Thursday, 10 August 2017

On This Day in Math - August 10

I have made this letter longer than usual, because I lack the time to make it short.
~Blaise Pascal

The 222nd day of the year; 222 is called a sphenic (Greek for wedge) number. They have three distinct prime factors. 30= 2x3x5 is the smallest sphenic number. Can you find two consecutive numbers that are both sphenic numbers?

More??
222 = (3!)3 + (2!)2 + (1!)1 + (0!)0 *Derek Orr ‏@Derektionary

222 is the number of lattices on 10 unlabeled nodes.
and 222 is the sum of consecutive primes.

EVENTS
1548 Tartaglia and Ferrari met in a mathematical debate in the church of Santa Maria del Giardino dei Minori Osservanti in Milan. In the presence of a distinguished audience, which included the governor of Milan as judge, they argued over a problem that Ferrari posed on 24 May 1547, and which Tartaglia could not resolve. The next day, Tartaglia left in disgrace for his native Brescia. *VFR  For details about this story you probably didn't know (I didn't) see this post from the Renaissance Mathematicus.

1675 Greenwich Observatory founded. *VFR The observatory was commissioned in 1675 by King Charles II, with the foundation stone being laid on 10 August. Charles II had appointed John Flamsteed as his first Astronomer Royal in March of that year and oversaw the laying of the foundation stone.  Rebekah Higgitt explains why this is "An auspicious day to found an observatory" at her Teleskopos blog.

1732 Pell equations are forever (mis)named. Euler writes to Goldbach and mentions the equation x2 -A y2 =1 and adds;
Dr. Pell, an Englishman, devised a unique way of solving problems of this kind, as shown in the works of Wallis."
Most historical authorities believe this was due to a cursory or misreading of Wallis' work in which Pell is often mentioned, but not in regard to this equation. "Pell has done it no other service than to set it forth again in a much read work," i.e., in the notes to the English translation which Brancker,4 in 1668, published of the "Teutschen Algebra" of Rahn. (Pell was a teacher of Rahn and much of the work is based on Pell's methods. Pell wsa also influential in the English translation of the work.) *Edward Everett Whitford, The Pell Equation

1792 Against his better judgment, Monge was forced into the Ministry of the Navy and the Colonies of France. *VFR

1846 The Smithsonian Institution established in Washington. Benjamin Peirce was on the ﬁve-member committee that drew up the program for its organization. *VFR In 1846, an Act of Congress signed by President James K. Polk established the Smithsonian Institution as a trust to administer the generous bequest of James Smithson, an amount over $500,000. In 1826, James Smithson, a British scientist, drew up his last will and testament, naming his nephew as beneficiary. Smithson stipulated that, should the nephew die without heirs (as he would in 1835), the estate should go “to the United States of America, to found at Washington, under the name of the Smithsonian Institution, an establishment for the increase and diffusion of knowledge among men.” The motives behind Smithson’s bequest remain mysterious; he had never traveled to the U.S. and seems to have had no correspondence with anyone there.*TIS 1912 “Some time between August 10 and August 16 it became clear to Einstein that Riemannian geometry is the correct mathematical tool for what we now call general relativity.” [From Abraham Pais, Subtle is the Lord ... The Science and the Life of Albert Einstein, as quoted in the New York Times Book Review, Nov. 28, 1982, p. 9]*VFR 1939 Albert Einstein “wrote” President F. D. Roosevelt that “Some recent work by E. Fermi and L. Szilard ... leads me to expect that the element uranium may be turned into a new and important source of energy in the immediate future. ... This new phenomenon would also lead to the construction of bombs, and it is conceivable—though much less certain—that extremely powerful bombs of a new type may be constructed.” The letter, drafted by Fermi, Szilard, and Wigner and seems not to have actually been signed by Einstein until August 10, and was then given to Alexander Sachs, a confident of Roosevelt, who did not deliver it to him until October 30. Roosevelt quickly started the Manhattan Project. Einstein later regretted signing this letter. *(VFR & Brody & Brody); (the letter can be read at Letters of Note) They recognized the process could generate a lot of energy leading to power and possibly weapons. There was also concern the Nazi government of Germany was already searching for an atomic weapon. This letter would accomplish little more than the creation of a "Uranium Committee" with a budget of$6,000 to buy uranium and graphite for experiments.
Sir Fred Soddy's book, The Interpretation of Radium, inspired H G Wells to write The World Set Free in 1914, and he dedicated the novel to Soddy's book. Twenty years later, Wells' book set Leo Szilard to thinking about the possibility of Chain reactions, and how they might be used to create a bomb, leading to his getting a British patent on the idea in 1936. A few years later Szilard encouraged his friend, Albert Einstein , to write a letter to President Roosevelt about the potential for an atomic bomb. The prize-winning sc1802 Germain Henri Hess (August 7, 1802 – November 30, 1850)Swiss-born Russian chemist whose studies of heat in chemical reactions formed the foundation of thermochemistry. He formulated an empirical law, Hess's law of constant heat summation (1840), which states that the heat evolved or absorbed in a chemical process is the same whether the process takes place in one or in several steps. It is explained by thermodynamic theory, which holds that enthalpy is a state function. Chemists have made great use of the law of Hess in establishing the heats of formation of compounds which are not easily formed from their constituent elements. His early investigations concerned minerals and the natural gas found near Baku, and he also discovered the oxidation of sugars to yield saccharic acid.*TIS

ience-fiction writer, Frederik Pohl , talks about Szilard's epiphany in Chasing Science (pg 25),
".. we know the exact spot where Leo Szilard got the idea that led to the atomic bomb. There isn't even a plaque to mark it, but it happened in 1938, while he was waiting for a traffic light to change on London's Southampton Row. Szilard had been remembering H. G. Well's old science-fiction novel about atomic power, The World Set Free and had been reading about the nuclear-fission experiment of Otto Hahn and Lise Meitner, and the lightbulb went on over his head."

BIRTHS
787 Albumasar (10 Aug 787, 9 Mar 886 at age 98)Persian astrologer, a.k.a. Abu Ma'shar al-Balkhi, or Ja'far ibn Muhammad, who was the leading astrologer of the Muslim world. He is known primarily for his theory that the world, created when the seven planets were in conjunction in the first degree of Aries, will come to an end at a like conjunction in the last degree of Pisces. *TIS

1602 Gilles Personne de Roberval born. *VFR(according to some, see August 9th)

1839 Aleksandr Grigorievich Stoletov (August 10, 1839 – May 27, 1896) was a Russian physicist, founder of electrical engineering, and professor in Moscow University. He was the brother of general Nikolai Stoletov. By the end of the 20th century his disciples had headed the chairs of Physics in five out of seven major universities in Russia.
His major contributions include pioneer work in the field of ferromagnetism and discovery of the laws and principles of the outer photoelectric effect.*Wik

1856 William Willett (10 August 1856 – 4 March 1915) English builder who invented Daylight Saving Time. He claimed he had the idea while taking an early summer morning ride in Petts Wood near to his home in Chislehurst, London. He observed that many blinds were still down, although there was already good daylight, yet many made no use of it. He used his wealth as a prominent home builder to campaign for a scheme of adjusting clocks with the season and published a pamphlet in 1907. His original idea was to make four weekly changes of 20-mins each, for a total of 80-mins. The first Daylight Saving Bill, proposing a single one hour at the change of season failed in 1908. After his death, the idea was adopted during WW I for wartime fuel savings. A memorial was erected in Petts Wood.*TIS A sun dial, right, Memorial was erected in the Pett"s Wood in his honor.

1859 Georg Alexander Pick (August 10, 1859 – July 26, 1942) was an Austrian mathematician. He died in the Theresienstadt concentration camp. Today he is best known for Pick's formula for determining the area of lattice polygons. He published it in an article in 1899; it was popularized when Hugo Dyonizy Steinhaus included it in the 1969 edition of Mathematical Snapshots. Pick headed the committee at the (then) German university of Prague which appointed Albert Einstein to a chair of mathematical physics in 1911. Pick introduced Einstein to the work of Italian mathematicians Gregorio Ricci-Curbastro and Tullio Levi-Civita in the field of absolute differential calculus, which later in 1915 helped Einstein to successfully formulate General relativity.*Wik A really nice article about this theorem with references and interactive graphics is Found at Alexander Bogomolny's Cut The Knot web site.
Does Pick’s theorem generalise to 3 dimensions? In 1957, John Reeve delivered some bad news. Reeve tetrahedra have vertices at: (0,0,0), (1,0,0), (0,1,0), & (1,1,r) where r is a positive integer. All Reeve tetrahedra contain the same number of lattice points (just their four vertices). But their volumes are different. But then, in 1967 Eugene Erhart found a way to do it in 3 dimensions and more. He showed that all integral polytopes had an Ehrhart polynomial that encodes the relationship between the volume (and several other characteristics, it seems) of a polytope and the number of integer points the polytope contains. *Richard Elwes, Pick’s Theorem & Ehrhart Polynomials

1889 Charles Brace Darrow (August 10, 1889 – August 28, 1967) was an American inventor who designed the board game Monopoly. He had invented the game on 7 Mar 1933, though it was preceded by other real-estate board games. On 31 Dec 1935, a patent was issued for the game of Monopoly assigned to Parker Brothers, Inc., by Ch*arles Darrow of Pennsylvania (No. 2,026,082). The patent titled it a "Board Game Apparatus" and described it as "intended primarily to provide a game of barter, thus involving trading and bargaining" in which "much of the interest in the game lies in trading and in striking shrewd bargains." Illustrations included with the patent showed not only the playing board and pieces, cards, and the scrip money. *TIS

1901 Franco Dino Rasetti (August 10, 1901 – December 5, 2001) was an Italian scientist. Together with Enrico Fermi, he discovered key processes leading to nuclear fission. Rasetti refused to work on the Manhattan Project, however, on moral grounds.*Wik

1926 Carol (Vander Velde)Karp (10 August 1926, Forest Grove, Ottawa County, Michigan – 20 August 1972, Maryland) was born in Forest Grove, Michigan. She received her Ph.D. in 1959 from Southern California under the direction of Leon Henkin. She created the ﬁeld of Inﬁnitary Logics which studies logics such as Lω,ω which allowed for the conjunction and disjunction of countably many formulas. This work has become very important in modern logic. *VFR

DEATHS

1802 Franz Aepinus (December 13, 1724 – August 10, 1802) was a German scientist who did important work on electricity and magnetism. Aepinus' study of electricity and magnetism led to the publication of his book Tentamen theoriae electricitatis et magnetismi (An Attempt at a Theory of Electricity and Magnetism) in 1759. It was the first work to apply mathematics to the theory of electricity and magnetism and "... is one of the most original and important books in the history of electricity."
Euler was working at the Berlin Academy during the time that Aepinus worked there, and in fact Aepinus lived in Euler's house for the two years that he was in Berlin.
Other achievements of Aepinus include improvements to the microscope, and his demonstration of the effects of parallax in the transit of a planet across the Sun's disk (1764). However, except for his masterpiece on electricity and magnetism, his work was no better than competent.*SAU

1843 Robert Adrain (30 September 1775 – 10 August 1843) was a scientist and mathematician, considered one of the most brilliant mathematical minds of the time in America.. Irish born,  Adrain was an editor of and contributor to the Mathematical Correspondent, the first mathematical journal in the United States. Later he twice attempted to found his own journal, The Analyst, or, Mathematical Museum, but in both the 1808 and 1814 attempts it did not attract sufficient subscribers and quickly ceased publication. In 1825 he founded a somewhat more successful publication targeting a wider readership, The Mathematical Diary, which was published through 1832.He is chiefly remembered for his formulation of the method of least squares, published in 1808. Adrain certainly did not know of the work of C.F. Gauss on least squares (published 1809), although it is possible that he had read A.M. Legendre's article on the topic (published 1804).*Wik He was one of the ﬁrst American mathematicians to do creative work. *VFR

1915 Henry Gwyn Jeffreys (23 November 1887 – 10 August 1915) Moseley English physicist who experimentally demonstrated that the major properties of an element are determined by the atomic number, not by the atomic weight, and firmly established the relationship between atomic number and the charge of the atomic nucleus. He began his research under Ernest Rutherford while serving as lecturer at the Univ. of Manchester. Using X-ray photographic techniques, he determined a mathematical relation between the radiation wavelength and the atomic numbers of the emitting elements. Moseley obtained several quantitative relationships from which he predicted the existence of three missing elements (numbers 43, 61, and 75) in the periodic table, all of which were subsequently identified. Moseley was killed in action during WW I.*TIS
When World War I broke out in Western Europe, Moseley left his research work at the University of Oxford behind to volunteer for the Royal Engineers of the British Army. Moseley was assigned to the force of British Empire soldiers that invaded the region of Gallipoli, Turkey, in April 1915, as a telecommunications officer. Moseley was shot and killed during the Battle of Gallipoli on August 10, 1915, at the age of just 27. Some prominent authors have speculated that Moseley could have been awarded the Nobel Prize in Physics in 1916, had he not died in the service of the British Army.*Wik

1929 Pierre Joseph Louis Fatou (28 February 1878 – 10 August 1929) was a French mathematician working in the field of complex analytic dynamics. He entered the École Normale Supérieure in Paris in 1898 to study mathematics and graduated in 1901 when he was appointed an astronomy post in the Paris Observatory. Fatou continued his mathematical explorations and studied iterative and recursive processes such as z == z2+C . Fatou was particularly interested in the case where Z0 = 0, which was later analysed with computers by Benoît Mandelbrot to generate graphical representations of the behaviour of this series for each point, c, in the complex plane – now popularly called the Mandelbrot set.
Fatou wrote many papers developing a Fundamental theory of iteration in 1917, which he published in the December 1917 part of Comptes Rendus. His findings were very similar to those of Gaston Maurice Julia, who submitted a paper to the Académie des Sciences in Paris for their 1918 Grand Prix on the subject of iteration from a global point of view. Their work is now commonly referred to as the generalised Fatou–Julia theorem.*Wik

1945 Robert Hutchings Goddard (October 5, 1882 – August 10, 1945) American professor, physicist and inventor, "father of modern rocketry". From age 17 Goddard was interested in rockets (1899) and by 1908 he conducted static tests with small solid-fuel rockets. He developed mathematical theory of rocket propulsion (1912) and proved that rockets would functioned in a vacuum for space flight (1915). During WW I, Goddard developed rocket weapons. He wrote A Method of Reaching Extreme Altitudes, in 1919. Over the following two decades he produced a number of large liquid-fuel rockets at his shop and rocket range at Roswell, N.M. During WW II he developed rocket-assisted takeoff of Navy carrier planes and variable-thrust liquid-fuel rocket motors. At the time of his death Goddard held 214 patents in rocketry.*TIS Goddard is buried at Hope Cemetery in Worcester, Massachusetts, his birthplace.

1960 Oswald Veblen, (June 24, 1880 – August 10, 1960) a world famous geometer, died in Brookline, MA, at age 80. *VFR American mathematician who made important contributions in early topology, and in projective and differential geometry - work which found applications in atomic physics and the theory of relativity. In 1905, he proved the Jordan curve theorem, which states that every non-self-intersecting loop in the plane divides the plane into an "inside" and an "outside". Although it may seem obvious in its statement, it is a very difficult theorem to prove. During WW II, he was involved in overseeing the work that produced the pioneering ENIAC electronic digital computer. His name is commemorated by the American Mathematical Society's Oswald Veblen Prize. Awarded every five years, it is the most prestigious award in recognition of outstanding research in geometry.*TIS

1981 Jack Carl Kiefer (January 25, 1924 – August 10, 1981) Kiefer's main research area was the optimal design of experiments, and about half his 100 publications dealt with that topic. However he also wrote papers on a whole variety of topics in mathematical statistics including decision theory, inventory theory, stochastic approximation, queuing theory, nonparametric inference, estimation, sequential analysis, and conditional inference. His first paper Almost subminimax and biased minimax procedures written jointly with his fellow graduate student at Columbia, Peter Frank, was published in 1951. A paper Sequential minimax search for a maximum which Kiefer published in the Proceedings of the American Mathematical Society in 1953 was based on his master's thesis. The method of search proposed in the paper, namely the Fibonacci Search, became a widely used tool. *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