## Sunday 10 March 2024

### On This Day in Math - March 10

 Rings of Uranus from Voyager 2, *astronomynotes.com

A rule of thumb for any good math talk is that it should have one proof and one joke
and they should not be the same.

~Ron Graham

The 69th day of the year; the square and the cube of 69 together contain all ten numerals.
692 = 4761, 693 =328509

1069+69 is prime and;
10069-69 is prime

On Many scientific calculators, 69! is the largest factorial that can be calculated, with an overflow error for larger numbers. 69! is appx 1.711 (1098)

Don S. McDonald ‏@McDONewt pointed out that $\binom{69}{5}$ = 11238513, 7 Fibonacci #'s almost in order.

The first squared square to be found was a square filled with 69 smaller squares. ( electrical network theory was used to make the discovery, previously most mathematicians felt that there were not likely to be any squared squares see Jan 21).. (I have since found out that this was not the first. In 1938 Roland Sprague found a solution using several copies of various squared rectangles and produced a squared square with 55 squares, and side lengths of 4205)

A "simple" squared square is one where no subset of more than one of the squares forms a rectangle or square, otherwise it is "compound".

 Lowest-order perfect squared square *Wik

 The Sprague Square

EVENTS

Coptic ostrakon noting an eclipse of the sun which had occurred at midday on 10 March 601 CE, Egypt.* @HistAstro

1615 Henry Briggs was completely engaged in the study of logarithms by this date for he wrote “Neper, lord of Markinston, hath set my head and hands a work with his new and admirable logarithms. I hope to see him this summer, if it please God, for I never saw a book, which pleased me better, and made me more wonder.” *VFR

1625 Henry Briggs writes to Kepler that work was underway to edit Thomas Harriot’s papers, “since we may expect and hope for a posthumous book from that author any day”. *Thomas Harriot’s Doctrine of Triangular Numbers, Beery & Stedall, pg 28

Thomas Harriot (1560–1621) was a mathematician and astronomer who founded the English school of algebra. He is known not only for his work in algebra and geometry but also as a prolific writer with wide-ranging interests in ballistics, navigation, and optics. (He discovered the sine law of refraction now known as Snell's law.)

By about 1614, Harriot had developed finite difference interpolation methods for navigational tables. In 1618 (or slightly later) he composed a treatise entitled ‘De numeris triangularibus et inde de progressionibus arithmeticis, Magisteria magna', in which he derived symbolic interpolation formulae and showed how to use them. This treatise was never published.

The ideas in the ‘Magisteria' were spread primarily through personal communication and unpublished manuscripts, and so, quite apart from their intrinsic mathematical interest, their survival in England during the seventeenth century provides an important case study in the dissemination of mathematics through informal networks of friends and acquaintances. Harriot's method was not superseded until Newton, apparently independently, made a similar discovery in the 1660s.

1672 From Hooke's Journal: Hooke’s first weather report was for Sunday 10 March 1672"[mercury] fell from 170 to 185. most part of ye Day cleer but cold & somewhat windy at the South–[I was this morning better with my cold then I had been 3 months before] [moon] apogeum–It grew cloudy about 4. [mercury] falling still"
Instead of writing the words ‘mercury’ and ‘moon’ (transcribed in square brackets here), Hooke depicted them with their astrological symbols ☿ and ☽ as a kind of shorthand. *felicityhen, Hooke's London.com

1695 John Evelyn writes in his journal of a visit to the Earl of Sunderland, who had acquired one of the best math libraries in Europe from the estate of Charles Scarborough; "My Lord showed me his library, now again improved by many books bought at the sale of Sir Charles Scarborough, an eminent physician, which was the very best collection, especially of mathematical books, that was I believe in Europe" *John Evelyn's Diary  *AMS

1763 Euler's E812. Read before the Academy of Berlin 10 March 1763 but only published posthumously in 1862. "Reflexions sur une espese singulier de loterie nommée loterie genoise." Opera postuma I, 1862, p. 319–335. The paper determined the probability that a particular number be drawn in a lottery.
Euler's interest in lotteries began at the latest in 1749 when he was commissioned by Frederick the Great to render an opinion on a proposed lottery. The first of two letters began 15 September 1749. A second series began on 17 August 1763. *Ed Sandifer, How Euler Did It

1773 Laplace introduces inverse probability.  Stephen Stigler called it the most influential paper published in probability to appear before 1800.  *Springer’s 1985 Statistics Calendar

In probability theory, inverse probability is an old term for the probability distribution of an unobserved variable.

The term "inverse probability" appears in an 1837 paper of De Morgan, in reference to Laplace's method of probability

1797 The surveyor Caspar Wessel presented his one and only mathematics paper to the Danish Academy of Sciences. It established his priority in publishing a geometrical representation of complex numbers. The paper was essentially unknown until 1895 when Christian Juel pointed out its signiﬁcance. *VFR (this paper introduced what are now often called Argand Diagrams) He represented complex numbers as points in a Cartesian plane, with the real portion of the number on the x axis and the imaginary part on the y axis. This was also independently devised a few years later, by Jean-Robert Argand, an amateur mathematician who self-published his ideas in an anomymous monograph (1806). Through publicity generated when Argand came forward and identified himself as the author, it was his name that has the lasting association with the Argand diagram

1797 Thomas Jefferson (1743-1826) presented a paper on the megalonyx to the American Philosophical Society. It was published as "A Memoir on the Discovery of Certain Bones of a Quadruped of the Clawed Kind in the Western Parts of Virginia," Transactions of American Philosophical Society 4:255-256, along with an account by Caspar Wistar (1761-1818). This is arguably the first American publication in paleontology, but the only paleontology paper written by Jefferson. In 1822, this huge extinct sloth was named Megalonyx jeffersoni by a French naturalist. (Megalonyx Gr. large claw). It was a bear-sized ground sloth, over 2 meters tall, widespread in North America during the last Ice Age.

1812 Jean Jacques Bret became docteur d´es sciences, having previously been professor of transcen-dental mathematics at the lyc´ee in Grenoble. Later he was involved in a prolonged polemic with J. B. E. Dubourguet concerning the fundamental theorem of algebra. *VFR

1820
Founding of the Royal Astronomical Society of England. Charles Babbage was one of the founding members. *Goldstine, The Computer from Pascal to von Neumann, p. 10 *VFR.
The 'Astronomical Society of London' was conceived on 12 January 1820 when 14 gentlemen sat down to dinner at the Freemason's Tavern, in Lincoln's Inn Fields, London. After an unusually short gestation the new Society was born on 10 March 1820 with the first meeting of the Council and the Society as a whole. An early setback, when Sir Joseph Banks induced the Duke of Somerset to withdraw his agreement to be the first President, was overcome when Sir William Herschel agreed to be the titular first President, though he never actually took the Chair at a meeting. *Royal Astronomical Society

1876  Alexander Graham Bell and his assistant, Thomas A Watson,  talked by telephone over a two-mile wire stretched between Boston and Cambridge Massachusetts. The message was a simple statement, "Mr Watson, come here, I want to see you."  The common story is that he had invented the device by accident and would not have one in his home because he saw it as a distraction.

Whatever his objections, years later on January 25 of 1915, he place another call to his former assistant, between Bell in New York and Watson in San Francisco, and they repeated the exact same dialogue as their first message.  The call was a public relations stunt by A T & T to demonstrate their ability to make transcontinental calls, a 3,400 mile communication.  The call was timed to agree with the opening of the 1915 Panama–Pacific International Exposition in San Francisco which would open on Feb 20. A telephone line was also established to New York City so people across the continent could hear the Pacific Ocean.

The transcontinental line was completed on June 17, of 1914 and successfully voice tested in July. A postage stamp commemorating the completion was released in 1914 also.

1897 Schering in Gottingen in response to a note from Fuchs that he had found materials related to Guass' Disquisitiones Arithmetica in the papers of Dirichlet describes a story that he had shared with Kronecker a decade before,
"The piece of Guass's Disquisitiones Arithmeticiae, which is found among Dirichlet's papers, is probably that portion which, as Dirichlet told me himself, he saved from the hand of Gauss when the latter lit his pipe with his manuscript of the Disquisitiones Arithmeticae on the day of his doctoral jubilee."
On 28 April of the same year, Dedekind expressed skepticism of the tale since he reasoned, if Gauss had saved the paper for fifty years he obviously valued it, and that if the anecdote were true, Dirichlet surely would have shared it with him as well. *Uta Merzbach, An Early Version of Gauss's Disquisitiones Arithmeticae, Mathematical Perspectives, 1981

 *Wik
1926 Amazing Stories was the first magazine devoted solely to science fiction. Before Amazing, science fiction stories had made regular appearances in other magazines, including some published by Gernsback, but Amazing helped define and launch a new genre of pulp fiction.The first issue appeared on 10 March 1926, with a cover date of April 1926. *Wik

1977 Rings of Planet Uranus discovered. The rings of Uranus were discovered by James L. Elliot, Edward W. Dunham, and Douglas J. Mink. More than 200 years ago, William Herschel also reported observing rings (in 1789); some modern astronomers are skeptical that he could have actually seen them, as they are very dark and faint – others are not. In 1977, the rings of Uranus were discovered from earth by stellar occultation experiments made when Uranus occulted (passed in front of) a star and it was noticed that there were dips in the brightness of the star before and after it passed behind the body of Uranus. This data suggested that Uranus was surrounded by at least five rings. Four more rings were suggested by subsequent occultation measurements from the Earth, and two additional ones were found by space probe Voyager 2, bringing the total to 11. *TIS  Uranus has two sets of rings. The inner system of nine rings consists mostly of narrow, dark grey rings. There are two outer rings: the innermost one is reddish like dusty rings elsewhere in the solar system, and the outer ring is blue like Saturn's E ring.

 *Wik

1981 Czechoslovakia issued a stamp picturing the philosopher/mathematician Bernhard Bolzano (1781–1848). [Scott #2352] *VFR

In 1982, a syzygy occurred when all nine planets aligned on the same side of the Sun. The planets are spread out over 98 degrees on this date. The four major planets, Jupiter, Saturn, Uranus, and Neptune, span an arc of some 73 degrees. *TIS The next "grand" syzygy is May 19, 2161, when eight planets (excluding Pluto) will be found within 69 degrees of each other, according to astronomers at the Kitt Peak National Observatory.

1988 An article in the Washington Post reported that young Japanese mathematician Yoichi Miyaoka had solved Fermat's Last Theorem. It would be followed with one in the New York Times the next day. Quickly however, a mistake was found. *Magnificent Mistakes in Mathematics by Alfred S. Posamentier, Ingmar Lehmann

BIRTHS
1622 Johann Heinrich Rahn (10 March 1622 in Zürich, Switzerland - 25 May 1676 in Zürich, Switzerland) mathematician who was the first to use the symbol "÷",called an obelus, for a division symbol in Teutsche Algebra (1659). The invention is also sometimes credited to British Mathematician John Pell. Here is more on the various symbols used for division .
Pell's equation y^2=ax^2+1, where a is a non-square integer, was first studied by Brahmagupta and Bhaskara II. Its complete theory was worked out by Lagrange, not Pell. It is often said that Euler mistakenly attributed Brouncker's work on this equation to Pell. However the equation appears in a book by Rahn which was certainly written with Pell's help: some say entirely written by Pell. Perhaps Euler knew what he was doing in naming the equation. *SAU He introduced the division sign (obelus, ÷) into England. The obelus was first used by Johann Rahn (1622-1676) in 1659 in Teutsche Algebra. Rahn's book was interpreted into English and published, with additions made by John Pell. According to some sources, John Pell was a key influence on Rahn and he may be responsible for the development of the symbol. The word obelus comes from a Greek word meaning a "roasting spit." The symbol wasn't new. It had been used to mark passages in writings that were considered dubious, corrupt or spurious.*TIS
The obelus as used br Rahn (Pell?) was not a mathematical operator, but a shorthand for an operation.  In the cimage below you can see that down the left column he gives instructions for how to proceed in a solution.  Notice the obelus only appears in the left column, never as an operation.  In the columns where steps of solution occur, he uses a vinculum (division bar) as the division operator.

1748 John Playfair (10 Mar 1748; 20 Jul 1819 at age 71) Scottish mathematician, He is responsible for introducing (although we now know that it was known to Proclus in the ﬁfth century) the commonly used equivalent of Euclid’s Fifth Postulate: Through a given point not on a given straight line only one line parallel to the given line may be drawn. *VFR His Illustrations of the Huttonian Theory of the Earth (1802) gave strong support to James Hutton's principle of uniformitarianism, essential to a proper understanding of geology. Playfair was the first scientist to recognise that a river cuts its own valley, and he cited British examples of the gradual, fluvial origins of valleys, to challenge the catastrophic theory (based on the Biblical Flood in Genesis) that was still widely accepted. He was also the first to link the relocation of loose rocks to the movement of glaciers. Playfair published texts on geometry, physics, and astronomy.*TIS

1762 Jeremias Benjamin Richter (10 Mar 1762; 4 Apr 1807 at age 45) was a German chemist who discovered law of equivalent proportions. He studied chemistry in his spare time while in the Prussian army (1778-1785) and afterwards while earning a Ph.D. in mathematics (1789). Richter was much influenced by Kant, whose lectures he may have attended, in the contention that science is applied mathematics. Richter looked for mathematical relationships in chemisty, convinced that substances reacted with each other in fixed proportions. He showed such a relationship when acids and bases neutralize to produce salts (1791). Thus he was the first to establish stoichiometry, which became the basis of quantitative chemical analysis. He died of tuberculosis at age 45 years.*TIS

1818 Joel E. Hendricks, (March 10, 1818 - June 9, 1893) a noted mathematician, was born in Bucks County, Pennsylvania, March 10, 1818. He early developed a love of mathematics and began to teach school at nineteen years of age. He chanced to procure Moore's Navigation and Ostrander's Astronomy and, without instruction, soon became able to work in trigonometry and calculate solar and lunar eclipses. He took up algebra while teaching and soon became master of that science without instruction. He taught mathematics two years in Neville Academy, Ohio, and then occupied a position on a Government survey in Colorado in 1861. In 1864 he located in Des Moines, Iowa and pursued his mathematical studies. In 1874 he began the publication of the Analyst, a journal of pure and applied mathematics and soon won a reputation in Europe among eminent scholars as one of the most advanced mathematicians of the day. His Analyst was taken by the colleges and universities of Europe and found a place in the best foreign libraries. His name became famous among all mathematical experts of the world. Among his correspondents were Benjamin Silliman, John W. Draper and James D. Dana; while his journal was authority at Yale and Johns Hopkins Universities. For ten years, up to 1884, this world-famous Analyst was published at Des Moines by Dr. Joel E. Hendricks. Up to the time it was discontinued, no journal of mathematics had been published so long in America. It is one of the remarkable events of the Nineteenth Century that a self-educated man should, by his own genius and industry, without instruction, reach such an exalted place among the world's great scholars. Dr. Hendricks died in Des Moines on the 9th of June, 1893. *History of Iowa From the Earliest Times to the Beginning of the Twentieth Century/Volume 4 by Benjamin F. Gue
A more complete mathematical biography of Mr. Hendricks can be found in The American Mathematical Monthly, Vol 1, #3, 1894.

1864 William Fogg Osgood (March 10, 1864, Boston - July 22, 1943, Belmont, Massachusetts) From 1899 to 1902, he served as editor of the Annals of Mathematics and in 1904–1905 was president of the American Mathematical Society, whose Transactions he edited in 1909–1910.
The works of Osgood dealt with complex analysis, in particular conformal mapping and uniformization of analytic functions, and calculus of variations. He was invited by Felix Klein to write an article on complex analysis in the Enzyklopädie der mathematischen Wissenschaften which was later expanded in the book Lehrbuch der Funktionentheorie. Besides his research on analysis, Osgood was also interested in mathematical physics and wrote on the theory of the gyroscope. Osgood's cousin, Louise Osgood, was the mother of Bernard Koopman, the statistician. *Wik Although his nickname was “Foggy,” this was not an apt description of him as a teacher. He instilled the habit of careful thought in Harvard students for 43 years. His A First Course in Differential and Integral Calculus (1907) was revised once and reprinted 17 times.*VFR
An interesting anecdote about the book dates to about 1940. Osgood chose not to use limits in his book and used infinitesimals instead. Leonidas Alaoglu taught the course at Harvard, he apparently didn't agree with Osgood's choice, and instructed the class, "Gentleman, please take pages 123 to 150 (Chapter 7 on infinitesimals) between thumb and forefinger and tear them out." *Steven Krantz, Mathematical Apocrypha Redux

1869 Benjamin Fedorovich Kagan (10 March 1869 in Shavli, Kovno (now Kaunas, Lithuania)
- 8 May 1953 in Moscow, USSR) Kagan worked on the foundations of geometry and his first work was on Lobachevsky's geometry. In 1902 he proposed axioms and definitions very different from Hilbert. Kagan studied tensor differential geometry after going to Moscow because of an interest in relativity.
Kagan wrote a history of non-euclidean geometry and also a detailed biography of Lobachevsky. He edited Lobachevsky's complete works which appeared in five volumes between 1946 and 1951. *SAU

1872 Mary Ann Elizabeth Stephansen (10 March 1872 in Bergen, Norway - 23 Feb 1961 in Espeland, Norway)received her Ph.D. in mathematics from the University of Zurich in 1902. She was the first woman from Norway to receive a doctoral degree in any subject. Her thesis area was in partial differential equations. It was not until 1971 that another Norwegian woman obtained a doctorate in mathematics. Stephansen taught at the Norwegian Agricultural College from 1906 until her retirement in 1937. She began as an assistant in physics and mathematics, then was appointed to a newly created docent position in mathematics in 1921. She published four mathematical research papers on partial differential equations and difference equations.
A extensive biography of Elizabeth Stephansen is available as a pdf document at the web site of Professor Kari Hag. This also includes description of her mathematical work. *Agnes Scott College Web site

1912 Frank Smithies FRSE (10 March 1912 Edinburgh, Scotland – 16 November 2002 Cambridge, England) was a British mathematician who worked on integral equations, functional analysis, and the history of mathematics. He was elected as a fellow of the Royal Society of Edinburgh in 1961.*Wik

1923 Val Logsdon Fitch (March 10, 1923 – February 5, 2015) American particle physicist who was co-recipient with James Watson Cronin of the Nobel Prize for Physics in 1980 for an experiment conducted in 1964 that disproved the long-held theory that particle interaction should be indifferent to the direction of time. Working with Leo James Rainwater, Fitch had been the first to observe radiation from muonic atoms; i.e., from species in which a muon is orbiting a nucleus rather than an electron. This work indicated that the sizes of atomic nuclei were smaller than had been supposed. He went on to study kaons and in 1964 began his collaboration with James Cronin, James Christenson, and René Turley which led to the discovery of violations of fundamental symmetry principles in the decay of neutral K-mesons. *TIS His birthplace is in Merriman, a village in Cherry County, Nebraska, United States. The population was 118 at the 2000 census.

DEATHS

1825 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

1888  Lucy Myers Wright Mitchell ( March 20, 1845 – March 10, 1888) Persian-American archaeologist who, though self-taught, was one of the first American women in the field, and became an internationally recognized authority on ancient Greek and Roman sculpture. She spoke Syriac, Arabic, French, German, and Italian and pursued an interest in the study of languages in classical literature. By 1873 she changed her focus to classical archeology, and subsequently became one of the foremost archeologists of her time. In Rome (1876-78) she gave parlour lectures to ladies on Greek and Roman sculpture, and also them to the museums. She was given aid and encouragement by many of the leading European archeologists. Her book, A History of Ancient Sculpture, was one of the first in the field by an American. *TIS

1921 Francis Robbins Upton (born 1852 in Peabody, Mass, 10 Mar 1921) American mathematician and physicist who, as assistant to Thomas Edison, contributed to the development of the American electric industry. Upton was the best educated of Edison's Menlo Park assistants. He was recruited by investors who felt it couldn't hurt to supplement Edison's wizardry with some advanced scientific training. He joined Edison in 1878, working at Edison's Menlo Park laboratory on mathematical problems relating to the development of the light bulb, the watt-hour meter and large dynamos. He later became a partner and general manager of the Edison Lamp Company (est. 1880). Upton's articles for Scientific American and Scribner's Monthly introduced many of Edison's inventions to the public. *TIS Upton graduated from Phillips Academy, Andover in 1870. He studied at Bowdoin College in Brunswick, Maine, at Princeton University where he received his M.S., and in Berlin, where he worked together with Hermann von Helmholtz.*Wik

1948 Evgeny Evgenievich Slutsky (19 April 1880 in Novoe, Yaroslavl guberniya, Russia - 10 March 1948 in Moscow, USSR) Slutsky was important in the application of mathematical methods in economics. Slutsky introduced stochastic concepts of limits, derivatives and integrals between 1925 to 1928 while he worked at the Conjuncture Institute. In 1927 he showed that subjecting a sequence of independent random variables to a sequence of moving averages generated an almost periodic sequence. This work stimulated the creation of stationary stochastic processes. He also studied correlations of related series for a limited number of trials. He obtained conditions for measurability of random functions in 1937. He applied his theories widely, in addition to economics mentioned above he also studied solar activity using data from 500 BC onwards. Other applications were to diverse topics such as the pricing of grain and the study of chromosomes. *SAU

1971 Lester Halbert Germer (10 Oct 1896, Chicago, Ill; 10 Mar 1971) was a American physicist who, with his colleague Clinton Joseph Davisson, conducted an experiment (1927) that first demonstrated the wave properties of the electron. They showed that a beam of electrons scattered by a crystal produces a diffraction pattern characteristic of a wave. This experiment confirmed the hypothesis of Louis-Victor de Broglie, a founder of wave mechanics, that the electron should show the properties of an electromagnetic wave as well as a particle. He also studied thermionics, erosion of metals, and contact physics.*TIS
Lester Germer (right) with Clinton Joseph Davisson (left) 1927

1981 Yaroslav Borisovich Lopatynsky (9 Nov 1906 in Tbilisi, Georgia, Russia - 10 March 1981 in Donetsk, USSR) Lopatynsky's contributions to the theory of differential equations are particularly important, with important contributions to the theory of linear and nonlinear partial differential equations. He worked on the general theory of boundary value problems for linear systems of partial differential equations of elliptic type, finding general methods of solving boundary value problems. *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 & Campbell