Sunday, 9 April 2017

On This Day in Math - April 9

A Few Good Men

Frustra fit per plura, quod fieri potest per pauciora.
It is vain to do with more what can be done with less.
~William of Ockham

If 99 divides some 4-digit number ABCD, then 99 also divides BCDA, CDAB, and DABC

There are 9 ways to express 99 as p + 2q, where p and q are prime. (Students might wonder why this strange p+2q idea should be interesting. It is related to a conjecture of Lemoine. 
The conjecture states that any odd number greater than 5 can be written as p+2q where p and q are primes. Students might try to find the several numbers smaller than 99 that can be expressed in p+2q form over 10 ways.)  

99 is the largest number that is equal to the sum of its digits plus the product of its digits: 99 = 9 + 9 + 9 * 9

and 99 is the alphanumeric value of THIRTEEN *Number Gossip

992 = 9801 and 98 + 01 = 99 so it is a Kaprekar number, named after D. R. Kaprekar, an Indian recreational mathematician.

and David Marain ‏@dmarain recently reminded me 1/992 = 0.000102030405060708091011121314151617181920212223242526272... The question for students, It must be a repeating decimal, when does it start to repeat?

(and there was something about bottles of beer on the wall, but they don't seem to be there anymore. Maybe someone took them down...)

1626 English philosopher, Francis Bacon, died a month after performing his first scientific experiment. He stuffed a chicken with snow to see if this would cause it to spoil less rapidly. The chill he caught during this experiment led to his death. [A. Hellemans and B. Bunch. The Timetables of Science, p . 32]. *VFR

1673 Leibniz elected Fellow of the Royal Society of London, a position of which he was very desirous. [The Correspondence of Henry Oldenburg, 9, p. 583]. *VFR

1752 A letter from James Short is read to the Royal Society to inform them of a paper by Euler on "Correcting the Aberrations in the Object-Glasses of Refracting Telescopes." *Phil Trans. 1753 48:287-296

1790 John Dalton wrote to George Bewley asking for advice on his career and describing a physiological experiment on himself. *ScienceMuseumArchive ‏@GalileosBalls

1810 Laplace announced his central limit theorem. Nowhere in his work did Laplace state a general theorem which would have corresponded to the CLT in today’s sense. He only treated particular problems concerning the approximation of probabilities of sums or linear combinations of a great number of random variables.

In 1895, a spectrogram made by American astronomer James Keeler proved that the rings of Saturn were indeed composed of meteoric particles, as predicted by James Maxwell. If the rings were solid, observations would show uniform rotation. However, Keeler's spectrogram of light reflected from Saturn's rings showed a Doppler shift indicating a variation in radial velocity. Thus, particles in the inner part of a ring, closer to Saturn, move at a different rotational speed from those in more distance parts of a ring, as predicted by Kepler's 3rd law. Keeler published A Spectroscopic Proof of the Meteoric Constitution of Saturn's Rings in the May 1895 issue of Astrophysical Journal, vol. 1, p.416, the journal he co-founded with George E. Hale.*TIS

1940 The German Army crossed the border and invaded Denmark. In response, the Hungarian chemist George de Hevesy dissolved the gold Nobel Prizes of Max von Laue and James Franck in aqua regia to prevent the Nazis from stealing them. He placed the resulting solution on a shelf in his laboratory at the Niels Bohr Institute. After the war, he returned to find the solution undisturbed and precipitated the gold out of the acid. The Nobel Society then recast the Nobel Prizes using the original gold. *Wik

1959 Legendary architect Frank Lloyd Wright died on this day in 1959. He was posthumously recognized as "the greatest American architect of all time" by the AIA *Shaun Usher ‏@LettersOfNote

In 1959, NASA announced the selection of America's first seven astronauts for project Mercury. Scott Carpenter, Gordon Cooper, John Glenn, Gus Grissom, Wally Schirra, Alan Shepard and Donald Slayton were chosen from 110 applicants. Their training program at Langley, which ranged from a graduate-level course in introductory space science to simulator training and scuba-diving. Project Mercury, NASA's first high profile program, was an effort to learn if humans could survive in space. NASA required astronaut candidates to be male, not older than 40 years of age, not more than 5' 11" height and in excellent physical condition. On 5 May 1961, Shepard became the first American in space. *TIS

In 1981, Nature published the longest scientific name in history. With 16,569 nucleotides, the systematic name for human mitochondrial DNA is 207,000 letters long. *TIS

1650 Jean Le Fevre, born in 1650 (*SAU gives 1652 for D.O.B.) in Lisieux and died in 1706 in Paris ,was a French astronomer.
Worker weaver until the age of thirty years, Jean Le Fevre was an autodidact who acquired, during his leisure hours, great knowledge in mathematics and astronomy. He calculated several eclipses with great accuracy and accomplished excellent observations using instruments that had been provided.
Le Fevre advised Picard through Philippe de La Hire. Le Fevre has successfully computed a table of the passage of the Moon from the meridian completed in 1680 in Paris where he was given a pension of the Academy of Sciences.
Then he delivered the famous astronomical tables correctly represent the solar and lunar eclipses and continued writing the Knowledge of time. He knew better than calculating eclipses La Hire with whom he worked on a number of projects until he accused it of stealing astronomical tables that were published. *French Wikipedia.

1770 Thomas Johann Seebeck (9 Apr 1770; 10 Dec 1831 at age 61) German physicist who discovered (1821) that an electric current flows between different conductive materials that are kept at different temperatures, known as the Seebeck effect. It is the basis of the thermocouple and is considered the most accurate measurement of temperature. It is also a key component of the semi-conductor, the foundation of the modern computer business. Seebeck's work was the basis of German physicist Georg Simon Ohm (1789-1854) discoveries in electricity and of French physicist Jean Charles Athanase Peltier (1785-1845), whose Peltier effect became well known as a way to use electricity to freeze water (air conditioning, refrigeration). *TIS

1791 George Peacock (9 Apr 1791; 8 Nov 1858 at age 67)
English mathematician who, with fellow Cambridge undergraduates Charles Babbage and John Herschel brought reform to nomenclature in English mathematics. They formed the Analytical Society (1815) whose aims were to bring the advanced methods of calculus from Europe to Cambridge to replace the increasingly stagnant notation of Isaac Newton from the previous century. The Society produced a translation of a book of Lacroix in the differential and integral calculus. In 1830, he published Treatise on Algebra which attempted to give algebra a logical treatment, and which went at least partway toward the establishment of symbolic algebra. Instead of using only numbers he used objects, and showed the associativity and commutativity of these objects. reformed British Algebra, Dean of Ely Cathedral. *TIS

1806 The great Victorian engineer Isambard Kingdom Brunel was born. In 1822, young Isambard began work in his father’s cramped little office in the City. The older Brunel, who had designed machines for making army boots and, significantly, a tunneling shield which made underwater tunneling possible, was involved in projects ranging from suspension bridges and dock installations to a projected canal in Panama. Three years later he began his greatest undertaking, the construction of the first tunnel under the Thames, from Rotherhithe to Wapping. His son hurled himself into it with the superhuman energy and resourcefulness that would mark his whole adult life. He was lucky to survive the desperate moment in 1828 when the river broke into the tunnel and a massive wave swept along it. Six of the workforce were killed and young Isambard was badly hurt and took months to recover.
He went on to start a brilliantly successful separate career of his own and to create the Great Western Railway and the first transatlantic steamships. His father, knighted in 1841, died in 1849 at the age of eighty. The even more famous son lived on for only another ten years, to die at fifty-three in 1859. *History Today ‏@HistoryToday

1813 Robert R Anstice (9 April 1813 in Madeley, Shropshire, England - 17 Dec 1853 in Wigginton (near Tring), Hertfordshire, England) During his time as vicor at Wigginton, Anstice became interested in the mathematical work of another rector, Kirkman, who had written on the subject of Steiner triple systems (as they are now called). In one of his papers Kirkman gave an elegant construction of a resolvable Steiner triple system on 15 elements (the famous Kirkman 15 schoolgirls problem), making use of what are now known as a Room square of order 8 and the Fano plane. Kirkman stated that the generalisation of this construction seemed very hard. *SAU

1816 Charles-Eugène Delaunay (9 Apr 1816; 5 Aug 1872 at age 56) French mathematician and astronomer whose theory of lunar motion advanced the development of planetary-motion theories. After 20 years of work, he published two volumes on lunar theory, La Théorie du mouvement de la lune (1860,1867). This is an important case of the three body problem. Delaunay found the longitude, latitude and parallax of the Moon as infinite series. These gave results correct to 1 second of arc but were not too practical as the series converged slowly. However this work was important in the beginnings of functional analysis. Delaunay succeeded Le Verrier as director of the Paris Observatory in 1870 but two years later he and three companions drowned in a boating accident. *TIS

1830 Eadweard Muybridge (9 Apr 1830; died 8 May 1904 at age 74) English photographer important for his pioneering work in photographic studies of motion and in motion-picture projection. For his work on human and animal motion, he invented a superfast shutter. Leland Stanford, former governor of California, hired Muybridge to settle a hotly debated issue: Is there a moment in a horse’s gait when all four hooves are off the ground at once? In 1972, Muybridge took up the challenge. In 1878, he succeeded in taking a sequence of photographs with 12 cameras that captured the moment when the animal’s hooves were tucked under its belly. Publication of these photographs made Muybridge an international celebrity. Another noteworthy event in his life was that he was tried (but acquitted) for the murder of his wife's lover. *TIS

1834 Edmond N. Laguerre (9 April 1834 in Bar-le-Duc, France - 14 Aug 1886 in Bar-le-Duc, France)studied approximation methods and is best remembered for the special functions: the Laguerre polynomials.*SAU

1865 Charles Proteus Steinmetz (9 Apr 1865; 26 Oct 1923 at age 58)
German-American electrical engineer and inventor whose theories and mathematical analysis of alternating current systems helped establish them as the preferred form of electrical energy in the United States, and throughout the world. In 1893, Steinmetz joined the newly organized General Electric Company where he was an engineer then consultant until his death. His early research on hysteresis (loss of power due to magnetic resistance) led him to study alternating current, which could eliminate hysteresis loss in motors. He did extensive new work on the theory of a.c. for electrical engineers to use. His last research was on lightning, and its threat to the new AC power lines. He was responsible for the expansion of the electric power industry in the U.S. In 1888 he was about to receive his Ph.D. in mathematics from the University of Breslau but fled the country to avoid arrest as a socialist. This hunchback with a high squeaky voice published several papers in mathematics, but earned his living as an electrical engineer. [A Century of American Mathematics, Part 1, p. 14]. *VFR.. His theories and mathematical analysis of alternating current systems helped establish them as the preferred form of electrical energy in the United States, and throughout the world.

1869 Élie-Joseph Cartan (9 Apr 1869; 6 May 1951 at age 82) French mathematician who greatly developed the theory of Lie groups and contributed to the theory of subalgebras. By 1904 Cartan was turning to papers on differential equations and from 1916 on he published mainly on differential geometry. Cartan also published work on relativity and the theory of spinors. He is certainly one of the most important mathematicians of the first half of the 20th century. *TIS

1878 Marcel Grossmann (9 April 1878 in Budapest, Hungary
Died: 7 Sept 1936 in Zürich, Switzerland) was a classmate of Albert Einstein. When Einstein sought to formulate his ideas on general relativity mathematically, he turned to Grossmann for assistance. *VFR

1900 Hendrik Douwe Kloosterman (9 April 1900 in Rottevalle, The Netherlands - 1968 in Leiden, The Netherlands) The group he studied was the special linear group of 2 by 2 matrices over the ring of integers modulo pn. Schur had solved the problem for the case n = 1, where the matrices are over a prime field, and the case of n = 2 had been solved in the 1930s. Kloosterman solved the general case in two papers The behaviour of general theta functions under the modular group and the characters of binary modular congruence groups which occupy 130 pages of the Annals of Mathematics in 1946. *SAU

1919 John Presper Eckert (9 Apr 1919; died 3 Jun 1995 at age 76) American electrical engineer and computer pioneer. With John Mauchly he invented the first general-purpose electronic digital computer (ENIAC), presented the first course in computing topics (the Moore School Lectures), founded the first commercial computer company (the Eckert-Mauchly Computer Corporation), and designed the first commercial computer in the U.S., the UNIVAC, which incorporated Eckert's invention of the mercury delay line memory. *Wik Thanks to Arjen Dijksman)

1931 Heisuke Hironaka (9 Apr 1931, ) Japanese mathematician who was awarded the Fields Medal in 1970 for his work in algebraic geometry giving a number of technical results, including the resolution of certain singularities and torus imbeddings with implications in the theory of analytic functions, and complex and Kähler manifolds. In simple terms, an algebraic variety is the set of all the solutions of a system of polynomial equations in some number of variables. Nonsingular varieties would be those that may not cross themselves. The problem is whether any variety is equivalent to one that is nonsingular. Oscar Zariski had shown earlier that this was true for varieties with dimension up to three. Hironaka showed that it is true for other dimensions.

1348 William of Ockham (about 1288 in Ockham (near Ripley, Surrey), England - 9 April 1348 in Munich, Bavaria (now Germany))was an English Philosopher of the Early 14th Century. He is most remembered today for the quotation "Entia non sunt multiplicanda praeter necessitatem . The direct translation is close to "Entities ought not to be multiplied except from necessity." Occam's razor has become a scientific rule of thumb for deciding between two theories to explain a single phenomenon. Given two otherwise equal theories, the more simple one is the better.*SAU
The modern spelling is Ockham, and the remains of the estate is located off the M25 in London near Woking. All Saints Church, which dates to the 13th century, contains a modern stained-glass window of William of Occham. There is also a statue. Behind the church is a gate into the grounds of Ockham Park, but it is private land. It may be of interest to students of mathematics and computer science that Ada Lovelace's husband, also named William, was the Baron of Ockham in the 19th century.

1564 Georg Hartmann (sometimes spelled Hartman; February 9, 1489 – April 9, 1564) was a German engineer, instrument maker, author, printer, humanist, churchman, and astronomer. After finishing his studies, he travelled through Italy and finally settled in Nuremberg in 1518. There he constructed astrolabes, globes, sundials, and quadrants. In addition to these traditional scientific instruments Hartmann also made gunner's levels and sights. Hartmann was possibly the first to discover the inclination of Earth's magnetic field. He died in Nuremberg.
His two published works were Perspectiva Communis (Nuremberg, 1542), a reprint of John Peckham's 1292 book on optics and Directorium (Nuremberg, 1554), a book on astrology. He also left Collectanea mathematica praeprimis gnomonicam spectania, 151 f. MS Vienna, Österreichische Nationalbibliothek, Quarto, Saec. 16 (1527–1528), an unpublished work on sundials and astrolabes that was translated by John Lamprey and published under the title ofHartmann's Practika in 2002. *Wik

1626 Francis Bacon (22 Jan 1561, 9 Apr 1626 at age 65)English philosopher remembered for his influence promoting a scientific method. He held that the aim of scientific investigation is practical application of the understanding of nature to improve man's condition. He wrote that scientists should concentrate on certain important kinds of experimentally reproducible situations, (which he called "prerogative instances"). After tabulating such phenomena, the investigator should also aim to make a gradual ascent to more and more comprehensive laws, and will acquire greater and greater certainty as he or she moves up the pyramid of laws. At the same time each law that is reached should lead him to new kinds of experiment, that is, to kinds of experiment over and above those that led to the discovery of the law. *TIS

1643 Benedetto Castelli (1578 – April 9, 1643), born Antonio Castelli, was an Italian mathematician. Benedetto was his name in religion on entering the Benedictine Order. Born in Brescia (Tartaglia's home town also), he studied at the University of Padua and later became an abbot at the Benedictine monastery in Monte Cassino.
He was a long-time friend and supporter of his teacher, Galileo Galilei, and in turn teacher to Galileo's son. He assisted Galileo's study of sunspots and participated in the examination of the theories of Nicolaus Copernicus.
On 5 December 1610 Castelli wrote to Galileo
If the position of Copernicus, that Venus revolves around the sun, is true (as I believe), it is clear that it would necessarily sometimes be seen by us horned and sometimes not, even though the planet maintains the same position relative to the sun. ... Now I want to know from you if you, with the help of your marvellous glasses, have observed such a phenomenon, which will be, beyond doubt, a sure means to convince even the most obstinate mind. I also suspect a similar thing with Mars near the quadrature with the sun; I don't mean a horned or non-horned shape, but only a semicircular and a more full one.
It is now impossible to prove whether this idea occurred to both Galileo and Castelli at the same time, or whether this letter of Castelli made Galileo turn his telescope on Venus to see if it showed phases. Certainly by 11 December Galileo had discovered that Venus did indeed appear as a crescent for on that day he wrote to Giuliano d'Medici expressing the discovery in code. It is of little consequence which scenario is correct, for in either case Castelli came up with one of the most important ideas of the time.

Castelli was most interested in mathematics and hydraulics. He was appointed as a mathematician to the University of Pisa, replacing Galileo, and later at the University of Rome La Sapienza.

Castelli published Mensuration of Running Water, an important work on fluids in motion, and then his Geometrical Demonstrations of the Measure of Running Waters.

Castelli died in Rome. His students included Giovanni Alfonso Borelli and Evangelista Torricelli, the inventor of the barometer and an early proponent of the air pump.
*Wik *SAU

1754 Christian von Wolfe (baron) (24 Jan 1679, 9 Apr 1754 at age 75) philosopher, mathematician, and scientist who worked in many subjects but who is best known as the German spokesman of the Enlightenment, the 18th-century philosophical movement characterized by Rationalism. Wolff's first interest was mathematics. Though he made no original contribution to the discipline, he was important in the teaching of mathematics and instrumental in introducing the new mathematics into German universities. Later, as a philosopher, he developed the most impressive coherent system of his century. Thoroughly eclectic, influenced by Leibniz and Descartes, yet he continued fundamental themes of Aristotle. His system was important in making the discoveries of modern science known in Germany. *TIS

1920 Moritz Benedikt Cantor (23 Aug 1829 in Mannheim, Baden (now Germany)- 9 April 1920 in Heidelberg, Germany) best remembered for the four volume work Vorlesungen über Geschichte der Mathematik which traces the history of mathematics up to 1799. The first volume was published in 1880 and the last volume appeared in 1908. *SAU

1951 Vilhelm F(riman) K(oren) Bjerknes (14 Mar 1862, 9 Apr 1951 at age 89) was a Norwegian meteorologist and physicist, one of the founders of the modern science of weather forecasting. As a young boy, Bjerknes assisted his father, Carl Bjerknes (a professor of mathematics) in carrying out experiments to verify the theoretical predictions that resulted from his father's hydrodynamic research. After graduating from university, Bjerknes moved on to his own work applying hydrodynamic and thermodynamic theories to atmospheric and hydrospheric conditions in order to predict future weather conditions. His work in meteorology and on electric waves was important in the early development of wireless telegraphy. He evolved a theory of cyclones known as the polar front theory with his son Jakob. *TIS

1953 Hans Reichenbach (26 Sept 1891 in Hamburg, Germany - 9 April 1953 in Los Angeles, California, USA) wrote on induction, probability and the philosophy of science. However, in the United States he also wrote major works on the philosophical foundations of quantum mechanics and on time. "...Let us assume that the three dimensions of space are visualized in the customary fashion, and let us substitute a color for the fourth dimension. Every physical object is liable to changes in color as well as in position. An object might, for example, be capable of going through all shades from red through violet to blue. A physical reaction between any two bodies is possible only if they are close to each other in space as well as in color. Bodies of different colors would penetrate each other witout interference ... "*SAU

1983 Yozo Matsushima (February 11, 1921 – April 9, 1983) was a Japanese mathematician. The first paper published by Matsushima contained a proof that a conjecture of Hans Zassenhaus was false. Zassenhaus had conjectured that every semisimple Lie algebra L over a field of prime characteristic, with [L, L] = L, is the direct sum of simple ideals. Matsushima constructed a counterexample. He then developed a proof that Cartan subalgebras of a complex Lie algebra are conjugate. However, Japanese researchers were out of touch with the research done in the West, and Matsushima was unaware that French mathematician Claude Chevalley had already published a proof. When he obtained details of another paper of Chevalley through a review in Mathematical Reviews, he was able to construct the proofs for himself. *Wik

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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