Wednesday, 31 August 2011

On This Day in Math - Aug 31

The pursuit of the good and evil are now linked in astronomy as in almost all science. ... The fate of human civilization will depend on whether the rockets of the future carry the astronomer's telescope or a hydrogen bomb.
~Sir Bernard Lovell

The 243rd day of the year; 243 is the largest three digit number that can be expressed as a fifth power (35). It is also the sum of five consecutive prime numbers (41 + 43 + 47 + 53 + 59).

1682 Michael Rolle published an elegant solution to a difficult problem publicly posed by Ozanam: Find four integers the difference of any two of which is a perfect square as well as the sum of the first three will be a perfect square. This brought him public recognition. *VFR Ozanam believed that the smallest of the four numbers that would satisfy these properties would have at least 50 digits. Rolle found four numbers, all satisfying the conditions Ozanam posed, containing only seven digits in each of the four numbers. *Michel Rolle and His Method of Cascades, Christopher Washington

In 1831, New London Bridge opened to traffic in London. In 1821, a committee was formed by Parliament to consider the poor condition of the existing centuries-old bridge. The arches had been badly damaged by the Great Freeze, so it was decided to build a new bridge. Building commenced under John Rennie in 1825, and completed in 1831, at the expense of the city. The bridge is composed of five arches, and built of Dartmoor granite. It was opened with great splendour by King William the fourth, accompanied by Queen Adelaide, and many of the members of the royal family, August 1st, 1831. In the 1960's it was auctioned and sold for $2,460,000 to Robert McCulloch who moved it to Havasu City, Arizona. The rebuilt London Bridge was completed and dedicated on 10 Oct 1971. *TIS

In 1842, the U.S. Naval Observatory was authorized by an act of Congress, one of the oldest scientific agencies in the U.S. James Melville Gilliss (1811-1865) is considered its founder, who in 1842 he secured the Congressional appropriation for the Depot of Charts and Instruments (est. 1830) to become the Naval Observatory. Its primary task was to care for the Navy's charts, navigational instruments and chronometers, which were calibrated by timing the transit of stars across the meridian. Initially located at Foggy Bottom, the observatory moved in 1893 to its present facility in Washington, DC. Gillis visited Europe to procure instruments, and the books that formed the core of the Naval Observatory Library. Matthew Fontaine Maury was the first director, followed by Gillis (1861-65)*TIS

1846 Le Verrier's announces his prediction of the location of the yet to be discovered planet Neptune. Using only mathematics and astronomical observations of the known planet Uranus and encouraged by physicist Arago, Director of the Paris Observatory, Le Verrier was intensely engaged for months in complex calculations to explain small but systematic discrepancies between Uranus's observed orbit and the one predicted from the laws of gravity of Newton. At the same time, but unknown to Le Verrier, similar calculations were made by John Couch Adams in England. Le Verrier announced his final predicted position for Uranus's unseen perturbing planet publicly to the French Academy on 31 August 1846, two days before Adams's final solution, which turned out to be 12° off the mark, was privately mailed to the Royal Greenwich Observatory. Le Verrier transmitted his own prediction by 18 September letter to Johann Galle of the Berlin Observatory. The letter arrived five days later, and the planet was found with the Berlin Fraunhofer refractor that same evening, 23 September 1846, by Galle and Heinrich d'Arrest within 1° of the predicted location near the boundary between Capricorn and Aquarius. *Wik

In 1886, the first U.S. earthquake on record with significant human consequence - the loss of some 100 lives - hit Charleston, S.C. and its massive effect spread through many eastern States. The epicenter was 15 miles northwest of Charleston, where 41 people died, 90 percent of the city's 6,956 brick buildings were damaged, and nearly all of its 14,000 chimneys were broken off at the roof. However, geologically the most severe earthquakes in U.S. history had occurred earlier in the century near the present town of New Madrid, Missouri (16 Dec 1811). The epicenter then was in a sparsely populated region and caused no known casualties, so the human consequences were relatively not significant, although the violent movement of the ground changed the course of the Mississippi River and created many new lakes.*TIS

1899 Cantor, in a letter to Dedekind, remarked that his “diagonal process” can be used to show that the power set of a set has more elements than the set itself. *VFR

1950 G¨odel addressed the International Congress of Mathematicians, in Cambridge, Massachusetts, on his work in relativity theory. *VFR

2012 A Blue Moon, or the second of two full moons in a single month. August 2012 will have a blue moon on August 31 The last month with two full moons was March of 2010 March 1 and March 30. The next month with a blue moon will be in 2012: August 2, August 31. Once in a Blue moon really isn’t all that often.

1663 Guillaume Amontons (31 Aug 1663; 11 Oct 1705)French physicist, who developed the air thermometer - which relies on increase in volume of a gas (rather than a liquid) with temperature - and used it (1702) to measure change in temperature in terms of a proportional change in pressure. This observation led to the concept of absolute zero in the19th century. Deaf since childhood, Amontons worked on inventions for the deaf, such as the first telegraph, which relied on a telescope, light, and several stations to transmit information over large distances. Amontons' laws of friction, relied upon by engineers for 300 years, state that the frictional force on a body sliding over a surface is proportional to the load that presses them together and is also independent of the areas of the surfaces. *TIS

1821 Hermann Ludwig Ferdinand von Helmholtz (31 Aug 1821; 8 Sep 1894) was a German scientist who contributed much to physiology, optics, electrodynamics, mathematics, and meteorology, including the law of the conservation of energy (1847). He also developed thermodynamics, in particular introducing concept of free energy. In 1850, he measured the speed of a nerve impulse and, in 1851, invented the ophthalmoscope. He discovered the function of the cochlea in the inner ear and developed Thomas Young's theory of color vision (published 1856). His study of muscle action led him to formulate a much more accurate theory concerning the conservation of energy than earlier proposed by Julius Mayer and James Joule. *TIS

1864 Robert Hardie graduated from Oxford and occupied various posts in the Philosophy department of Edinburgh University. He was a founder member of the EMS. *SAU

1880 Heinrich Franz Friedrich Tietze contributed to the foundations of general topology and developed important work on subdivisions of cell complexes. The bulk of this work was carried out after he took up the chair at Munich in 1925.*SAU

1884 Birthdate of George Alfred L´eon Sarton, historian of science and founder of the journal Isis. *VFR

1885 Herbert Westren Turnbull (31 Aug 1885; 4 May 1961)English mathematician who made extensive and notable contributions to the study of algebraic invariants and concomitants of quadratics. Turnbull was also interested in the history of mathematics, writing The Mathematical Discoveries of Newton (1945), and began work on the Correspondence of Isaac Newton.*TIS

1913 Sir Alfred Charles Bernard Lovell (31 Aug 1913, ) is an English radio astronomer who established and directed (1951-81) Jodrell Bank Experimental Station, Cheshire, England, with (then) the world's largest steerable radiotelescope, now named after him Prior to WW II, he worked at Manchester University on cosmic ray research. During the war, he helped develop aircraft onboard radar systems. After the war, to escape interference to radar equipment from city trams, he moved his research to the University's more remote Jodrell Bank property. In 1946, he showed that radar echoes could detect optically invisible daytime meteor showers. He gained funding to build the 250-ft-diam. telescope. When completed in 1957, it was able to track the first artificial satellite, Sputnik I. *TIS

1916 Robert Hanbury Brown (31 Aug 1916; 16 Jan 2002) British astronomer who was a pioneer in radar and observational astronomy. During and after WW II he worked with R.A. Watson-Watt and then E.G. Bowen to develop radar for uses in aerial combat. In the 1950s he applied this experience to radio astronomy, developing radio-telescope technology at Jodrell Bank Observatory and mapping stellar radio sources. He designed a radio interferometer capable of resolving radio stars while eliminating atmospheric distortion from the image (1952). With R.Q. Twiss, Brown applied this method to measuring the angular size of bright visible stars, thus developing the technique of intensity interferometry. They set up an intensity interferometer at Narrabri in New South Wales, Australia, for measurements of hot stars.*TIS

1721 John Keill (1 Dec 1671, 31 Aug 1721) Scottish mathematician and natural philosopher, who was a major proponent of Newton’s theories. He began his university education at Edinburgh under David Gregory, whom he followed to Oxford, where Keill lectured on Newton's work, and eventually became professor of astronomy. In his book, An Examination of Dr. Burnett's Theory of the Earth (1698), Keill applied Newtonian principles challenging Burnett's unsupportable speculations on Earth's formation. In 1701, Keill published Introductio ad Veram Physicam, which was the first series of experimental lectures and provided a clear and influential introduction to Isaac Newton’s Principia. He supported Newton against priority claims by Leibnitz for the invention of calculus.*TIS

1811 Louis-Antoine de Bougainville was a French soldier and explorer who wrote a calculus book, but is better known for his other exploits.*SAU A contemporary of James Cook, he took part in the French and Indian War and the unsuccessful French attempt to defend Canada from Britain. He later gained fame for his expeditions to settle the Falkland Islands and his voyages into the Pacific Ocean.*Wik

1918 André-Louis Cholesky (October 15, 1875, August 31, 1918, ) was a French military officer and mathematician. He worked in geodesy and map-making, was involved in surveying in Crete and North Africa before World War I. But he is primarily remembered for the development of a matrix decomposition known as the Cholesky decomposition which he used in his surveying work. He served the French military as engineer officer and was killed in battle a few months before the end of World War I; his discovery was published posthumously by his fellow officer in the "Bulletin Géodésique". *Wik

1945 Stefan Banach died. (30 Mar 1892, 31 Aug 1945) Polish mathematician who founded modern functional analysis and helped develop the theory of topological vector spaces. In addition, he contributed to measure theory, integration, the theory of sets, and orthogonal series. In his dissertation, written in 1920, he defined axiomatically what today is called a Banach space. The idea was introduced by others at about the same time (for example Wiener introduced the notion but did not develop the theory). The name 'Banach space' was coined by Fréchet. Banach algebras were also named after him. The importance of Banach's contribution is that he developed a systematic theory of functional analysis, where before there had only been isolated results which were later seen to fit into the new theory. *TIS

2005 Sir Joseph Rotblat (4 Nov 1908, 31 Aug 2005)Polish-born British physicist who is a leading critic of nuclear weaponry. Rotblat and the Pugwash Conferences, "for their efforts to diminish the part played by nuclear arms in international politics and in the longer run to eliminate such arms," received the Nobel Peace Prize in 1995. Forty years earlier, he and other scientists, with philosopher Bertrand Russell and Albert Einstein, published a manifesto calling on researchers to take responsibility for their work, particularly those working on the atomic bomb. This led to the Pugwash Conferences on Science and World Affairs, first convened in 1957 in Pugwash, Nova Scotia, Canada. He was secretary-general (1957-73), and president (from 1988) of this London-based worldwide organization. *TIS

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

Tuesday, 30 August 2011

On This Day in Math - Aug 30

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

The 242nd day of the year; 242 has six divisors...but 243, 244, and 245 also each has six divisors. 242 is the smallest integer to begin a run of four consecutive integers all of which have the same number of divisors. (What is the smallest integer that begins a run of three consecutive integers with an equal number of divisors?)

In 1831, Charles Darwin replied to the letter from Revd. Henslow telling him of the offer to sail on the H.M.S. Beagle. Darwin's had learned natural history from Henslow, who had recommended him for the unpaid position as a naturalist. Darwin told Henslow that his father would not permit him to leave on such a voyage. Meanwhile, his father had written to his brother-in-law, Josiah Wedgwood II, about his concerns regarding the proposed two-year jaunt. This afternoon Darwin prepared to join the Wedgwoods for the next day's beginning of the shooting season by riding to Maer Hall, the Wedgwood home. The Darwin family was related to the Wedgwood family through the marriage of Darwin's father to the daughter of the first Josiah Wedgwood, the famous potter. *TIS

1791  Thomas Jefferson sends a letter to Benjamin Banneker after receiving his almanac and a letter announcing that, "Sir, I freely and cheerfully acknowledge, that I am of the African race, and in that color which is natural to them of the deepest dye".  Jefferson responds that, " I thank you sincerely for your letter of the 19th. instant and for the Almanac it contained. no body wishes more than I do to see such proofs as you exhibit, that nature has given to our black brethren, talents equal to those of the other colours of men, & that the appearance of a want of them is owing merely to the degraded condition of their existence both in Africa & America. I can add with truth that no body wishes more ardently to see a good system commenced for raising the condition both of their body & mind to what it ought to be, as fast as the imbecillity of their present existence, and other circumstance which cannot be neglected, will admit. I have taken the liberty of sending your almanac to Monsieur de Condorcet, Secretary of the Academy of sciences at Paris, and member of the Philanthropic society because I considered it as a document to which your whole colour had a right for their justification against the doubts which have been entertained of them. I am with great esteem, Sir, Your most obedt. humble servt. Th. Jefferson" *Mathematicians of the African Diaspora, SUNY at Buffalo

In 1831, Michael Faraday demonstrated the first electrical transformer.*TIS

1908 A committee appointed by the Swiss society of naturalists reported its willingness, provided sufficient financial assistance could be secured, to publish the complete works of Euler in about 40 volumes. Today 80 volumes of Euler’s Opera Omnia have been published, and the end is hardly in sight.*VFR

In 1963, the "Hot Line" communications link between the White House, Washington D.C. and the Kremlin, Moscow, went into operation to provide a direct two-way communications channel between the American and Soviet governments in the event of an international crisis. This was one year after the Cuban Missile Crisis. It consisted of one full-time duplex wire telegraph circuit, routed Washington- London- Copenhagen- Stockholm- Helsinki- Moscow, used for the transmission of messages and one full-time duplex radiotelegraph circuit, routed Washington- Tangier- Moscow used for service communications and for coordination of operations between the two terminal points. Note, this was not a telephone voice link.*TIS

In 1979, Comet Howard-Koomen-Michels (SOLWIND I) collided with the Sun, the first recorded comet to collide with Sun and the first discovered by a spacecraft. The coronographs taken on 30 and 31 Aug 1979 from the satellite P78-1 used to monitor solar corona activity were not inspected until Sep 1981, by Russ Howard. The recording instruments were designed and operated by Martin Koomen and Don Michels. The remarkable series of images showed the comet heading around the Sun. Its perihelion distance was too small, and the head did not reappear from behind the Sun, presumably disintegrated by the heat of the sun. The decapitated comet's tail continued, becoming fan-like, brightening the corona, until dissipated and blown away from the Sun*TIS

1804 Ernst Grebe is remembered only for a thoughtful paper appeared in 1847  concerning some interesting properties of the triangle: If on each side of a given (arbitrary) triangle ABC one describes a square ( exterior to ABC ), then the extended outside sides of the squares, thus obtained, form a similar triangle A'B'C'. The center of similarity of both triangles is the meeting point of the straight lines AA', BB', CC'. In German this point was first called _Grebe'schen Punkt_ [Grebe's point], a TERM which seems to have been first referred to by E. Hain as early as 1875, in his paper "Ueber den Grebe'schen Punkt" [ _Archiv der Mathematik und Physik_ (= Grunert's _Archive_) volume LVIII (1876), pp. 84-89 ] *Julio Gonzalez Cabillon , Posting to the Historia Matematica discussion group

1819 Joseph Alfred Serret (30 Aug 1819 in Paris, France - 2 March 1885 in Versailles, France) He was a French mathematician best remembered for the Serret-Frenet formulas for a space-curve. In 1860 Serret succeeded Poinsot in the Académie des Sciences. In 1871 he retired to Versailles as his health began to deteriorate.
Serret also worked in number theory, calculus and mechanics. He edited the works of Lagrange which were published in 14 volumes between 1867 and 1892. He also edited the 5th edition of Monge in 1850.*SAU
1856 Carl David Tolmé Runge worked on a procedure for the numerical solution of algebraic equations and later studied the wavelengths of the spectral lines of elements. *SAU In numerical analysis, the Runge–Kutta methods that are named for him are an important family of implicit and explicit iterative methods for the approximation of solutions of ordinary differential equations. These techniques were developed around 1900 Runge and M.W. Kutta.*Wik When your regular walking partners include Felix Klein, David Hilbert, and Hermann Minkowski, you can't count on easily impressing them with your mental math skills, but it seems that Runge did so frequently. Once on their regular walks Klein brought up some departmental event that required them to know what date Easter would occur the next year. The group immediately turned to the idea of where they might acquire a calendar for the following year along the walk; all that is, except Runge who fell silent for a few yards, and then announced the date.

1871 Sir Ernest Rutherford (30 Aug 1871; 19 Oct 1937). (baron) New Zealand-born British physicist who laid the groundwork for the development of nuclear physics. He worked under Sir J. J. Thomson at Cambridge University (1895-98). Then he collaborated with Frederick Soddy in studying radioactivity. In 1899 he discovered alpha particles and beta particles, followed by the discovery of gamma radiation the following year. In 1905, with Soddy, he announced that radioactive decay involves a series of transformations. In 1907, with Hans Geiger and Ernest Marsden, he devised the alpha-particle scattering experiment that led in 1911 to the discovery of the atomic nucleus. In 1919 he achieved the artificial splitting of light atoms. In 1908 he was awarded the Nobel Prize for Chemistry. *TIS A story is told by A.. V. Hill that Rutherford had told him once, "I've just been reading some of my early papers, and when I had read them for a bit I said to myself, "Ernest my boy, you used to be a darn clever fellow.'" *Walter Gratzer, Eurekas and Euphorias, pg 27
 [I love this quote from a few years before his death. "The energy produced by the breaking down of the atom is a very poor kind of thing. Anyone who expects a source of power from the transformation of these atoms is talking moonshine."]

1906 Olga Taussky-Todd ,  She received her Ph.D. in 1930 under Philip Furtwangler at Vienna in number theory. Her first job involved editing Hilbert’s papers on number theory.*VFR

1907 John Mauchly (30 Aug 1907; 8 Jan 1980) American physicist and engineer, who with John P. Eckert invented (1946) the Electronic Numerical Integrator and Computer (ENIAC), the first general-purpose electronic computer. Mauchly initially conceived of the computer's architecture, and Eckert possessed the engineering skills to bring the idea to life. ENIAC was developed (1946) for the US Army Ordnance Department as what was probably the first general-purpose electronic computer. It was a vast machine, consuming 100 kW of electric power and containing 18,000 electronic valves. Their successful UNIVAC computer (1951) was the first commercial computer, and introduced magnetic tape for programming.*TIS

1907 Gordon Brown founded the Servomechanisms Laboratory at MIT, which pioneered the development of feedback-control theory, computer technology, and automatic control of machine tools and had many famous graduate students who went on to become major contributors in the fields of Electrical Engineering and Computer Science. *CHM

1912 E.M. Purcell (30 Aug 1912; 7 Mar 1997) American physicist who shared, with Felix Bloch of the United States, the Nobel Prize for Physics in 1952 for his independent discovery (1946) of nuclear magnetic resonance in liquids and in solids. Nuclear magnetic resonance (NMR) has become widely used to study the molecular structure of pure materials and the composition of mixtures. The method detects and measures the magnetic fields of atomic nuclei. *TIS

1621 Baha' ad-Din al-Amili (27 Feb 1547 in Baalbek, now in Lebanon - 30 Aug 1621 in Isfahan, Iran) was a Lebanese-born mathematician who wrote influential works on arithmetic, astronomy and grammar. Perhaps his most famous mathematical work was Quintessence of Calculation which was a treatise in ten sections, strongly influenced by The Key to Arithmetic (1427) by Jamshid al-Kashi. *SAU

1844 Francis Baily (28 Apr 1774, 30 Aug 1844)English astronomer who detected the phenomenon called "Baily's beads" during an annular eclipse of the Sun on 15 May 1836. His vivid description aroused new interest in the study of eclipses. After retiring in 1825 from a successful business career, Baily turned to science. Baily revised several star catalogs, repeated Henry Cavendish's experiments to determine the density of the Earth, and measured its elliptical shape. His protests regarding the British Nautical Almanac, then notorious for its errors, were instrumental in bringing about its reform.*TIS  A really nice discussion of the many contributions of Baily is in this post at The Renaissance Mathematicus, To whet your appetite, " Baily’s Flamsteed memoir had a major influence on the history and the historiography of science; he had succeeded in pricking Newton’s hagiographic bubble. St Isaac had been taken down a peg or two. Baily’s work marks a turning point in our understanding of Newton moving him along the road from plastic saint to real, if somewhat unpleasant, human being. Sometimes editing star catalogues can lead to unexpected results for the history of science."

1928 Wilhelm Wien (13 Jan 1864, 30 Aug 1928)German physicist who received the Nobel Prize for Physics in 1911 for his displacement law concerning the radiation emitted by the perfectly efficient blackbody (a surface that absorbs all radiant energy falling on it). While studying streams of ionized gas Wien, in 1898, identified a positive particle equal in mass to the hydrogen atom. Wien, with this work, laid the foundation of mass spectroscopy. J J Thomson refined Wien's apparatus and conducted further experiments in 1913 then, after work by E Rutherford in 1919, Wien's particle was accepted and named the proton. Wien also made important contributions to the study of cathode rays, X-rays and canal rays.*TIS [I find it curiously interesting that all three of the great physicists mentioned here either were born or died this day]

1940 Sir J(oseph) J(ohn) Thomson (born 18 Dec 1856, 30 Aug 1940 )was an English physicist who helped revolutionize the knowledge of atomic structure by his discovery of the electron (1897). He received the Nobel Prize for Physics in 1906 and was knighted in 1908. Thomson experimented with currents of electricity inside empty glass tubes, investigating a long-standing puzzle known as "cathode rays." His experiments prompted him to make a bold proposal: these mysterious rays are streams of particles much smaller than atoms. He called these particles "corpuscles," and suggested that they might make up all of the matter in atoms. It was startling to imagine a particles inside the atom at a time when most people thought that the atom was indivisible, the most fundamental unit of matter.*TIS

1995 Fischer Sheffey Black (January 11, 1938, August 30, 1995) was an American economist, best known as one of the authors of the famous Black–Scholes equation.In 1973, Black, along with Myron Scholes, published the paper 'The Pricing of Options and Corporate Liabilities' in 'The Journal of Political Economy'. This was his most famous work and included the Black–Scholes equation. The Nobel Prize is not given posthumously, so it was not awarded to Black in 1997 when his co-author Myron Scholes received the honor for their landmark work on option pricing along with Robert C. Merton, another pioneer in the development of valuation of stock options. In the announcement of the award that year, the Nobel committee prominently mentioned Black's key role.*Wik

2004 Fred Lawrence Whipple (5 Nov 1906, 30 Aug 2004) was an American astronomer who proposed the "dirty snowball" model for comet nuclei. In the 1930s, using a new, two-station method of photography, he determined meteor trajectories and found that nearly all visible meteors are made up of fragile material from comets, and that none come from beyond the solar system. Whipple suggested (1950) that comets have icy cores inside thin insulating layers of dirt, and that jets of material ejected as a result of solar heating were the cause of orbital changes. This model was confirmed in 1986 when spacecraft flew past comet Halley. Whipple’s work on tracking artificial satellites led to improved knowledge of the shape of the earth and greatly improved positions on earth. *TIS

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

Monday, 29 August 2011

On This Day in Math - Aug 29

In most sciences one generation tears down what another has built,
and what one has established, another undoes.
In mathematics alone each generation adds a new storey to the old structure.
~Hermann Hankel

The 241st day of the year; 241 is the larger of a pair of twin primes. The larger of a pair of twin primes is always one more than a multiple of six; the smaller is always one less than a multiple of six.

1609 Galileo writes to his brother in Florence to tell him about his telescope presentation to the Doge on the 24th of August.

1654 Fermat to Pascal Saturday, August 29, 1654
Our interchange of blows still continues, and I am well pleased that our thoughts are in such complete adjustment as it seems since they have taken the same direction and followed the same road. Your recent Trait´e du triangle arithmetique and its applications are an authentic proof and if my computations do me no wrong, your eleventh consequence went by post from Paris to Toulouse while my theorem, on figurate numbers, which is virtually the same, was going from Toulouse to Paris. I have not been on watch for failure while I have been at work on the problem and I am persuaded that the true way to escape failure is by concurring with you. But if I should say more, it would he of the nature of a Compliment and we have banished that enemy of sweet and easy conversation. It is now my turn to give you some of my numerical discoveries, but the end of the parliament augments my duties and I hope that out of your goodness you will allow me due and almost necessary respite.
In the same letter he states that, "Meditate however, if you find it convenient, on this theorem: The squared powers of 2 augmented by unity [I.e. 22n+1] are always prime numbers. [That is,] The square of 2 augmented by unity makes 5 which is a prime number;The square of the square makes 16 which, when unity is added makes 17, a prime number; The square of 16 makes 256 which, when unity is added, makes 257, a prime number; The square of 256 makes 65536 which, when unity is added, makes 65537, a prime number; and so to infinity. This is a property whose truth I will answer to you. The proof of it is very difficult (impossible, since the statement, as Euler would show later, is not true)and I assure you that I have not yet been able to find it fully." * York University Maths Dept

1831 Michael Faraday discovered electrical induction. *VFR In 1831, Michael Faraday wound a thick iron ring on one side with insulated wire that was connected to a battery. He then wound the opposite side with wire connected to a galvanometer. He found that upon closing the battery circuit, there was a deflection of the galvanometer in the second circuit. Then he was astonished to see the galvanometer needle jump in the opposite direction when the battery circuit was opened. He had discovered that a current was induced in the secondary when a current in the primary was connected and an induced current in the opposite direction when the primary current was disconnected.*TIS

1899 Dedekind sends a letter to Georg Cantor that includes a proof of the Schroder-Bernstein Theorem (Let A and B be sets. If there is a 1-1 correspondence from A to B and a 1-1 corespondence from B to A, then the sets have the same cardinality.) *Cantorian Set Theory and Limitation of Size By Michael Hallett

In 1940, Sir Henry Tizard led a mission of leading British and Canadian scientists to the USA to brief official American representatives on devices under active development for war use and to enlist the support of American scientists. Thus began a close cooperation of Anglo-American scientists in such fields as aeronautics and rocketry. His influence probably made the difference between defeat or victory at the Battle of Britain in 1940. *TIS

1949 the USSR tested their first atomic device, "First Lightning." It was an an implosive type plutonium bomb, detonated at the Semipalatinsk test range, giving up to a 20 kiloton yield. In the U.S. it was calledJoe No. 1 ("Joe" was nickname for Y. Stalin.) This event came five years earlier than anyone in the West had predicted, largely due to one man, the spy Klaus Fuchs. As a Los Alamos physicist, Fuchs had passed detailed blue prints of the original American Trinity bomb design to the Russians. With the emergence of the USSR as a nuclear rival, America's monopoly of atomic weaponry was ended giving the U.S. strong motivation for intensifying its program of nuclear testing. Thus the Cold War was launched.*TIS

1990 The British Computer Misuse Act goes into effect One of the earliest laws anywhere designed to address computer fraud, the Act resulted from a long debate in the 1980s over failed prosecutions of hackers -- in one well-publicized case, two men hacked into a British Telecom computer leaving messages in the Duke of Edinburgh's private mailbox. *CHM


1876 Charles F. Kettering (29 Aug 1876; 25 Nov 1958) was an American engineer whose 140 patents included the electric starter, car lighting and ignition systems. In his early career, with the National Cash Register Co., Dayton (1904-09), he created the first electric cash register with an electric motor that opened the drawer. When he co-founded the Dayton Engineering Laboratories Company (DELCO, with Edward A. Deeds) he invented the key-operated self-starting motor for the Cadillac (1912) and it spread to nearly all new cars by the 1920's. As vice president and director of research for General Motors Corp. (1920-47) he developed engines, quick-drying lacquer finishes, anti-knock fuels, and variable-speed transmissions.*TIS

1881 Ferdinand Springer born, The founder of an important publishing house,. Today Springer-Verlag is one of the most important publishers of advanced work on mathematics. *VFR

1904 Leonard Roth British Mathematician who worked primarily in Algebraic Geometry. *SAU

1873 Hermann Hankel He studied and worked with, among others, Möbius, Riemann, Weierstrass and Kronecker. His 1867 exposition on complex numbers and quaternions is particularly memorable. For example, Fischbein notes that he solved the problem of products of negative numbers by proving the following theorem: "The only multiplication in R which may be considered as an extension of the usual multiplication in R+ by respecting the law of distributivity to the left and the right is that which conforms to the rule of signs." *Wik

1930 James Bolam was educated at Newcastle. He became head of the Government Navigation School (later the Leith Nautical College). He was a founder member of the EMS and became an honorary member in 1923. *SAU

1937 Otto Ludwig Hölder worked on the convergence of Fourier series and in 1884 he discovered the inequality now named after him. He became interested in group theory through Kronecker and Klein and proved the uniqueness of the factor groups in a composition series. *SAU

1967 Charles Brace Darrow (10 Aug 1889, 29 Aug 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 Charles 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

1975 Éamon de Valera (14 October 1882, 29 August 1975) was one of the dominant political figures in twentieth century Ireland, serving as head of government of the Irish Free State and head of government and head of state of Ireland. He also introduced the Constitution of Ireland.
De Valera was a leader of Ireland's struggle for independence from Britain in the Irish War of Independence and of the anti-Treaty forces in the ensuing Irish Civil War (1922–23). In 1926, he founded Fianna Fáil and was head of government from 1932–48, 1951–54 and 1957–59 and President of Ireland from 1959–73.
In his youth he had trained as a mathematician and taught mathematics prior to the Easter Rising. Throughout his life he maintained an interest in mathematics and returned to it with a passion in his later life. *Wik

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

Sunday, 28 August 2011

On This Day in Math - Aug 28

As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection.
~Joseph Louis Lagrange

The 240th day of the year; 240 has more divisors (20 of them) than any previous number. What would be the first number that has more?

412 BC The ancient city of Syracuse suffered heavily under siege by the Athenians during the Peloponnesian War. A turn of events occurred during the Second Battle of Syracuse: on Aug. 28, 412 B.C. a lunar eclipse occurred, causing the superstitious Athenians to delay departure. The Syracuseans took advantage of Athenian indecision and decisively defeated the unprotected Athenian expedition as it sat exposed in the harbor. *
In 1789, Sir William Herschel discovered Saturn's moon Enceladus. *TIS

1845 , the first issue of the Scientific American was published by Rufus Porter (1792-1884), a versatile if eccentric Yankee, who was by turns a portrait-painter, schoolmaster, inventor and editor. While the paper was still a small weekly journal with a circulation less than 300, he offered it for sale. It was bought for $800 in July 1846 by 20-year-old Alfred Ely Beach (1826-1896) as editor, and Orson Desaix Munn (1824-1907). Together, they built it over the years into a great and unique periodical. Their circulation reached 10,000 by 1848, 20,000 by 1852, and 30,000 by 1853.*TIS

1961 The Board of Governors of the MAA voted to name Dr. Mina S. Rees, (first) Dean of Graduate Studies at the City University of New York, the first recipient of their Award for Distinguished Service to Mathematics. From 1946 to 1953 she held several important positions at the Office of Naval Research and was instrumental in getting ONR to adopt the policy that mathematics was part of this country’s total scientific effort and should be properly supported by government-sponsored research programs. [AMM 69(1962), pp. 185-187]. *VFR

1974 Sweden issued a stamp picturing a spool and thread, with the thread stretched to form a string figure of a hyperbola. [Scott #1094]. *VFR

1993, a picture was taken showing the first moon of an asteroid. The asteroid 243 Ida and its newly-discovered moon, Dactyl was imaged by NASA's Galileo spacecraft, about 14 minutes before its closest approach (within 2,400-km or 1,500 miles) to the asteroid. Ida is about 52 km (32 mi) in length and is irregularly shaped. It shows numerous craters, including many degraded craters, indicating Ida's surface is older than previously thought. Dactyl is only about 1.4-km in diameter, and it is spectrally different from Ida data. The picture was released on 26 Mar 1994. Galileo had encountered the first asteroid - 951 Gaspra - on 29 Oct 1991. Galileo continued on its mission to study Jupiter, beginning its orbit of the planet on 7 Dec 1995.*TIS

1749 Johann Wolfgang von Goethe born.

1796 Irénée-Jules Bienaymé (28 August 1796, 19 October 1878), was a French statistician. He built on the legacy of Laplace generalizing his least squares method. He contributed to the fields and probability, and statistics and to their application to finance, demography and social sciences. In particular, he formulated the Bienaymé-Chebyshev inequality concerning the law of large numbers and the Bienaymé formula for the variance of a sum of uncorrelated random variables.*Wik

1801 Antoine-Augustin Cournot (28 Aug 1801; 31 Mar 1877) French economist and mathematician, who was the first economist who applied mathematics to the treatment of economic questions. In 1838, he published Recherches sur les principes mathématiques de la théorie des richesses (Researches into the Mathematical Principles of the Theory of Wealth) which was a treatment of mathematical economics. In particular, he considered the supply-and-demand functions. Further, he studied the conditions for equilibrium with monopoly, duopoly and perfect competition. He included the effect of taxes, treated as changes in production costs, and discussed problems of international trade. His definition of a market is still the basis for that presently used in economics. In other work, he applied probability to legal statistics *TIS

1863 Andre-Eugene Blondel (28 Aug 1863; 15 Nov 1938) was a French physicist who invented (1893) the electromagnetic oscillograph, a device that allowed electrical researchers to observe the intensity of alternating currents. In 1894, he proposed the lumen and other new photometric units for use in photometry, based on the metre and the Violle candle. Endorsed in 1896 by the International Electrical Congress, his system is still in use with only minor modifications. Blondel was a pioneer in the high voltage long distance transport of electric power, and also contributed to developments in wireless telegraphy, acoustics, and mechanics. He proposed theories for induction motors and coupling of a.c. generators.*TIS

1867 Maxime Bˆochner born. After receiving his doctorate under Felix Klein in 1891 he returned to Harvard for a lifetime of teaching and research in differential equations. *VFR

1883 Jan A Schouten worked on tensor analysis and its applications.*SAU

1901 Kurt Otto Friedrichs (September 28, 1901 – December 31, 1982) was a noted German American mathematician. He was the co-founder of the Courant Institute at New York University and recipient of the National Medal of Science.*Wik

1911 Shizuo Kakutani (角谷 静夫 Kakutani Shizuo?, August 28 1911, August 17 2004) was a Japanese-born American mathematician, best known for his eponymous fixed-point theorem. *Wik

1919 Sir Godfrey Newbold Hounsfield (28 Aug 1919; 12 Aug 2004) English electrical engineer who shared the 1979 Nobel Prize for Physiology or Medicine (with Allan Cormack) for creation of computerised axial tomography (CAT) scanners. He originated the idea during a country walk in 1967 when he realized that the contents of a box could be reconstructed by taking readings at all angles through it. He applied the concept for scanning the brain using hundreds of X-ray beams imaging cross-sections that were reconstructed as high-resolution graphics by a computer program handling complex algebraic calculations. By 1973 his CAT scanner could produce cross-section images of a brain in 4-1/2-min, invaluable for the diagnosis of brain diseases. He later built larger machines able to make a full body scan. *TIS

1939 John Frank Charles Kingman worked in Statistics and made significant advances in queuing theory.

2005 George Szekeres was a Hungarian-born mathematician who worked for most of his life in Australia on geometry and combinatorics. *SAU

2007 Paul Beattie MacCready (29 Sep 1925, 28 Aug 2007) was an American engineer who invented not only the first human-powered flying machines, but also the first solar-powered aircraft to make sustained flights. On 23 Aug 1977, the pedal-powered aircraft, the Gossamer Condor successfully flew a 1.15 mile figure-8 course to demonstrate sustained, maneuverable manpowered flight, for which he won the £50,000 ($95,000) Kremer Prize. MacCready designed the Condor with Dr. Peter Lissamen. Its frame was made of thin aluminum tubes, covered with mylar plastic supported with stainless steel wire. In 1979, the Gossamer Albatross won the second Kremer Prize for making a flight across the English Channel. *TIS

2011 Anthony Edgar Sale (or Tony Sale) (30 January 1931 - 28 August 2011) led the construction of a Colossus computer replica at Bletchley Park, completed in 2007 *Wik

In 1994, a team led by Tony Sale began a reconstruction of a Colossus at Bletchley Park. Here, in 2006, Sale (right) supervises the breaking of an enciphered message with the completed machine. *Wik Photo
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum