## Sunday, 7 August 2016

### On This Day in Math - August 7

One geometry cannot be more true than another; it can only be more convenient.
~Henri Poincare

The 220th day of the year; 220 is the smallest amicable number, paired with 284. Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other. Amicable numbers were known to the Pythagoreans, who credited them with many mystical properties. (what is the next pair?)

220 is the the largest difference between two consecutive primes less than 100,000,000.

220 is the sum of four consecutive primes.

EVENTS

1620 Kepler’s mother was arrested (imprisoned) for witchcraft. *VFR In 1615, Ursula Reingold, a woman in a financial dispute with Kepler's brother Christoph, claimed Kepler's mother Katharina had made her sick with an evil brew. The dispute escalated, and in 1617, Katharina was accused of witchcraft; witchcraft trials were relatively common in central Europe at this time. Beginning in August 1620 she was imprisoned for fourteen months. She was released in October 1621, thanks in part to the extensive legal defense drawn up by Kepler. The accusers had no stronger evidence than rumors, along with a distorted, second-hand version of Kepler's Somnium, in which a woman mixes potions and enlists the aid of a demon. Katharina was subjected to territio verbalis, a graphic description of the torture awaiting her as a witch, in a final attempt to make her confess. Throughout the trial, Kepler postponed his other work to focus on his "harmonic theory". The result, published in 1619, was Harmonices Mundi ("Harmony of the Worlds").. *Wik

1657 Sir Christopher Wren selected as the Gresham College Professor of Astronomy.

1665 After Newton, and most others who had the capacity, had departed Trinity College authorized the payment of stipends to "Fellows and Scholars which now go into the Country on occasion of the Pestilence." Newton would not return until 1667 after the Great Fire had helped minimize the plague. *Thomas Levenson, Newton and The Counterfeiter

1799 The second, greatly augmented edition of Montucla’s Histoire des Mathe´matiques appeared. *VFR In 1754 he published an anonymous treatise entitled Histoire des récherches sur la quadrature du cercle, and in 1758 the first part of his great work, Histoire des mathématiques, the first history of mathematics worthy of the name. He was appointed intendant-secretary of Grenoble in 1758, secretary to the expedition for colonizing Cayenne in 1764, and chief architect and censor-royal for mathematical books in 1765.
The French Revolution deprived him of his income and left him in great destitution. The offer in 1795 of a mathematical chair in one of the schools of Paris was declined on account of his infirm health, and he was still in straitened circumstances in 1798, when he published a second edition of the first part of his Histoire.  After his death, his Histoire was completed by Jérôme Lalande, and published at Paris in 1799-1802 *Wik

1814 A shocked Herschel responds to a letter from Charles Babbage, " I am married and I have quarreled with my father - Good God Babbage - How is it possible for a man to pen those two sentences, then ... pass off to functional expressions?" Babbage had eloped with Georgiana Whitmore, a marriage of which his father did not approve because he felt Babbage was not financially secure enough to take a wife. John Herschel seems to have known nothing of his secret romance. .*Anthony Hyman, Charles Babbage: Pioneer of the Computer

1869 The Baily's beads were first photographed at the eclipse of August 7, 1869 by C. F. Hines and members of the Philadelphia Photographic Corps, observing from Ottumwa, Iowa. *NSEC

1869 August 07, 1869 Charles Augustinus Young and William Harkness (US) independently discover a new bright (emission) line in the spectrum of the Sun's corona, never before observed on earth; they ascribe it to a new element and it is named coronium. In 1941, this green line is identified by Bength Edlén (Sweden) as iron that has lost 13 electrons *NSEC

1944 Harvard MARK I dedicated. *Goldstein, Computer from Pascal to von Neumann, p. 111 IBM president Thomas J. Watson Sr. formally presents the Automatic Sequence Controlled Calculator (ASCC) to Harvard University. One of the earliest digital computers, known at Harvard as the Mark I, this giant relay-based machine was the result of Professor Howard Aiken's research into computation.
The Mark I was a curious mixture of punch card technology and simple electronics which became out-of-date almost as soon as it was completed. It was 51 feet long, 8 feet high, and weighed 5 tons.
Nonetheless, IBM learned about large calculator development with the Mark I and applied these skills in its own Selective Sequence Controlled Calculator (SSEC), another Giant Brain project undertaken when Aiken snubbed IBM by claiming he had invented the ASCC. *CHM
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BIRTHS
1726 James Bowdoin (August 7, 1726 – November 6, 1790) American founder and first president of the American Academy of Arts and Sciences (1780). He was a scientist prominent in physics and astronomy, and wrote several papers including one on electricity with Benjamin Franklin, a close friend. In one of his letters to Franklin, Bowdoin suggested the theory, since generally accepted, that the phosphorescence of the sea, under certain conditions, is due to the presence of minute animals. Bowdoin was also a political leader in Massachusetts during the American revolution (1775-83), and governor of Massachusetts (1785-87). His remarkable library of 1,200 volumes, ranged from science and math to philosophy, religion, poetry, and fiction. He left it in his will to the Academy.*TIS

1802 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

1852 Philipp Forchheimer (7 August 1852 in Vienna; 2 October 1933 in Dürnstein, Lower Austria) Austrian hydraulic engineer who made significant studies of groundwater hydrology. Early in his academic career, he worked on problems of soil mechanics. Later, he turned to hydraulic problems, establishing the scientific basis of the discipline by applying standard techniques of mathematical physics - in particular Laplace's equation - to problems of groundwater movement. Laplace's equation had already been well developed for heat flow and fluid flow. Forchheimer extended the preexisting mathematical theory to calculations of groundwater flow. He was also the first to both mathematically and experimentally examine the features of dambreak waves in a rectangular channel (with his PhD student Armin Schoklitsch)*TIS

1868 Ladislaus Josephowitsch Bortkiewicz (7 Aug 1868 in St Petersburg, Russia -15 July 1931 in Berlin, Germany) worked on mathematical statistics and applications to actuarial science and political economy. His work on actuarial science was largely concerned with mortality tables. He examined life expectancy in an increasing population and showed in 1893, contrary to what had previously been believed, that life expectancy in such a population could only be computed from mortality tables and was not a function of the observed birth rate and death rate. He published on mortality rates again in publication of 1904 and 1911 where he examined methods to compare mortality rates.
Good argues that the Poisson distribution should have been named the von Bortkiewicz distribution. Bortkiewicz was interested in the law of small numbers and he used the divergence coefficient Q, deducing its expectation and standard deviation. He published a work The Law of Small Numbers in 1898. In this he was the first to note that events with low frequency in a large population followed a Poisson distribution even when the probabilities of the events varied.*SAU

1869 Mary Frances Winston Newson (August 7, 1869 – December 5, 1959) born in Forreston, Illinois. She did graduate work at Bryn Mawr and Chicago, and then, after meeting Felix Klein at the zeroeth International Congress of Mathematicians in 1893, she attended G¨ottingen. Three years later, in 1896, she ﬁnished her dissertation on diﬀerential equations and passed her exams magna cum laude. In 1897 she became the ﬁrst American woman to receive her Ph.D. from a European University. *VFR

1886 (Louis) Alan Hazeltine (August 7, 1886 – May 24, 1964) was an American electrical engineer and physicist who invented the neutrodyne circuit, which made commercial radio possible. As one of the few experts in radio engineering at the outbreak of WW I, he designed a radio receiver for the U.S. Navy. In 1922, Hazeltine invented the "neutrodyne" receiver to eliminate the squeaks and howls of the early radio receivers, using neutralizing capacitors to in effect siphon off the high pitched squeals. The Hazeltine amplifier neutralized the grid-to-plate capacitative coupling which was a cause of oscillation in triode amplifiers. The neutrodyne was the first commercial receiver suited to general public reception. By 1927 some ten million of these receivers were being used by listeners in the U.S. *TIS

1889 Léon Nicolas Brillouin (August 7, 1889;Sèvres, near Paris, France – October 4, 1969; New York, USA) was a French physicist. He made contributions to quantum mechanics, radio wave propagation in the atmosphere, solid state physics, and information theory.
Brillouin was born in Sèvres, near Paris, France. His father, Marcel Brillouin, grandfather, Éleuthère Mascart, and great-grandfather, Charles Briot, were physicists as well. Brillouin offered a solution to the problem of Maxwell's demon. In his book, Relativity Reexamined, he called for a "painful and complete re-appraisal" of relativity theory which "is now absolutely necessary." *Wik

1928 Dikran "Dick" Tahta (7 August 1928 – 2 December 2006) was a British-Armenian mathematician, teacher and author.
Dikran Tahta is a descendant of an Ottoman Armenian family who settled in Manchester after the First World War. Much of his childhood, and the influence of his Armenian religious upbringing, is reflected upon in his penultimate book Ararat Associations, in which he notes how his parents were keen for their children to have an English education, yet made sure that they spoke Armenian at home. He was christened by Bishop Tourian in the Armenian Church in Manchester, and his name Dikran was shortened to Dick, but he never forgot his Armenian roots.
From Rossall School, in Fleetwood, Lancashire, he gained a scholarship to Christ Church, Oxford, in 1946. His main subject was Mathematics, but he also read widely in English literature, philosophy and history.
In the 1970s he was involved in the ATV television programme of mathematics for schools entitled 'Leapfrogs' (produced and directed by Paul Martin) and promoted visual approaches to mathematics. His paper "On Geometry" argued that geometrical approaches to mathematics could not be reduced to algebraic approaches. In line with this thinking, he produced the ATM book Geometric Images, and co-authored Images of Infinity with Ray Hemmings. The Leapfrogs group of Tahta and Hemmings, together with David Sturgess, Leo Rogers and Derick Last also produced hands-on teaching materials including workbooks for the polycube. He also drew upon insights into pedagogy in the writings of Mary Boole on mathematics education.
After retirement, he went to teach in the United States and South Africa, and became a tutor for the Open University.
His last book was The Fifteen Schoolgirls about Thomas Kirkman, known for the Kirkman's schoolgirl problem, a problem in combinatorics, which also delved into the byways of Victorian amateur mathematics.
In his obituary, The Guardian newspaper described Dick as "one of the outstanding mathematics teachers of his generation", who was notable for having inspired physicist Stephen Hawking. The Guardian commented on his death that "He was a wise and generous man who inspired love and an increase of intellectual energy in everyone who came within his ambit." *Wik

DEATHS

1834 Joseph Marie Jacquard (7 July 1752 – 7 August 1834) French silk weaver, (born Lyons), inventor of the Jacquard programmable power loom for brocaded fabric. His loom would mechanically produce any pattern, controlled by perforated control cards (1805). This served as the impetus for the technological revolution of the textile industry and is the basis of the modern automatic loom. The concept of using punched cards was later applied by Hollerith to keeping track of the 1890 US census data. The idea further evolved to computer input punched cards. *TIS

1848 Jöns Jacob Berzelius (20 August 1779 – 7 August 1848) was a Swedish scientist, one of the founders of modern chemistry. He is especially noted for his determination of atomic weights, the development of modern chemical symbols, his electrochemical theory, the discovery and isolation of several elements, the development of classical analytical techniques, and his investigation.*TIS

1958 Herbert Osborne Yardley (April 13, 1889 – August 7, 1958) American cryptographer who organized and directed the U.S. government's first formal code-breaking efforts during and after World War I. He began his career as a code clerk in the State Department. During WW I, he served as a cryptologic officer with the American Expeditionary Forces in France during WWI. In the 1920s, when he was chief of MI-8, the first U.S. peacetime cryptanalytic organization, he and a team of cryptanalysts exploited nearly two dozen foreign diplomatic cipher systems. MI-8 was disbanded in 1929 when the State Department withdrew funding. Jobless, Yardley caused a sensation in 1931 by publishing his memoirs of MI-8, The American Black Chamber, which caused new security laws to be enacted.*TIS

1983 Bart Jan Bok (28 April 1906 – 5 August 1983) was a Dutch-American astronomer whose name remains associated with the "Bok globules" he was the first to investigate - dark clouds of dense gas and dust visible against a background of bright nebulae. Bok globules have a mass of 10 to 50 times the mass of the Sun and are about a light year across. He began their observation in the 1940's and in a 1947 paper with E.F. Reilly proposed that these were sites of new star formation as the gas clouds underwent gravitational collapse. Bok's other important work was on the structure and evolution of the Milky Way Galaxy. His enthusiasm for astronomy began as a young boy. Bok bicycled to Norway to observe the solar eclipse of 1927. He moved to the U.S. in 1929.*TIS

1985 G´abor Szeg˝o, (January 20, 1895 – August 7, 1985) Professor Emeritus at Stanford, died at the age of 90. He co-authored with George (originally Gy¨orogy) P´olya (who died exactly a month later) the renown book Problems and Theorems in Analysis. *VFR worked in the area of extremal problems and Toeplitz matrices.*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