Saturday 9 May 2020

On This Day in Math - May 9

Margarita philosophica of Gregor Reisch *MAA

If you ask a drunkard what number is larger, 2/3 or 3/5, he might not be able to tell you. But if you rephrase the question: What is better, 2 bottles of vodka for 3 people, or 3 bottles of vodka for 5 people, he will tell you right away.
Israel Gelfand (from Love and Math, by Edward Frenkel)

The 130th day of the year; 130 is the sum of the factorials of the first five terms of the Fibonacci sequence.
Did you know that any four terms of the Fibonacci sequence will give you a Pythagorean triangle? If we use 3, 5, 8, 13 you can get 3+13 = 39, 2*5*8 = 80, and 3*8 + 5 * 13 = 89, and {39, 80, 89} is a Pythagorean Right triangle with an area of 1560 (which is 3 * 5 * 8 * 13) Which makes it a Heronian triangle. First observed by Charles W. Raine in 1948. For more on this Pythagonacci connection

130 is the sum of the squares of the divisors of 10, ( \( 1^2 + 2^2 + 5^2 + 10^2 = 130 \)
130 is also the only number equal to the sum of the squares of its first 4 divisors: 130 = 1^2 + 2^2 + 5^2 + 10^2.*Prime Curios

This is the 46th day of the year that is the sum of two squares.


1562 In the evening Don Carlos, son of Phillip II of Spain, and heir to the throne lay dying from a fall on a staircase a month earlier. In hopes of a miracle, the king prayed, and then caused, or allowed, the body of a 15th-Century priest from the village to be brought and laid by his son. Within days the young man recovered, and the grateful father commissioned the royal clockmaker, Juanelo Turriano, to create one of the first human form automatons in Europe, the praying monk. The incredible wind up device would walk lifelike in a square, nodding his head as his mouth moves in prayer, sometimes beating his chest, and kissing his cross and rosary. The device is now in the Smithsonian, and it still works.
For more about the story read here,  and more pictures of the automaton just search Praying Monk on your favorite search engine. 

1664 Hooke speaks to Royal Society on finding the Giant Red Spot on Jupiter OUHOS Collections@OUHOSCollection

1694 Johann Bernoulli, in a letter to Leibniz, introduced the term and the explicit process of “sepera­tio indeterminatarum” or separation of variables for solving differential equations. He published it in Acta eruditorum in November, 1694. [Ince, 531] *VFR In 1691 the inverse problem of tangents led Leibniz to the implicit discovery of the method of separation of variables.

1831 Galois party toast will lead to his arrest. Derbyshire describes the events in "Unknown Quantity, a real and imaginary history of Algebra."

1848 “Proficiency in Algebra, the elements of geometry, trigonometry, and surveying, will give you the art of developing truth by the skilful use of the reasoning powers, and, besides, store your mind with a species of knowledge of daily practical utility to a lawyer. ... It is the helm of the mind, stering it over the shortest route from the point of departure to the destination—from cause to effect.” So wrote the American soldier Albert Sindney Johnson (1803–1862) to his son. From William Preston Johnson (the son), The Life of General Albert Sindney Johnson (1878),p. 162, as quoted by Florian Cajori in Mathematics in Liberal Education (1928), p. 103. *VFR

1854  There is a "letter from Rankine to Thomson of 9 May 1854 in which he suggests more reasonably that the leading term in the departure from the perfect-gas laws is linear in the density, or (1/V). This turned out to be so .."  (JAMES JOULE, WILLIAM THOMSON AND THE CONCEPT OF A PERFECT GAS by J. S. ROWLINSON)

1914 Think of all the work that mothers do in raising their children. Mothers need to be celebrated! President Woodrow Wilson proclaimed May 9, 1914, the first Mother's Day. He asked Americans on that day to give a public "thank you" to their mothers and all mothers.
Anna Jarvis of Philadelphia wanted to remember her own mother along with all mothers. Anna’s mother had been very active in working to improve the health of people in her community. Jarvis’s mother also organized a Mother’s Friendship event in her community to bring confederate and union soldiers together for a peaceful celebration. Many other women such as Julia Ward Howe, Elizabeth Cady Stanton and Elizabeth Smith also fought for peace and encouraged mothers to speak out. Anna Jarvis convinced her mother’s church to celebrate Mother’s Day on the anniversary of her mother’s death, and campaigned for a national day honoring mothers. Because of Jarvis’s hard work, Woodrow Wilson chose that date for the national holiday. (Library of Congress web site) This year it's May 13... Happy Birthday to Mom's everywhere.

1926 Americans Richard Byrd and Floyd Bennett became the first men to fly over the North Pole. *TIS

1972 100 high school students took the first U.S.A. Mathematical Olympiad. The purpose was to discover secondary school students with superior mathematical talent. One of the five problems on the exam was: “A random number selector can only select one of the nine integers 1, 2,..., 9, and it makes these selections with equal probability. Determine the probability that after n selections (for n larger than 1), the product of the n numbers selected will be divisible by 10.” For the winners, the other problems, and the solutions, see AMM 80 (1973), pp 276–281. *VFR

2013 Surfs Up, Sun's Not, in Hawaii, at least for a moment. Solar Eclipse in Honolulu *Carey Johnson ‏@TheTelescopeGuy

2016 It happens only a little more than once a decade – and the next chance to see it is TODAY!. Throughout the U.S., sky watchers can watch Mercury pass between Earth and the sun in a rare astronomical event known as a planetary transit. Mercury will appear as a tiny black dot as it glides in front of the sun’s blazing disk over a period of seven and a half hours. Three NASA satellites will be providing images of the transit and one of them will have a near-live feed. *NASA


1746  Gaspard Monge, (9 May 1746 – 28 July 1818) noted geometer, son of a peddler and knife grinder   at Beaune, France. Today there is a statue of him in his home town. (I stumbled across it while visiting vineyards).*VFR One of the founders of descriptive geometry (the mathematics of projecting solid figures onto a plane, upon which modern engineering drawing is based) and the application of the techniques of analysis to the theory of curvature. The latter ultimately led to the revolutionary work of Georg Riemann on geometry and curvature. He became a close friend of Napoleon and was appointed minister for the navy (1792-93), but was stripped of all honours on the restoration of the Bourbons. He died in poverty. *TIS
As an active Jacobin, he was acting head of the government on the day Louis XVI was executed.  He was also Minister of the Navy. He was in official disfavor when he died and had been expelled from the Academy in 1816 (along with Lazare Carnot), but his students erected a monument with a bust. MONGE was buried in the cemetery of Père Lachaise (Mausoleum at right below) but in 1989, he was translated to the Panthéon.

1785 James Pollard Espy (9 May 1785, 24 Jan 1860) American meteorologist who was one of the first to collect meteorological observations by telegraph. He gave apparently the first essentially correct explanation of the thermodynamics of cloud formation and growth. Every great atmospheric disturbance begins with a rising mass of heated, thus less dense air. While rising, the air mass dilates and cools. Then, as water vapour precipitates as clouds, latent heat is liberated so the dilation and rising continues until the moisture of the air forming the upward current is practically exhausted. The heavier air flows in beneath, and, finding a diminished pressure above it, rushes upward with constantly increasing violence. Water vapour precipitated during this atmospheric disturbance results in heavy rains.*TIS

1876 Gilbert Ames Bliss (9 May 1876, Chicago – 8 May 1951, Harvey, Illinois) did important work in the calculus of variations. Through­out his career at Chicago he stressed the importance of a strong union between teaching and research. *VFR  This is another one who died within a week of their birthday (he died on May 8). 

1898 Arend Heyting
(May 9, 1898 – July 9, 1980) is important in the development of intuitionistic logic and algebra.He was a student of Luitzen Egbertus Jan Brouwer at the University of Amsterdam, and did much to put intuitionistic logic on a footing where it could become part of mathematical logic. Heyting gave the first formal development of intuitionistic logic in order to codify Brouwer's way of doing mathematics. The inclusion of Brouwer's name in the Brouwer–Heyting–Kolmogorov interpretation is largely honorific, as Brouwer was opposed in principle to any formalisation of intuitionistic logic (and went as far as calling Heyting's work a "sterile exercise").   *Wik

1936 Alexandre Aleksandrovich Kirillov (May 9,1936) is a Soviet and Russian mathematician, renowned for his works in the fields of representation theory, topological groups and Lie groups. In particular he introduced the orbit method into representation theory.
Kirillov studied at Moscow State University where he was a student of Israel Gelfand. His Ph.D. (kandidat) dissertation Unitary representations of nilpotent Lie groups 1962 was so successful that he was awarded the much higher degree of Doctor of Science instead. At the time he was the youngest Doctor of Science in the Soviet Union. He worked at the Moscow State University until 1994 when he became the Francis J. Carey Professor of Mathematics at the University of Pennsylvania.
During his school years, Kirillov was a winner of many mathematics competitions, and he is still an active organizer of Russian mathematical contests. Kirillov is an author of many popular school-oriented books and articles.
In 2012 he became a fellow of the American Mathematical Society.
Kirillov's son, Alexander Kirillov, Jr., is also a mathematician, working on the representation theory of Lie groups at the State University of New York at Stony Brook. *Wik

1950 Esteban Terrades i Illa (15 September 1883;Barcelona,- 9 May 1950,Madrid,) was a Spanish mathematician, scientist and engineer. He researched and taught widely in the fields of mathematics and the physical sciences, working not only in his native Catalonia, but also in the rest of Spain and in South America. He was also active as a consultant in the Spanish aeronautics, electric power, telephone and railway industries. *Wik


1525 Gregor Reisch (born at Balingen in Württemberg, about 1467; died at Freiburg, Baden, 9 May 1525) was a German Carthusian humanist writer. He is best known for his Margarita philosophica, which first appeared at Freiburg in 1503. It is an encyclopedia of knowledge intended as a text-book for youthful students, and contains in twelve books Latin grammar, dialectics, rhetoric, arithmetic, music, geometry, astronomy, physics, natural history, physiology, psychology, and ethics. The usefulness of the work was increased by numerous woodcuts and a full index. *Wik
Image of Calculating-Table by Gregor Reisch: Margarita Philosophica, 1503. The woodcut shows Arithmetica instructing an algorist and an abacist (inaccurately represented as Boethius and Pythagoras). There was keen competition between the two from the introduction of the Algebra into Europe in the 12th century until its triumph in the 16th.

1931 Albert Abraham Michelson (December 19, 1852 – May 9, 1931) German-born American physicist who accurately measured the speed of light and received the 1907 Nobel Prize for Physics "for his optical precision instruments and the spectroscopic and metrological investigations" he carried out with them. He designed the highly accurate Michelson interferometer and used it to establish the speed of light as a fundamental constant. With Edward Morley, he also used it in an attempt to measure the velocity of the earth through the ether (1887). The experiment yielded null results that eventually led Einstein to his theory of relativity. He measured the standard meter bar in Paris to be 1,553,163.5 wavelengths of the red cadmium line (1892-3). *TIS  There is a marker near the place where the experiment was done.  It says, "Near this spot, in July 1887, Dr. Albert A. Michelson of Case and Dr. Edward W. Morley of Western Reserve University conducted the world-famous Michelson-Morley experiment, one of the outstanding scientific achievements of the 19th century and a cornerstone of modern physics. In commemoration, this tablet has been set in stone by both colleges on December 19, 1952, the 100th anniversary of Dr. Michelson's birth.

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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