s + \frac{s}{3} + \frac{s}{3*4} -\frac{s}{3*4*34} \) . (This result, 577/408 is a solution to the Pell equation.
A 4x4 magic square using the integers 1 to 16 has a magic constant of 34. An early example is in the tenth century Parshvanath Jain temple in Khajuraho. The image below was taken by Debra Gross Aczel, the wife of the late Amir D. Aczel who used the image in his last book, Finding Zero. 4x4 magic squares were written about in India by a mathematician named Nagarjuna as early as the first century.
EVENTS
1692 De la Pryme records in his diary that Newton had a fire in his study that destroyed the manuscript of his Optics. “Every one thought he would have run mad; he was so troubled ... *VFR C. Huygens diary has an entry mentioning that he had been told "Newton had become deranged in his mind..." over the fire by Colin. He later related the same to Leibniz.*R. Smith, The Friend, 1829; pg 410The historical story is that Newton's dog, Diamond, had overturned a candle and set the documents afire.
1673(1672 os) Leibniz writes to Oldenburg describing his “accidental” meeting with the mathematician John Pell at the house of Robert Boyle. They discussed infinite series and after Leibniz described his work on the topic, Pell informed him that Nicholas Mercator had already written extensively on the topic. *Gerhart, The Early Mathematical Manuscripts of Leibniz, pg 162 On his return to France, Leibniz acquired Mercator's Book.
1806 Lagrange presented an attempt to prove Euclid’s parallel postulate to the mathematical and physical classe of the Institute National (as the Acad´emie des Sciences was known during the French Revolutionary Period). Here is how Biot, who, incidentally, died on this date in 1862 (see below), recalled the embarrassing incident in 1837: “Then one day Lagrange took out of his pocket a paper which he read at the Acad´emie [sic], and which contained a demonstration of the famous Postulatum of Euclid, relative to the theory of parallels. This demonstration rested on an obvious paralogism, which appeared as such to everybody; and probably Lagrange also recognized it as such during his lecture. For, when he had finished, he put the paper in his pocket, and spoke no more of it. A moment of universial silence followed, and one passed immediately to other concerns. [Grattan-Guiness, 1990, p. 263] *VFR In his "A Budget of Paradoxes, De Morgan described the event thus:"Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty. He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him which he had not observed: he muttered Il faut que j'y songe encore,("I shall have to think it over again.") and put the paper in his pocket. *Augustus De Morgan. A Budget of Paradoxes, Volume I .
1817 The first known publication of the Chinese Puzzle we now call Tangram was published in London on Feb 3 of this by James Leuchar. It featured a set of nine wooden tiles with a mahogany box and a set of 47 cards showing challenges to make with the tiles. The images to depict were common English items.
The puzzle had suddenly become very popular, and by the end of the month another but it only had one small section (four paragraphs) and the remainder seemed to be copied from a Chinese book, This came with seven tiles, seemingly like most modern sets.
1851 In the Meridian Hall at the Paris Observatory, invited scientist of Paris watched the Earth rotate on its axis as indicated by Foucault’s 11 meter long pendulum centered on the meridian line. You may see the same pendulum swinging today in the Musee de Arts et Metiers on the rue Saint-Martin in Paris. Foucault also presented his “sine law” for the period it takes the pendulum to sweep a full circle at any given latitude. *Amir D Aczel, Pendulum, pg 90-103
In 1862, as a boy almost 15 yrs old, Thomas Edison (1847-1931), became the first publisher of a newspaper produced and sold on a moving train. He had set up a small press in the baggage car of the Grand Trunk Railroad train from Port Huron to Detroit, Mich. Already obsessed with telegraphy, he worked out the logistics of getting advance news. His weekly Grand Trunk Herald, a single sheet measuring 7-in. x 8-in., included local news and advertisements for his fathers store. He had been selling candy and newspapers on commission on that train run since age 12. Now, promoting his own newspaper he earned more. Edison became renowned as a pioneering boy journalist. At its peak, he sold about 200 copies a day to train riders. *TIS
In 1862, as a boy almost 15 yrs old, Thomas Edison (1847-1931), became the first publisher of a newspaper produced and sold on a moving train. He had set up a small press in the baggage car of the Grand Trunk Railroad train from Port Huron to Detroit, Mich. Already obsessed with telegraphy, he worked out the logistics of getting advance news. His weekly Grand Trunk Herald, a single sheet measuring 7-in. x 8-in., included local news and advertisements for his fathers store. He had been selling candy and newspapers on commission on that train run since age 12. Now, promoting his own newspaper he earned more. Edison became renowned as a pioneering boy journalist. At its peak, he sold about 200 copies a day to train riders. *TIS
1879 The organizers of the “International Centennial of Light” in the United States, preparing to celebrate the 100th anniversary of the invention of the light bulb by Thomas Edison on Oct. 21, 1979, were a bit surprised to learn that the British were organizing their own "Electric Lamp Centenary,” and that they were honoring not Edison, but Swan. The English festivities were to begin almost 8 months earlier, on Feb. 3, 1979, commemorating the date that Swan demonstrated his light bulb to an audience in his home city of Newcastle-on-Tyne. Swan, it turns out, had been trying to develop an electric bulb since 1845. Unlike Edison 30 years later, Swan avoided metal filaments, because they fused and burned up. By 1855, Swan had settled on carbon as the ideal filament. But because vacuum pumps were not very good in 1855, the carbon filaments oxidized and burned out much too quickly. Swan gave up and turned to photography, inventing the carbon print photographic process in the 1860s and manufacturing dry photographic plates in the early 1870s. Meanwhile, someone finally invented a decent vacuum pump, and in 1877, Swan returned to his light bulb experiments. Now the carbon filaments in his high-vacuum bulbs continued to glow for a long time. He demonstrated his light bulb to a crowd of 700 in Newcastle on Feb. 3, 1879, and then went out and electrified his house, and then an entire street in Newcastle.
In 1880, Swan began manufacturing light bulbs. The Edison people came over to England and threatened a lawsuit for patent infringement, and quickly discovered that they had no grounds, and that if they pursued a suit, the Edison patents would almost certainly be invalidated, since Swan's work preceded his. So instead of suing Swan's company, they merged with it, forming the Edison and Swan Company, which manufactured bulbs, using the brand name Ediswan, right up until the 1930s
1885 For many living mathematicians and scientist, Edwin Abbot's wonderful book Flatland, a Romance in Many Dimensions, is loved and treasured. It did not however, find smooth sailing after it came to print in 1884. Only a few months after thr publishing the New York Times printed this review:"A very puzzling book and a very distressing one, and to be enjoyed by about six, or at the outside seven, persons in the whole of the United States and Canada."
The book was discovered again after Albert Einstein's general theory of relativity was published, which brought to prominence the concept of a fourth dimension. Flatland was mentioned in a letter by William Garnett entitled "Euclid, Newton and Einstein" published in Nature on 12 February 1920. In this letter, Abbott is depicted, in a sense, as a prophet due to his intuition of the importance of time to explain certain phenomena:
Some thirty or more years ago a little jeu d'esprit was written by Dr. Edwin Abbott entitled Flatland. At the time of its publication it did not attract as much attention as it deserved... If there is motion of our three-dimensional space relative to the fourth dimension, all the changes we experience and assign to the flow of time will be due simply to this movement, the whole of the future as well as the past always existing in the fourth dimension.
The Oxford Dictionary of National Biography subsequently revised his biography, and as of 2020 it states that [Abbott] "is most remembered as the author of Flatland: A Romance of Many Dimensions".
1958 NEW MATH. New mathematics is found in Time magazine of Feb. 3, 1958, in the heading, "The new mathematics" [OED].
New math is found again in an article which appeared in numerous newspapers on Sept. 25, 1960: “But the ‘new math’ is being promoted energetically by such influential bodies as the U. S. Office of Education, the National Science Foundation, the National Education Association, the Mathematical Association of America, the College Entrance Examination Board and the Carnegie Corporation.”
* Jeff Niller
New math is found again in an article which appeared in numerous newspapers on Sept. 25, 1960: “But the ‘new math’ is being promoted energetically by such influential bodies as the U. S. Office of Education, the National Science Foundation, the National Education Association, the Mathematical Association of America, the College Entrance Examination Board and the Carnegie Corporation.”
* Jeff Niller
New Mathematics or New Math was a dramatic but temporary change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries and elsewhere, during the 1950s–1970s.
Topics introduced in the New Math include set theory, modular arithmetic, algebraic inequalities, bases other than 10, matrices, symbolic logic, Boolean algebra, and abstract algebra.
Parents and teachers who opposed the New Math in the U.S. complained that the new curriculum was too far outside of students' ordinary experience and was not worth taking time away from more traditional topics, such as arithmetic. The material also put new demands on teachers, many of whom were required to teach material they did not fully understand. Parents were concerned that they did not understand what their children were learning and could not help them with their studies. In an effort to learn the material, many parents attended their children's classes. In the end, it was concluded that the experiment was not working, and New Math fell out of favor before the end of the 1960s, though it continued to be taught for years thereafter in some school districts.
And as I always try to do when this topic comes up, let's look back with love and a smile with Tom Lehrer
1961 Historian Gerald Holton echoed the words of Newton (5 February 1675/76) in opening a session of a meeting where three of the four speakers were Nobel laureates in Physics when he said “How good it is to be able to sit at the feet of giants on whose shoulders we stand.” *The Physics Teacher, 26 (1988), p 264
1965 According to Interesting Times, the official Ted Nelson newsletter, he first used the word hyper-text (and hyper-media) in 1965
In a Vassar College Miscellany News article dated February 3, 1965, "Professor Nelson Talk Analyzes P.R.I.D.E.," written by Laurie Wedeles, Nelson is quoted as having used the word "hyper-text."
In 1967 he wrote, "(...)'Hypertext' is a recent coinage. 'Hyper-' is used in the mathematical sense of extension and generality (as in 'hyperspace,' 'hypercube') rather than the medical sense of 'excessive' ('hyperactivity'). There is no implication about size— a hypertext could contain only 500 words or so. 'Hyper-' refers to structure and not size."
1966 Luna 9, internal designation Ye-6 No.13, was an unmanned space mission of the Soviet Union's Luna program. On 3 February 1966 the Luna 9 spacecraft became the first spacecraft to achieve a soft landing on the Moon, or any planetary body other than Earth, and to transmit photographic data to Earth from the surface of another planetary body. *Wik
1997 The Sciencenter's Sagan Planet Walk is a walkable scale model of the Solar System, located in Ithaca, New York. The model scales the entire Solar System—both planet size and distances between them—down to one five billionth of its actual size. The exhibition was originally created in 1997 in memory of Ithaca resident and Cornell Professor Carl Sagan.
From Uranus, visitors follow Willow Avenue northwest and cross the Carl Sagan bridge at Adams street to reach the Neptune Obelisk. The Carl Sagan Bridge, built in 2000, features nine circular windows adorned with the signs of the nine planets. The obelisk for Neptune is located just across the bridge in Conley Park. *Wik
BIRTHS
1774 Karl Brandan Mollweide (3 Feb 1774 in Wolfenbüttel, Brunswick, now Germany - 10 March 1825 in Leipzig, Germany) He is remembered for his invention of the Mollweide projection of the sphere, a map projection which he produced to correct the distortions in the Mercator projection, first used by Gerardus Mercator in 1569. Mollweide announced his projection in 1805. While the Mercator projection is well adapted for sea charts, its very great exaggeration of land areas in high latitudes makes it unsuitable for most other purposes. In the Mercator projection the angles of intersection between the parallels and meridians, and the general configuration of the land, are preserved but as a consequence areas and distances are increasingly exaggerated as one moves away from the equator. To correct these defects, Mollweide drew his elliptical projection; but in preserving the correct relation between the areas he was compelled to sacrifice configuration and angular measurement.The second piece of work to which Mollweide's name is attached today is the Mollweide equations which are sometimes called Mollweide's formulas. These trigonometric identities ares
sin(½(A - B)) / cos(½C) = (a - b) / c, and
cos(½(A - B)) / sin(½C) = (a + b) / c,
where A, B, C are the three angles of a triangle opposite to sides a, b, c, respectively. These trigonometric identities appear in Mollweide's paper Zusätze zur ebenen und sphärischen Trigonometrie (1808). *SAU
1862 William Jackson Humphreys (3 Feb 1862; 10 Nov 1949) American atmospheric physicist who applied basic physical laws to explain the optical, electrical, acoustical, and thermal properties and phenomena of the atmosphere. His book, Physics of the Air (1920), covers most of classical physical meteorology.*TIS
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| *bugman123.com |
January 25, 1915, showed complete contempt for danger. Under an extremely violent bombardment, he succeeded despite his youth (22 years) to give a real example to his men. Struck by a bullet in the middle of his face causing a terrible injury, he could no longer speak but wrote on a ticket that he would not be evacuated. He only went to the ambulance when the attack had been driven back. It was the first time this officer had come under fire.When only 25 years of age, Julia published his 199 page masterpiece Mémoire sur l'iteration des fonctions rationelles which made him famous in the mathematics centres of his day. The beautiful paper, published in Journal de Math. Pure et Appl. 8 (1918), 47-245, concerned the iteration of a rational function f. Julia gave a precise description of the set J(f) of those z in C for which the nth iterate f n(z) stays bounded as n tends to infinity. (These are the Julia Sets popularized by Mandelbrot) *SAU
1898 Pavel Samuilovich Urysohn, Pavel Uryson (February 3, 1898, Odessa – August 17, 1924, Batz-sur-Mer) is best known for his contributions in the theory of dimension, and for developing Urysohn's Metrization Theorem and Urysohn's Lemma, both of which are fundamental results in topology. His name is also commemorated in the term Menger-Urysohn dimension and in the term Urysohn integral equation. The modern definition of compactness was given by him and Pavel Alexandrov in 1923.*Wik
1905 Arne Carl-August Beurling (February 3, 1905 – November 20, 1986) was a Swedish mathematician and professor of mathematics at Uppsala University (1937–1954) and later at the Institute for Advanced Study in Princeton, New Jersey.
Beurling worked extensively in harmonic analysis, complex analysis and potential theory. The "Beurling factorization" helped mathematical scientists to understand the Wold decomposition, and inspired further work on the invariant subspaces of linear operators and operator algebras.
In the summer of 1940 he single-handedly deciphered and reverse-engineered an early version of the Siemens and Halske T52 also known as the Geheimfernschreiber (secret teletypewriter) used by Nazi Germany in World War II for sending ciphered messages.[1] The T52 was one of the so-called "Fish cyphers", that using, transposition, created nearly one quintillion (893 622 318 929 520 960) different variations. It took Beurling two weeks to solve the problem using pen and paper. Using Beurling's work, a device was created that enabled Sweden to decipher German teleprinter traffic passing through Sweden from Norway on a cable. In this way, Swedish authorities knew about Operation Barbarossa before it occurred. Not wanting to reveal how this knowledge was attained the Swedish warning was not treated as credible by Soviets. *Wik
1951 Steven George Krantz (3 February 1951 San Francisco, California - ) is an American scholar, mathematician, and writer at Washington University in St. Louis. He has also taught at UCLA, Princeton, and Penn State. He is Editor-in-Chief of the Notices of the American Mathematical Society for the period (2010–2015). Krantz is also Editor-in-Chief of the Journal of Mathematical Analysis and Applications and Managing Editor and founder of the Journal of Geometric Analysis. He also edits for The American Mathematical Monthly, Complex Variables and Elliptic Equations, and The Bulletin of the American Mathematical Society.
Professor Krantz is author of many textbooks and popular books. His books Mathematical Apocrypha and Mathematical Apocrypha Redux are collections of anecdotes about famous mathematicians. Krantz's book An Episodic History of Mathematics: Mathematical Culture through Problem Solving is a blend of history and problem solving. A Mathematician's Survival Guide and The Survival of a Mathematician are about how to get into the mathematics profession and how to survive in the mathematics profession. Krantz's new book with Harold R. Parks entitled Mathematics: From Fascination to Insight is an entree to mathematics for the layman. *Wik
DEATHS
1468 Johannes Gensfleisch zur Laden zum Gutenberg (/ˈɡuːtənbɜːrɡ/; c. 1393–1406 – 3 February 1468) was a German inventor and craftsman who introduced letterpress printing to Europe with his movable-type printing press. Though not the first of its kind, earlier designs were restricted to East Asia, and Gutenberg's version was the first to spread across the world. His work led to an information revolution and the unprecedented mass-spread of literature throughout Europe. It also had a direct impact on the development of the Renaissance, Reformation and humanist movement.
His many contributions to printing include the invention of a process for mass-producing movable type; the use of oil-based ink for printing books; adjustable molds; mechanical movable type; and the use of a wooden printing press similar to the agricultural screw presses of the period.
1737 Thommaso Ceva (20 Dec 1648; 3 Feb 1737) Italian mathematician, poet, and brother of the mathematician Giovanni Ceva. At the age of fifteen he entered the Society of Jesus. His education was entirely within the Jesuit Order and he obtained a degree in theology. His first scientific work, De natura gravium (1669), dealt with physical subjects, such as gravity and free fall, in a philosophical way. Tommaso Ceva's mathematical work is summed up in Opuscula Mathematica (1699) which examines geometry (geometric-harmonic means, the cycloid, and conic sections), gravity and arithmetic. He also designed an instrument to divide a right angle into a given number of equal parts. He gave the greater part of his time to writing Latin prose. His poem Jesus Puer was translated into many languages. *TIS
1862 Jean-Baptiste Biot (21 Apr 1774, 3 Feb 1862) French mathematician and physicist who co-developed the Biot-Savart law, that the intensity of the magnetic field produced by current flow through a wire varies inversely with the distance from the wire. He did work in astronomy, elasticity, heat, optics, electricity and magnetism. In pure mathematics, he contibuted to geometry. In 1804 he made a 13,000-feet (5-km) high hot-air balloon ascent with Joseph Gay-Lussac to investigate the atmosphere. In 1806, he accompanied Arago to Spain to complete earlier work there to measure of the arc of the meridian. Biot discovered optical activity in 1815, the ability of a substance to rotate the plane of polarization of light, which laid the basis for saccharimetry, a useful technique of analyzing sugar solutions.*TIS
1919 Edward Charles Pickering, (19 Jul 1846, 3 Feb 1919) U.S. physicist and astronomer. After graduating from Harvard, he taught physics for ten years at MIT where he built the first instructional physics laboratory in the United States. At age 30, he directed the Harvard College Observatory for 42 years. His observations were assisted by a staff of women, including Annie Jump Cannon. He introduced the use of the meridian photometer to measure the magnitude of stars, and established the Harvard Photometry (1884), the first great photometric catalog. By establishing a station in Peru (1891) to make the southern photographs, he published the first all-sky photographic map (1903).*TIS
1923 Adam Wilhelm Siegmund Günther (6 Feb 1848 in Nuremberg, Germany - 3 Feb 1923 in Munich, Germany) Günther's contributions to mathematics include a treatise on the theory of determinants (1875), hyperbolic functions (1881), and the parabolic logarithm and parabolic trigonometry (1882). He also wrote numerous books and journal articles [which] encompass both pure mathematics and its history and physics physics, geophysics, meteorology, geography, and astronomy. The individual works on the history of science, worth reading even today, bear witness to a thorough study, a remarkable knowledge of the relevant secondary literature, and a superior descriptive ability. *SAU
1925 Oliver Heaviside (18 May 1850, 3 Feb 1925) English physicist who predicted the existence of the ionosphere. In 1870, he became a telegrapher, but increasing deafness forced him to retire in 1874. He then devoted himself to investigations of electricity. In 1902, Heaviside and Kennelly predicted that there should be an ionised layer in the upper atmosphere that would reflect radio waves. They pointed out that it would be useful for long distance communication, allowing radio signals to travel to distant parts of the earth by bouncing off the underside of this layer. The existence of the layer, now known as the Heaviside layer or the ionosphere, was demonstrated in the 1920s, when radio pulses were transmitted vertically upward and the returning pulses from the reflecting layer were received. *TIS He adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations (later found to be equivalent to Laplace transforms), reformulated Maxwell's field equations in terms of electric and magnetic forces and energy flux, and independently co-formulated vector analysis. Although at odds with the scientific establishment for most of his life, Heaviside changed the face of mathematics and science for years to come. Among many others, he coined the terms for admittance , conductance , impedance , permeability , and inductance. *Wik
1929 Agner Krarup Erlang (January 1, 1878 – February 3, 1929) was a Danish mathematician, statistician and engineer, who invented the fields of traffic engineering and queueing theory.*Wik
1943 Earle Raymond Hedrick (September 27, 1876 – February 3, 1943), was an American mathematician and a vice-president of the University of California.
Hedrick was born in Union City, Indiana. After undergraduate work at the University of Michigan, he obtained a Master of Arts from Harvard University. With a Parker fellowship, he went to Europe and obtained his PhD from Göttingen University in Germany under the supervision of David Hilbert in 1901. He then spent several months at the École Normale Supérieure in France, where he became acquainted with Édouard Goursat, Jacques Hadamard, Jules Tannery, Émile Picard and Paul Émile Appell, before becoming an instructor at Yale University. In 1903, he became professor at the University of Missouri.
He was involved in the creation of the Mathematical Association of America in 1916 and was its first president.
His work was on partial differential equations and on the theory of nonanalytic functions of complex variables. He also did work in applied mathematics, in particular on a generalization of Hooke's law and on transmission of heat in steam boilers. With Oliver Dimon Kellogg he authored a text on the applications of calculus to mechanics.
He moved in 1920 to UCLA to become head of the department of mathematics. In 1933, he was giving the first graduate lecture on mathematics at UCLA. He became provost and vice-president of the University of California in 1937. He humorously called his appointment The Accident, and told jokingly after this event, "I no longer have any intellectual interests —I just sit and talk to people." He played in fact a very important role in making of the University of California a leading institution. He retired from the UCLA faculty in 1942 and accepted a visiting professorship at Brown University. Soon after the beginning of this new appointment, he suffered a lung infection. He died at the Rhode Island hospital in Providence, Rhode Island. Two UCLA residence halls are named after him: Hedrick Hall in 1963, and Hedrick Summit in 2005.
Earle Raymond Hedrick worked on partial differential equations and on the theory of nonanalytic functions of complex variables. He also did work in applied mathematics, in particular on a generalization of Hooke's law and on transmission of heat in steam boilers. With Oliver Dimon Kellogg he authored a text on the applications of calculus to mechanics. *Wik
1956 (Félix-Édouard-Justin-) Émile Borel (7 Jan 1871; 3 Feb 1956) was a French mathematician who (with René Baire and Henri Lebesgue), was among the pioneers of measure theory and its application to probability theory. In one of his books on probability, he proposed the thought experiment that a monkey hitting keys at random on a typewriter keyboard will - with absolute certainty - eventually type every book in France's Bibliothèque nationale de France (National Library). This is now popularly known as the infinite monkey theorem. He was first to develop (1899) a systematic theory for a divergent series. He also published (1921-27) a number of research papers on game theory and became the first to define games of strategy. *TIS . “In Paris as a scholarship student preparing for the university, he entered the family circle of G. Darboux through friendship with his son, saw the “good life” of a leading mathematician, and set his heart on it.” *VFR [It began with Jonathon Swift and Gulliver's Travels, 1872, according to Professor Barrow. In the tale "a mythical professor of the Grand Academy of Lagado who aims to generate a catalogue of all scientific knowledge by having his students continuously generate random strings of letters..." (I think, see emphasis in the excerpt below, that it was random strings of words).. Anyway, according to the good Professor Barrow, the story was embellished in different forms until French Mathematician Emile Borel{there is a street and a square named for him in the 17th District in Paris} suggested that random typing monkeys could duplicate the French national library.] *Pballew, Typing Monkeys
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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