Saturday 13 August 2011

On This Day in Math - Aug 13

It is clear that Economics, if it is to be a science at all,
must be a mathematical science.
~William Jevons

The 225th day of the year; 225 is the ONLY three digit square with all prime digits. Can you find a four digit square with all prime digits?


3114 BC The first day of the current Mayan “long count” calendar (adjusted for the Gregorian Calendar). The long count calendar lasts 22,507,528 days and the current calendar will end on December 21 of 2012. What happens then depends on who you read. If the world does NOT end, we will be back to year zero of the Mayan calendar.

1642, Christiaan Huygens discovered the Martian south polar cap.*TIS

1661 , Sir Robert Moray, senior courtier to Charles II, advises Wren that since he did not have time to construct microscope-based drawings that the king had requested, the task was passed to Hooke.  This assignment from the king would lead to Hooke's publication of Micrographia in 1665.  *Lisa Jardine, Ingenious Pursuits, pg 62

1727 Charles-Etienne-Louis Camas elected to the French Academy of Sciences because he had earlier won half the prize money in their competition for the best manner of masting vessels. Did Euler get the other half? *VFR

1849 Gauss writes to his former student, Mobius, to thank him for sending a copy of Mobius' paper on third order curves and advises him to investigate the form of analytic curves from Gauss' 1799 dissertation. *Carl Friedrich Gauss: Titan of Science
By Guy Waldo Dunnington, Jeremy Gray, Fritz-Egbert Dohse
1903  the journal Nature reported that helium gas is produced by the radioactive decay of the radium. This key discovery by William Ramsay and Frederick Soddy helped to reveal the structure of atoms. In 1908, Rutherford confirmed that alpha rays and these radium emanations were one and the same: the nuclei of helium atoms, bearing a positive electrical charge. Each were future Nobel laureates in Chemistry. Ramsey won the Nobel Prize in 1904 for his discovery of the noble gases. Rutherford was recognized in 1908 for his investigations into the disintegration of the elements. Soddy was honoured in 1921 for his pioneering contributions to understanding the chemical properties of radioactive elements such as radium and uranium.*TIS


1625 Erasmus Bartholin..Bartholin was the editor of van Schooten's "Introduction to the geometry of Descartes", He also discovered double refraction of light using Icelandic Spar crystals. He worked with Ole Roamer in publishing some of Tycho Brahe's observations. His maternal grandfather was Thomas Fincke, the geometer who invented the terms tangent and secant. (*pb)

1704 Alexis Fontaine des Bertins, in 1734 he gave a solution of the tautochrone problem which was more general than that given by Huygens, Newton, Euler or Jacob Bernoulli, and in 1737 he gave a solution to an orthogonal trajectories problem. The methods which he developed to solve these problems led to the calculus of variations. He used what he called the "fluxio-differential" method, so called because it used two independent first-order Leibniz type differential operators. This technique was praised by Johann Bernoulli, Euler and d'Alembert. Fontaine then used differential coefficients instead of differentials and Greenberg shows how Fontaine progressed from a calculus of variations to a calculus of several variables. *SAU

1814 Anders Jonas Ångström was a Swedish physicist whose pioneering use of spectroscopy is recognised in the name of the angstrom, a unit of length equal to 10-10 meters. In 1853, he studied the spectrum of hydrogen for which Balmer derived a formula. He announced in 1862 that analysis of the solar spectrum showed that hydrogen is present in the Sun's atmosphere. In 1867 he was the first to examine the spectrum of aurora borealis (northern lights). He published his extensive research on the solar spectrum in Recherches sur le spectre solaire (1868), with detailed measurements of more than 1000 spectral lines. He also published works on thermal theory and carried out geomagnetical measurements in different places around Sweden.*TIS

1819 George Gabriel Stokes born. (1st Baronet) British mathematical physicist who studied viscous fluids and formulated his law of viscosity for the speed of a solid sphere falling in a fluid. Other laws and mathematical work for which he is known includes Stokes's theorem, in the field of vector analysis. Stokes also worked in optics, the wave theory of light, diffraction (1849), the ultraviolet spectrum and other spectrum analysis. He investigated the nature of fluorescence and was a founder of the field of geodesy with his study of variations in gravity (1849). From 1849 until his death in 1903, he held the Lucasian Chair of Mathematics at Cambridge (held earlier by Isaac Newton, and more recently by Stephen Hawking). He came from a family with generations of scientists, mathematicians and engineers.*TIS

1861 Cesare Burali-Forti, born. He discovered the antinomy(paradox) of the class of all ordinals in 1897. He never held a permanent university position for he failed his libera docenze, or license to teach, because of the antagonism to the new methods of vector analysis on the part of some members of the examining committee. *VFR


1822 Jean Robert Argand, Argand Diagrams, the method of drawing complex numbers as vectors on a coordinate plane, are named for Jean R. Argand (1768-1822), an amateur mathematician who described them in a paper in 1806. A similar method, although less complete, had been suggested as early as 120 years before by John Wallis, and developed extensively by Casper Wessel(1745-1818), a Norwegian surveyor. (Actually, at the time Wessel lived, the area where he was born was a part of Denmark. Norway became an independent government in 1905 after years of domination by Denmark and Sweden.) It may be that even after these multiple discoveries, the method was unknown to Gauss and he had to rediscover it for himself in 1831 although it has been suggested that Gauss may have discovered the idea as early as Wessel. Some parts of his Demonstratio Nova would seem almost miraculously derived without a knowledge of the ideas of the geometry of complex numbers.
Wessel's paper was published in Danish, and was not circulated in the languages more common to mathematics at that time. It was not until 1895 that his paper came to the attention of the mathematical community, long after the name Argand Diagram had stuck. Incredibly, there were at least three more individuals who may have independently discovered and written on the same idea; Abbe Bruee, C. V. Mourney, and John Warren.
Argand's Book, Essai sur une maniere de representer les quantities imaginaires dans les constructions geometriques, might have suffered the same fate as Wessel except for an unusual chain of events. I give here the version as presented by Michael Crowe in his A History of Vector Analysis
In 1813 J. F. Francais published a short memoir in volume IV of Gergonne's Annales de mathematiques in which Francais presented the geometrical representation of complex numbers. At the conclusion of his paper Francais stated that the fundamental ideas in his paper were not his own, he had found them in a letter written by Legendre to his (Francis') brother who had died. In this letter Legendre discussed the ideas of an unnamed mathematician. Francis added that he hoped this mathematician would make himself known and publish his results.
The unnamed mathematician had in fact already published his ideas, for Legendre's friend was Jean Robert Argand. Hearing of Francais' paper, Argand immediately sent a communication to Gergonne in which he identified himself as the mathematician in Legendre's letter, called attention to his book, summarized its contents, and finally presented an (unsuccessful) attempt to extend his system to three dimensions.
Even with so much interest and attention to the geometry of complex numbers, it was not until Gauss published a short work on the ideas that they became popular.
Translations of both Wallis' and Wessel's papers on the imaginaries can be found in A Sourcebook of Mathematics by David Eugene Smith. (*pb)

1882 Logician William Stanley Jevons died. was a British economist and logician.
Irving Fisher described his book The Theory of Political Economy (1871) as beginning the mathematical method in economics. It made the case that economics as a science concerned with quantities is necessarily mathematical. In so doing, it expounded upon the "final" (marginal) utility theory of value. Jevons' work, along with similar discoveries made by Carl Menger in Vienna (1871) and by Léon Walras in Switzerland (1874), marked the opening of a new period in the history of economic thought. Jevons' contribution to the marginal revolution in economics in the late 19th century established his reputation as a leading political economist and logician of the time. *Wik

1907 Hermann Karl Vogel German astronomer who discovered spectroscopic binaries (double-star systems that are too close for the individual stars to be discerned by any telescope but, through the analysis of their light, have been found to be two individual stars rapidly revolving around one another). He pioneered the study of light from distant stars, and introduced the use of photography in this field.*TIS

1910 Florence Nightingale​ died; (May 12, 1820 – August 13, 1910) She is best remembered for her work as a nurse during the Crimean War​ and her contribution towards the reform of the sanitary conditions in military field hospitals. However, what is less well known about this amazing woman is her love of mathematics, especially statistics, and how this love played an important part in her life's work. *SAU Florence Nightingale had exhibited a gift for mathematics from an early age and excelled in the subject under the tutorship of her father. Later, Nightingale became a pioneer in the visual presentation of information and statistical graphics. Among other things she used the pie chart, which had first been developed by William Playfair in 1801. While taken for granted now, it was at the time a relatively novel method of presenting data.
Indeed, Nightingale is described as "a true pioneer in the graphical representation of statistics", and is credited with developing a form of the pie chart now known as the polar area diagram, or occasionally the Nightingale rose diagram, equivalent to a modern circular histogram, in order to illustrate seasonal sources of patient mortality in the military field hospital she managed. Nightingale called a compilation of such diagrams a "coxcomb", but later that term has frequently been used for the individual diagrams. She made extensive use of coxcombs to present reports on the nature and magnitude of the conditions of medical care in the Crimean War to Members of Parliament and civil servants who would have been unlikely to read or understand traditional statistical reports.*Wik

1968 Oystein Ore, Ore is known for his work in ring theory, Galois connections, and most of all, graph theory. His early work was on algebraic number fields, how to decompose the ideal generated by a prime number into prime ideals. He then worked on noncommutative rings, proving his celebrated theorem on embedding a domain into a division ring. He then examined polynomial rings over skew fields, and attempted to extend his work on factorisation to non-commutative rings.
In 1930 the Collected Works of Richard Dedekind were published in three volumes, jointly edited by Ore and Emmy Noether. He then turned his attention to lattice theory becoming, together with Garrett Birkhoff, one of the two founders of American expertise in the subject. Ore's early work on lattice theory led him to the study of equivalence and closure relations, Galois connections, and finally to graph theory, which occupied him to the end of his life. Ore had a lively interest in the history of mathematics, and was an unusually able author of books for laypeople, such as his biographies of Cardano and Niels Henrik Abel.*Wik

2008 Henri Cartan is known for work in algebraic topology, in particular on cohomology operations, the method of "killing homotopy groups", and group cohomology. His seminar in Paris in the years after 1945 covered ground on several complex variables, sheaf theory, spectral sequences and homological algebra, in a way that deeply influenced Jean-Pierre Serre, Armand Borel, Alexander Grothendieck and Frank Adams, amongst others of the leading lights of the younger generation. The number of his official students was small, but includes Adrien Douady, Roger Godement, Max Karoubi, Jean-Louis Koszul, Jean-Pierre Serre and René Thom.
Cartan also was a founding member of the Bourbaki group and one of its most active participants. His book with Samuel Eilenberg Homological Algebra (1956)[3] was an important text, treating the subject with a moderate level of abstraction and category theory.*Wik

*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum

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