## Saturday, 26 March 2016

### On This Day in Math - March 26

 “Have you seen the world go around?"

Every human activity, good or bad, except mathematics, must come to an end.
~Paul Erdos

The 86th day of the year; 86 is conjectured to be the largest number n such that 2n (in decimal) doesn't contain a 0. *Tanya Khovanova, Number Gossip

The 86th prime is 443, and 4433 = 86,938,307. There is no other two digit n, such that the nth prime starts with n.

86 is the sum of four consecutive integers, 86= 20 + 21 + 22 + 23
and of four consecutive squares, 86= 32 + 42 + 52 + 62

The multiplicative persistence of a number is the number of times the iteration of finding the product of the digits takes to reach a one digit number. For 86, with persistence of three, we produce 8*6= 48, 4*8 = 32, and 3*2 = 6.... and 48+32+6 = 86. (how frequently does that occur?)

EVENTS

1619 Descartes reported (to Beekman) his ﬁrst glimpse of “an entirely new science, by which all problems that can be posed, concerning any kind of quantity, continuous or discrete, can be generally solved”  which was to become his analytic geometry (published 1637).
Descartes relies on the “single motions” of his “new types of compasses (often referred to by commentators as “proportional compasses”), which [he says] are no less exact and geometrical…than the common ones used to draw circles” in order to mark out a new class of problems that have legitimate geometrical solutions. He would apply them to to the problems of (1) dividing a given angle into any number of equal parts, (2) constructing the roots of three types of cubic equations, and (3) describing a conic section.
*Stanford Encyclopedia of Philosophy

1760 Guillaume le Gentil sailed from France planning to view the transit of Venus the following year from the east coast of India. Monsoons blew his ship off course, and on the day of the transit, he was becalmed in the Indian Ocean, unable to make any useful observations. Determined to redeem his expedition he books passage to India and builds an observatory to await the 1769 transit in Pondecherry. "The sky remained marvelously clear throughout May, only to cloud over on June 4, the morning of the transit, then clear again as soon as the transit was over."
His ordeal of a decade was not yet over. Stricken with dysentery he had to stay nine months more in India, and then booked passage on a Spanish warship. The ship lost its mast in a hurricane off the Cape of Good Hope, and finally limped into Cadiz. Le Gentil set out across the Pyrenees and returned to Paris after a total absence of eleven years, six months, and thirteen days, only to find that he had been presumed dead and his estate divided among his heirs. *Timothy Ferris, Coming of Age in the Milky Way (Thony Christie, The Renaissance Mathematicus, has a more detailed, and perhaps somewhat more accurate, version of Guillame's great adventure. See it here

1851 French Science reporter Terrien wrote in “le National, “Have you seen the world go around? Would you like to see it rotate? Go to the Parthenon on Thursday…the experiment devised by M. Leon Foucault is carried out there, in the presence of the public, under the finest conditions in the world.” *Amir D Aczel, Pendulum, pg 152
Foucault’s most famous pendulum . He suspended a 28 kg brass-coated lead bob with a 67 meter long wire from the dome of the Panthéon, Paris. The plane of the pendulum's swing rotated clockwise 11° per hour, making a full circle in 32.7 hours. *Wik

In 1859, Edmond Modeste Lescarbault, a French medical doctor and amateur astronomer, reported sighting a new planet in an orbit inside that of Mercury which he named Vulcan. He had seen a round black spot on the Sun with a transit time across the solar disk 4 hours 30 minutes. He sent this information and his calculations on the planet's movements to Jean LeVerrier, France's most famous astronomer. Le Verrier had already noticed that Mercury had deviated from its orbit. A gravitational pull from Vulcan would fit in nicely with what he was looking for. However, it was not consistently seen again and it is now believed to have been a "rogue asteroid" making a one-time pass close to the sun.*TIS (It was just pointed out to me by @Astroguyz,David Dickinson, that Leonard Nimoy, the actor who is best remembered for his role as the half-Vulcan character of Dr. Spock in the Star Trek series and films was also born on this day in 1931.)

1900 the Roentgen Society of the United States was organised a meeting of doctors from nine states held in Dr. Herber Robarts' office in St. Louis. Dr. Robarts was founder and editor of the American X-Ray Journal, and had been active in radiology since exposing his first X-ray plates in Feb 1896. Robarts was elected as president of the new society and and Dr. J. Rudis-Jicinsky as secretary. They arranged to hold the first annual meeting at the Grand Central Palace in New York City on 13-14 Dec 1900. In 1901, it was renamed as the Roentgen Society of America to include Canadians. It was reorganised at the next annual meeting on 10-11 Dec 1902 as the American Roentgen Ray Society.*TIS

1936 The 200" Hale mirror was SHIPPED, it had been cast in 1934. Still a great video: *David Dickinson ‏@Astroguyz
The 200-inch (5.1 m) Hale Telescope (f/3.3) was the world's largest effective telescope for 45 years (1948 - 1993). It is still a workhorse of modern astronomy. It is used nightly for a wide range of astronomical studies. On average the weather allows for at least some data collection about 290 nights a year. *Caltech Astronomy

1985 Alexander's Star is a puzzle similar to the Rubik's Cube, in the shape of a great dodecahedron.
Alexander's Star was invented by Adam Alexander, an American mathematician, in 1982. It was patented on 26 March 1985, with US patent number 4,506,891, and sold by the Ideal Toy Company. It came in two varieties: painted surfaces or stickers. Since the design of the puzzle practically forces the stickers to peel with continual use, the painted variety is likely a later edition.
*Wik

1994, A picture was released showing the first moon discovered to be in orbit around an asteroid. The potato-shaped asteroid Ida and its newly-discovered moon, Dactyl was imaged by NASA's Galileo spacecraft, about 14 minutes before its closest approach to the asteroid on 28 Aug 1993. Ida appears to be about about 36 miles long and 14 miles wide. It shows numerous craters, including many degraded craters, indicating Ida's surface is older than previously thought. The tiny moon is about one mile (1.5-km) across. The names are derived from the Dactyli, a group of mythological beings who lived on Mount Ida, where the infant Zeus was hidden (and raised, in some accounts) by the nymph Ida and protected by the Dactyli.

2010 Crocheting Adventures with Hyperbolic Planes by Dr Daina Taimina has won the 2009 Diagram Prize, having received the majority of the public vote for the oddest titled book of the year at thebookseller.com. The first award was given in 1978 for Proceedings of the Second International Workshop on Nude Mice

BIRTHS
1516 Conrad Gessner (Konrad Gessner, Conrad Geßner, Conrad von Gesner, Conradus Gesnerus, Conrad Gesner; 26 March 1516 – 13 December 1565) was a Swiss naturalist and bibliographer. His five-volume Historiae animalium (1551–1558) is considered the beginning of modern zoology, and the flowering plant genus Gesneria (Gesneriaceae) is named after him. He is denoted by the author abbreviation Gesner when citing a botanical name. Gessner in 1551 was the first to describe adipose tissue; and in 1565 the first to document the pencil. *Wik See more at The Renaissance Mathematicus blog.

1753 Count Benjamin Thompson Rumford (26 Mar 1753, 21 Aug 1814) American-born British physicist, government administrator, and a founder of the Royal Institution of Great Britain, London. Because he was a Redcoat officer and an English spy during the American revolution, he moved into exile in England. Through his investigations of heat he became one of the first scientists to declare that heat is a form of motion rather than a material substance, as was popularly believed until the mid-19th century. Among his numerous scientific contributions are the development of a calorimeter and a photometer. He invented a double boiler, a kitchen stove and a drip coffee pot. *TIS
1773 Nathaniel Bowditch (26 Mar 1773, 16 Mar 1838 at age 65) Self-educated American mathematician and astronomer. He learned Latin to study Newton's Principia and later other languages to study mathematics in these languages. Between 1795 and 1799 he made four sea voyages and in 1802 he was in command of a merchant ship. He was author of the best book on navigation of his time, New American Practical Navigator (1802), and his translation (assisted by Benjamin Peirce) of Laplace's Mécanique céleste gave him an international reputation. Bowditch was the discoverer of the Bowditch curves (more often called Lisajous figures for their co-discoverer), which have important applications in astronomy and physics.*TIS Bowditch was a navigator on the Wilkes Expedition and an island in the Stork Archipelago in the South Pacific is named for him (and sometimes called Fakaofu) *TIS Nathaniel Bowditch acquired his knowledge of mathematics through self-study while apprenticed to a ship’s chandler. He is most noted for his translation of Laplace’s M´ecanique c´eleste. [DSB 2, 368] *VFR

1789 William C. Redfield (26 Mar 1789, 12 Feb 1857 at age 67) American meteorologist who observed the whirlwind character of tropical storms. Following a hurricane that struck New England on 3 Sep 1821, he noted that in central Connecticut trees had toppled toward the northwest, but in the opposite direction 80-km further west. He found that hurricanes are generated in a belt between the Equator and the tropics, then veer eastward when meeting westerly winds at about latitude 30ºN. In 1831, he published his evidence that storm winds whirl counterclockwise about a centre that moves in the normal direction of the prevailing winds. He also promoted railroads and steamships. He co-founded the American Association for the Advancement of Sciences and was president at its first meeting (Sep 1848).*TIS

1803 Sir John William Lubbock, (London, England, 26 March 1803 - Downe, Kent, England, 20 June 1865 )English astronomer and mathematician. He made a special study of tides and of the lunar theory and developed a method for calculating the orbits of comets and planets. In mathematics he applied the theory of probability to life insurance problems. He was a strong proponent of Continental mathematics and astronomy.
Lubbock, third Baron Lubbock, was born into a London banking family. After attending Eton, he moved to Trinity College, Cambridge, where he became a student of William Whewell.(it was at the request of Lubbock that Whewell created the term "biometry".) He excelled in mathematics and traveled to France and Italy to deepen his knowledge of the works of Pierre-Simon de Laplace and Joseph Lagrange. Entering his father’s banking firm as a junior partner, he devoted his free time to science.
Lubbock strongly supported Lord Brougham’s Society for the Diffusion of Useful Knowledge [SDUK], which produced scientific and technical works designed for the working class. His articles on tides for the Society’s publications resulted in a book, *An Elementary Treatise on the Tides, in 1839. *Biographical Encyclopedia of Astronomers

1821 Ernst Engel (26 Mar 1821, 8 Dec 1896) German statistician, the head of the Prussian Statistical Bureau (1860-82), known for the "Engel curve," or Engel's law, which states that the proportion of expenditure on food will fall as income rises, i.e. food is a necessary good. Engel's law applies to goods as a whole. Demand for food, clothing and shelter - and for most manufactured products - doesn't keep pace with increases in incomes. Engel curves are useful for separating the effect of income on demand from the effects of changes in relative prices. Engel also examined the relationship between the size of the Prussian rye harvest and the average price of rye over a number of years prior to 1860, probably the first empirical study of the relationship between price and supply. *TIS

1848 Konstantin Alekseevich Andreev (26 March 1848 in Moscow, Russia - 29 Oct 1921 Near Sevastopol, Crimea) Andreev is best known for his work on geometry, although he also made contributions to analysis. In the area of geometry he did major pieces of work on projective geometry. Let us note one particular piece of work for which he has not received the credit he deserves. Gram determinants were introduced by J P Gram in 1879 but Andreev invented them independently in the context of problems of expansion of functions into orthogonal series and the best quadratic approximation to functions. *SAU

1862 Philbert Maurice d'Ocagne (26 March 1862 in Paris, France - 23 Sept 1938 in Le Havre, France) In 1891 he began publishing papers on nomography, the topic for which he is most remembered today. Nomography consists in the construction of graduated graphic tables, nomograms, or charts, representing formulas or equations to be solved, the solutions of which were provided by inspection of the tables. An advertisement for a colloquium at the Edinburgh Mathematical Society gave the following description of d'Ocagne's course:
It is now generally recognised that for most purposes the nomographic methods are superior to the older graphical methods of calculation. The introduction of some nomographic teaching in British Universities (and schools, for much of it is not too hard for schoolboys) is much to be desired.
*SAU
Nomographs are still used in wide areas of science and technology. The book below is an excellent coverage of the history and modern usage.

1875 Max Abraham (26 Mar 1875, 16 Nov 1922) German physicist whose life work was almost all related to Maxwell's theory. The text he wrote was the standard work on electrodynamics in Germany for a long time. Throughout his life, he remained strongly opposed to Einstein's Theory of Relativity, objecting to its postulates which he felt were contrary to classical common sense. He further held that the experimental evidence did not support that theory. In 1902, he had developed a theory of the electron in which he held that an electron was a perfectly rigid sphere with a charge distributed evenly over its surface. He also believed in the ether theory, thought that future astronomical data would validate it, and thus relativity was not in fact a good description of the real world. *TIS

1902 Marion Gray (26 March 1902, 16 Sept 1979) graduated from Edinburgh University and then went to Bryn Mawr College in the USA. She completed her doctorate there and returned to posts at Edinburgh and Imperial College London. She returned to the USA and worked for AT&T for the rest of her career. The Gray graph is named after her.*SAU The Gray graph is an undirected bipartite graph with 54 vertices and 81 edges. It is a cubic graph: every vertex touches exactly three edges. The Gray graph is interesting as the first known example of a cubic graph having the algebraic property of being edge but not vertex transitive *Wik

1903 Patrick du Val (March 26, 1903–January 22, 1987) was a British mathematician, known for his work on algebraic geometry, differential geometry, and general relativity. The concept of Du Val singularity of an algebraic surface is named after him. Du Val's early work before becoming a research student was on relativity, including a paper on the De Sitter model of the universe and Grassmann's tensor calculus. His doctorate was on algebraic geometry and in his thesis he generalised a result of Schoute. He worked on algebraic surfaces and later in his career became interested in elliptic functions.*Wik

1908 Theodore Samuel Motzkin (26 March 1908–15 December 1970) was an Israeli-American mathematician. Motzkin received his Ph.D. in 1934 from the University of Basel under the supervision of Alexander Ostrowski.
He was appointed at UCLA in 1950 and worked there until retirement.
The Motzkin transposition theorem, Motzkin numbers and the Fourier–Motzkin elimination are named after him. Motzkin first developed the "double description" algorithm of polyhedral combinatorics and computational geometry.[3] He was the first to prove the existence of principal ideal domains that are not Euclidean domains.
The quote "complete disorder is impossible," describing Ramsey theory is attributed to him. *Wik

1913 Paul Erdös (26 Mar 1913; 20 Sep 1996 at age 83) Hungarian mathematician, who was one of the century's top math experts and pioneered the fields of number theory and combinatorics. The type of mathematics he worked on were beautiful problems that were simple to understand, but notoriously difficult to solve. At age 20, he discovered a proof for a classic theorem of number theory that states that there is always at least one prime number between any positive integer and its double. In the 1930s, he studied in England and moved to the USA by the late 1930s when his Jewish origins made a return to Hungary impossible. Affected by McCarthyism in the 1950s, he spent much of the next ten years in Israel. Writing his many hundreds of papers made him one of history's most prolific mathematicians. *TIS His forte is posing and solving problems. One of his customs is to offer cash prizes for problems he poses. These awards range from $5 to$10,000 depending on how difficult he judges them to be. Erdos has written over 1,000 research papers, more than any other mathematician. The previous record was held by Arthur Cayley, who wrote 927. [Gallian, Contemporary Abstract Algebra, p 378]*VFR
McGill University Professor Willy Moser, a friend and collaborator of Erdos, tells of the "trial" of hosting Erdos. Once when Erdos was staying with him, Moser set up five dinners for him with five of erdos' old friends. Moser's wife pointed out that after the many times he had visited these homes and never brought a gift, perhaps Moser should remind him to bring candy or flowers. When he suggested the idea to Erdos, he thought it was a great idea and asked Moser, "Would you pick me up five boxes of chocolates?"

1922 Guido Stampacchia (March 26, 1922 - April 27, 1978) was a 20th century mathematician. Stampacchia was active in research and teaching throughout his career. He made key contributions to a number of fields, including calculus of variation and differential equations. In 1967 Stampacchia was elected President of the Unione Matematica Italiana. It was about this time that his research efforts shifted toward the emerging field of variational inequalities, which he modeled after boundary value problems for partial differential equations.
Stampacchia accepted the position of Professor Mathematical Analysis at the University of Rome in 1968 and returned to Pisa in 1970. He suffered a serious heart attack in early 1978 and died of heart arrest on April 27 of that year *Wik

1938 Sir Anthony James (Tony) Leggett (26 March 1938, ), has been a Professor of Physics at the University of Illinois at Urbana-Champaign since 1983.
Professor Leggett is widely recognized as a world leader in the theory of low-temperature physics, and his pioneering work on superfluidity was recognized by the 2003 Nobel Prize in Physics. He has shaped the theoretical understanding of normal and superfluid helium liquids and strongly coupled superfluids. He set directions for research in the quantum physics of macroscopic dissipative systems and use of condensed systems to test the foundations of quantum mechanics. *Wik

DEATHS

1609 John Dee (13 July 1527– *SAU gives 26 March 1609 in Mortlake, London, England) was an English mathematician, astronomer, astrologer, occultist, navigator, imperialist[4] and consultant to Queen Elizabeth I. He devoted much of his life to the study of alchemy, divination and Hermetic philosophy.
Dee straddled the worlds of science and magic just as they were becoming distinguishable. One of the most learned men of his age, he had been invited to lecture on advanced algebra at the University of Paris while still in his early twenties. Dee was an ardent promoter of mathematics and a respected astronomer, as well as a leading expert in navigation, having trained many of those who would conduct England's voyages of discovery.
Simultaneously with these efforts, Dee immersed himself in the worlds of magic, astrology and Hermetic philosophy. He devoted much time and effort in the last thirty years or so of his life to attempting to commune with angels in order to learn the universal language of creation and bring about the pre-apocalyptic unity of mankind. A student of the Renaissance Neo-Platonism of Marsilio Ficino, Dee did not draw distinctions between his mathematical research and his investigations into Hermetic magic, angel summoning and divination. Instead he considered all of his activities to constitute different facets of the same quest: the search for a transcendent understanding of the divine forms which underlie the visible world, which Dee called "pure verities".
In his lifetime Dee amassed one of the largest libraries in England. His high status as a scholar also allowed him to play a role in Elizabethan politics. He served as an occasional adviser and tutor to Elizabeth I and nurtured relationships with her ministers Francis Walsingham and William Cecil. Dee also tutored and enjoyed patronage relationships with Sir Philip Sidney, his uncle Robert Dudley, 1st Earl of Leicester, and Edward Dyer. He also enjoyed patronage from Sir Christopher Hatton.*Wik
I have Woolley's book, and enjoyed it.

1797 James Hutton (3 June 1726 in Edinburgh, Scotland - 26 March 1797 in Edinburgh, Scotland) geologist who initiated the principle of uniformitarianism with his Theory of the Earth (1785). He asserted that geological processes examined in the present time explain the formation of older rocks. John Playfair effectively championed Hutton's theory. Hutton, in effect, was the founder of modern geology, replacing a belief in the role of a biblical flood forming the Earth's crust. He introduced an understanding of the action of great heat beneath the Earth's crust in fusing sedimentary rocks, and the elevation of land forms from levels below the ocean to high land in a cyclical process. He established the igneous origin of granite (1788). He also had early thoughts on the evolution of animal forms and meterology. *TIS

1914 John S Mackay (22 Oct 1843 in Auchencairn near Kirkudbright, Kirkcudbrightshire, Scotland - 26 March 1914 in Edinburgh, Scotland)graduated from St Andrews University and taught at Perth Academy and Edinburgh Academy. He was a founder member of the EMS and became the first President in 1883 and an honorary member in 1894. He published numerous papers on Geometry in the EMS Proceedings.*SAU

1933 József Kürschák (14 March 1864 – 26 March 1933) was a Hungarian mathematician noted for his work on trigonometry and for his creation of the theory of valuations. He proved that every valued field can be embedded into a complete valued field which is algebraically closed. In 1918 he proved that the sum of reciprocals of consecutive natural numbers is never an integer. Extending Hilbert's argument, he proved that everything that can be constructed using a ruler and a compass, can be constructed by using a ruler and the ability of copying a fixed segment. He was elected a member of the Hungarian Academy of Sciences in 1897. *Wik

1974 Edward Uhler Condon (March 2, 1902 – March 26, 1974) was a distinguished American nuclear physicist, a pioneer in quantum mechanics, and a participant in the development of radar and nuclear weapons during World War II as part of the Manhattan Project. The Franck–Condon principle and the Slater–Condon rules are named after him.
He was the director of the National Bureau of Standards (now NIST) from 1945 to 1951. In 1946, Condon was president of the American Physical Society, and in 1953 was president of the American Association for the Advancement of Science.
During the McCarthy period, when efforts were being made to root out communist sympathizers in the United States, Edward Condon was a target of the House Un-American Activities Committee on the grounds that he was a 'follower' of a 'new revolutionary movement', quantum mechanics; Condon defended himself with a famous commitment to physics and science.
Condon became widely known in 1968 as principal author of the Condon Report, an official review funded by the United States Air Force that concluded that unidentified flying objects (UFOs) have prosaic explanations. The lunar crater Condon is named for him.
Years later, Carl Sagan reported how Condon described one encounter with a loyalty review board. A board member stated his concern: "Dr. Condon, it says here that you have been at the forefront of a revolutionary movement in physics called...quantum mechanics. It strikes this hearing that if you could be at the forefront of one revolutionary movement...you could be at the forefront of another". Condon said he replied: "I believe in Archimedes' Principle, formulated in the third century B.C. I believe in Kepler's laws of planetary motion, discovered in the seventeenth century. I believe in Newton's laws...." and continued with a catalog of scientists from earlier centuries, including the Bernoulli, Fourier, Ampère, Boltzmann, and Maxwell.[35] He once said privately: "I join every organization that seems to have noble goals. I don't ask whether it contains Communists".*Wik

1996 Hewlett-Packard Co-Founder David Packard Dies:
Hewlett-Packard Company co-founder David Packard dies after several weeks of illness. With fellow Stanford graduate Bill Hewlett, Packard founded Hewlett-Packard in a Palo Alto garage in 1938, spurring the development of what has come to be known as Silicon Valley. The company's first product was an oscillator, eight of which Disney used in its groundbreaking film ""Fantasia."" Since then, HP has made a name in personal computers, laser printers, calculators, accessories, and test equipment.*CHM

1966 Anna Johnson Pell Wheeler (5 May 1883 in Calliope (now Hawarden), Iowa, USA - 26 March 1966 in Bryn Mawr, Pennsylvania, USA) In 1899 she entered the University of South Dakota where she showed great promise in mathematics. The professor of mathematics, Alexander Pell, recognised her talents and helped persuade Anna Johnson that she should follow a career in mathematics. She received an A.B. degree in 1903.
After winning a scholarship to study for her master's degrees at the University of Iowa, she was awarded the degree for a thesis The extension of Galois theory to linear differential equations in 1904. A second master's degree from Radcliffe was awarded in 1905 and she remained there to study under Bôcher and Osgood.
Anna Johnson was awarded the Alice Freeman Palmer Fellowship from Wellesley College to study for a year at Göttingen University. There she attended lectures by Hilbert, Klein, Minkowski, Herglotz and Schwarzschild. She worked for her doctorate at Göttingen. While there Alexander Pell, her former mathematics professor came to Göttingen so that they could marry.
After returning to the United States, where her husband was by now Dean of Engineering, she taught courses in the theory of functions and differential equations. In 1908 Anna Pell returned to Göttingen where she completed the work for her doctorate but, after a disagreement with Hilbert, she returned to Chicago, where her husband was now on the university staff, without the degree being awarded.
At Chicago she became a student of Eliakim Moore and received her Ph.D. in 1909, her thesis Biorthogonal Systems of Functions with Applications to the Theory of Integral Equations being the one written originally at Göttingen. From 1911 Anna Pell taught at Mount Holyoke College and then at Bryn Mawr from 1918. Anna Pell's husband Alexander, who was 25 years older than she was, died in 1920. In 1924 Anna Pell became head of mathematics when Scott retired, becoming a full professor in 1925.
After a short second marriage to Arthur Wheeler, during which time they lived at Princeton and she taught only part-time, her second husband died in 1932. After this Anna Wheeler returned to full time work at Bryn Mawr where Emmy Noether joined her in 1933. However Emmy Noether died in 1935. The period from 1920 until 1935 certainly must have been one with much unhappiness for Anna Wheeler since during those years her father, mother, two husbands and close friend and colleague Emmy Noether died. Anna Wheeler remained at Bryn Mawr until her retirement in 1948.
The direction of Anna Wheeler's work was much influenced by Hilbert. Under his guidance she worked on integral equations studying infinite dimensional linear spaces. This work was done in the days when functional analysis was in its infancy and much of her work has lessened in importance as it became part of the more general theory.
Perhaps the most important honour she received was becoming the first woman to give the Colloquium Lectures at the American Mathematical Society meetings in 1927.
*SAU

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 & Campbel