## Thursday, 13 April 2017

### On This Day in Math - April 13

 Double False Position from Gemma Frisius  Arithmeticae Practicae Methodus Facilis (1540) *MAA Mathematical Treasures

The main objects of all science, the freedom and happiness of man. . . . [are] the sole objects of all legitimate government.
A plaque with this quotation, with the first phrase omitted, is in the stairwell of the pedestal of the Statue of Liberty.
~Thomas Jefferson

The 103rd day of the year; there are 103 geometrical forms of magic knight's tour of the chessboard.

103 is the reverse of 301. The same is true of their squares: 1032 = 10609 and 3012 = 90601. *Jim Wilder

The smallest prime whose reciprocal contains a period that is exactly 1/3 of the maximum length. (The period of the reciprocal of a prime p is always a divisor of p-1, so for 103 the period is 102/3 = 34. )

Using a standard dartboard, 103 is the smallest possible prime that cannot be scored with two darts.

EVENTS

In 1625, the word "microscope" was coined as a suggested term in a letter written by Johannes Faber of Bamberg, Germany, to Federigo Cesi, Duke of Aquasparata and founder of Italy's Accademia dei Lincei (Academy of the Lynx). This Academy, possibly the world's first scientific society took its name after the animal for its exceptional vision. *TIS

1668 Lord Brouncker, President of the Royal Society, publishes "the fist mathematical result to be published in a mathematical journal" in the Philosophical transactions of the Royal Society. His demonstration of the method of quadrature of the rectangular hyperboal, y= 1/x-1 extended the work of Wallis in Arithmetica infinitorium. Brouncker had been working with Wallis on extending the work of Torricelli's Opera geometrica hoping to apply the methods to the long-sought quadrature of the circle.
The rectangular hyperbola had eluded Fermat, and only been partially solved by de Saint Vincent by 1625. It was a fellow Jesuit of Saint Vincent, Alphonse Antonio de Sarasa he may have been the first to recognize that certain areas under the hyperbola are related to each other in the same was as logarithms. *Jacqueline Stedall, Mathematics Emerging, 2008.

1672 After presenting his paper on the composition of light as a, “heterogeneous mixture of differently refrangible rays” on 19 Feb, several critics emerged, most notably Robert Hooke. Newton responded to the critiques with a letter to the Royal Society, "Some Experiments propos'd in relation to Mr. Newtons Theory of light, printed in Numb. 80; together with the Observations made thereupon by the Author of that Theory; communicated in a Letter of his from Cambridge, April 13. 1672." Newton had performed a series of experiments to validate his theory, and here described the results. See the letter here.

1791 Legendre is named one of the French Academy’s three commissioners for the astronomical operations and triangulations necessary for determining the standard meter. The others were Mechain and Cassini IV. [DSB 8, 136]*VFR

BIRTHS

953 Abu Bekr ibn Muhammad ibn al-Husayn Al-Karaji (13 April 953 in Baghdad (now in Iraq) - died about 1029) Al-Karaji was an Islamic mathematician who wrote about the work of earlier mathematicians and who can be regarded as the first person to free algebra from geometrical operations and replace them with the type of operations which are at the core of algebra today. *SAU

1728 Paolo Frisi (13 Apr 1728; 22 Nov 1784 at age 56) Italian mathematician, astronomer, and physicist who is best known for his work in hydraulics (he designed a canal between Milan and Pavia). He was, however, the first to introduce the lightning conductor into Italy. His most significant contributions to science, however, were in the compilation, interpretation, and dissemination of the work of other scientists, such as Galileo Galilei and Sir Isaac Newton. His work on astronomy was based on Newton's theory of gravitation, studying the motion of the earth (De moto diurno terrae). He also studied the physical causes for the shape and the size of the earth using the theory of gravity (Disquisitio mathematica, 1751) and tackled the difficult problem of the motion of the moon. *TIS

1743 Thomas Jefferson, American President and Mathematical enthusiast, was born.
"Thomas Jefferson had four main accomplishments in mathematics. First, he took mathematics from the ranks of a secondary subject and raised it to such a prominence in the curriculum of the University of Virginia that it was not seen at any other college in the United States at the time. Through Jefferson’s influence, men like J.J. Sylvester, in 1841 (though unsuccessful), were recruited to build up the mathematics courses at the University of Virginia....David Eugene Smith sums it best in the following passage:
It is apparent that Jefferson was not a mathematician but that he was a man who appreciated the beauties, the grandeur, the values, the classics, and the uses of mathematics and did much to give to the science a recognized standing as a university subject. "
From an online article by Ajaz Siddiqui, See the short article here.

1802 George Palmer Williams (Woodstock, Vermont, April 13, 1802-Ann Arbor, September 4, 1881) Hegraduated Bachelor of Arts from the University of Vermont in 1825, and then studied about two years in the Theological Seminary at Andover, Massachusetts. He did not complete the course, but took up teaching, which proved to be his life work.
He was Principal of the Preparatory School at Kenyon College, Ohio, from 1827 to 1831. In 1831 he was elected to the chair of Ancient Languages in the Western University of Pennsylvania, but after two years he returned to Kenyon College, where he remained until called, in 1837, to the branch of the incipient University of Michigan at Pontiac.
In 1841, when the College proper was opened at Ann Arbor, he was made Professor of Natural Philosophy. In 1854 he was transferred to the chair of Mathematics and in 1863 to the chair of Physics. From 1875 to 1881 he was Emeritus Professor of Physics.
He received the degree of Doctor of Laws from Kenyon College in 1849. The University Senate in a memorandum relative to his death declared that: "Dr. Williams welcomed the first student that came to Ann Arbor for instruction; as President of the Faculty he gave diplomas to the first class that graduated, and from the day of his appointment to the hour of his death his official connection with the University was never broken."
In 1846 he was ordained to the ministry of the Protestant Episcopal Church; but he did no regular parish work, except for a short time in Ann Arbor. He was first and last a teacher, beloved by his colleagues and pupils and universally respected and honored.
Some years before his death the alumni raised a considerable fund, the proceeds of which were to be paid to him during his lifetime and after his death were to be used for maintaining a professorship named in honor of his memory. *Hinsdale and Demmon, History of the University of Michigan 221

1813 Duncan Farquharson Gregory (13 April 1813 in Edinburgh, Scotland - 23 Feb 1844 in Edinburgh, Scotland) Scottish mathematician who was one of the first to investigate modern ideas of abstract algebra.In this work Gregory built on the foundations of Peacock but went far further towards modern algebra. Gregory, in his turn, had a major influence on Boole and it was through his influence that Boole set out on his innovative research. *SAU

1869 Ada Isabel Maddison (April 12, 1869 - October 22, 1950) born in Cumberland, England. She attended Girton College, Cambridge, in the same class with Grace Chisholm Young and they attended lectures of Cayley. Then she came to Bryn Mawr, where she earned her Ph.D. in 1895. She continued there until retirement, involved mostly in administrative work. *WM

1879 Francesco Severi (13 April 1879 – 8 December 1961) was an Italian mathematicianborn in Arezzo, Italy. He is famous for his contributions to algebraic geometry and the theory of functions of several complex variables. He became the effective leader of the Italian school of algebraic geometry. Together with Federigo Enriques, he won the Bordin prize from the French Academy of Sciences.
He contributed in a major way to birational geometry, the theory of algebraic surfaces, in particular of the curves lying on them, the theory of moduli spaces and the theory of functions of several complex variables. He wrote prolifically, and some of his work has subsequently been shown to be not rigorous according to the then new standards set in particular by Oscar Zariski and David Mumford. At the personal level, according to Roth (1963) he was easily offended, and he was involved in a number of controversies. He died in Rome of cancer.*Wik

1889 Herbert Osborne Yardley 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

1905 Bruno Rossi (13 Apr 1905, 21 Nov 1993)Italian pioneer in the study of cosmic radiation. In the 1930s, his experimental investigations of cosmic rays and their interactions with matter laid the foundation for high energy particle physics. Cosmic rays are atomic particles that enter earth's atmosphere from outer space at speeds approaching that of light, bombarding atmospheric atoms to produce mesons as well as secondary particles possessing some of the original energy. He was one of the first to use rockets to study cosmic rays above the Earth's atmosphere. Finding X-rays from space he became the grandfather of high energy astrophysics, being largely responsible for starting X-ray astronomy, as well as the study of interplanetary plasma. *TIS

1909 Stanislaw M. Ulam (13 Apr 1909; 13 May 1984 at age 75) Polish-American mathematician who played a major role in the development of the hydrogen bomb at Los Alamos. He solved the problem of how to initiate fusion in the hydrogen bomb by suggesting that compression was essential to explosion and that shock waves from a fission bomb could produce the compression needed. He further suggested that careful design could focus mechanical shock waves in such a way that they would promote rapid burning of the fusion fuel. Ulam, with J.C. Everett, also proposed the "Orion" plan for nuclear propulsion of space vehicles. While Ulam was at Los Alamos, he developed "Monte-Carlo method" which searched for solutions to mathematical problems using a statistical sampling method with random numbers. *TIS He is buried in Santa Fe National Cemetery in Santa Fe, New Mexico, USA

DEATHS

1728 Samuel Molyneux (18 Jul 1689, 13 Apr 1728 at age 38)British astronomer (Royal Observatory at Kew) and politician. Together with assistant James Bradley, he made measurements of abberation - the diversion of light from stars. They made observations of the star Â Draconis with a vertical telescope. Starting in 1725 they had the proof of the movement of the earth giving support to the Copernican model of the earth revolving around the sun. The star oscillated with an excursion of 39 arcsecs between its lowest declination in May and its the highest point of its oscillation in September. He was unfortunate to fall ill in 1728 and into the care of the Anatomist to the Royal Family, Dr Nathaniel St Andre, whose qualifications were as a dancing master. Molyneux died shortly thereafter. *TIS

1906 Walter Frank Raphael Weldon DSc FRS (Highgate, London, 15 March 1860 – Oxford, 13 April 1906) generally called Raphael Weldon, was an English evolutionary biologist and a founder of biometry. He was the joint founding editor of Biometrika, with Francis Galton and Karl Pearson.*Wik Pearson said of him, "He was by nature a poet, and these give the best to science, for they give ideas." *SAU

1941 Annie Jump Cannon (11 Dec 1863; 13 Apr 1941) American, deaf astronomer who specialized in the classification of stellar spectra. In 1896 she was hired at the Harvard College Observatory, remaining there for her entire career. The Harvard spectral classification system had been first developed by Edward C. Pickering, Director of the Observatory, around the turn of the century using objective prism spectra taken on improved photographic plates. In conjunction with Pickering Cannon was to further develop, refine, and implement the Harvard system. She reorganized the classification of stars in terms of surface temperature in spectral classes O, B, A, F, G, K, M, and cataloged over 225,000 stars for the monumental Henry Draper Catalog of stellar spectra, (1918-24).*TIS

2004 David Herbert Fowler (April 28, 1937 – April 13, 2004) was a historian of Greek mathematics who published work on pre-Eudoxian ratio theory (using the process he called anthyphaeresis). He disputed the standard story of Greek mathematical discovery, in which the discovery of the phenomenon of incommensurability came as a shock.
His thesis was that, not having the real numbers, nor division, the Greeks faced difficulties in defining rigorously the notion of ratio. They called ratio 'logos'. Euclid Book V is an exposition of Eudoxus's theory of proportion, which Eudoxus discovered about 350BC, and which has been described as the jewel in the crown of Greek mathematics. Eudoxus showed by a form of abstract algebra how to handle rigorously the case when two ratios are equal, without actually having to define them. His theory was so successful that, in effect, it killed off perfectly good earlier theories of ratio, and Fowler's aim had been to find the evidence for the rediscovery of these previous theories.
In particular Thaetetus (c 414-369BC) introduced a definition of ratio using a procedure called anthyphairesis, based on the Euclidean subtraction algorithm. Fowler developed his ideas in a series of papers, culminating in the book The Mathematics of Plato's Academy: A New Reconstruction, which was published in 1987. This book is based on a study of the primary sources and on their assimilation and transformation.*Wik

2008 John Archibald Wheeler (9 Jul 1911, 13 Apr 2008 at age 96) was the first American physicist involved in the theoretical development of the atomic bomb. He also originated a novel approach to the unified field theory. Wheeler was awarded the 1997 Wolf Prize "for his seminal contributions to black hole physics, to quantum gravity, and to the theories of nuclear scattering and nuclear fission." After recognizing that any large

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