Saturday, 31 December 2011

On This Day in Math - Dec 31

For other great mathematicians or philosophers, he [Gauss] used the epithets magnus, or clarus, or clarissimus; for Newton alone he kept the prefix summus.
~W.W.R. Ball

The 365th (and last) day of the year; 365 is a centered square number, and thus the sum of two consecutive squares and also one more than four times a triangular number. (Students could explore which triangular number and which square numbers produce 365.)

1831  Gauss writes to his close friend, Wilhelm Olbers regarding an essay published by Laplace, "The essay...  is quite unworthy of this great geometer. I find two different, very gross blunders in it.  I had always imagined that among geometers of the first rank the calculation was always only the dress in which they present that which they created not by calculation, but by mediation about the subject itself. ". *Carl Friedrich Gauss: Titan of Science by Guy Waldo Dunnington, Jeremy Gray, Fritz-Egbert Dohse

1915 The Mathematical Association of America was founded in Columbus, Ohio. Starting with 1045 charter members, the Association now has some 34,000 members who are interested in the improvement of mathematical instruction at the collegiate level. *VFR

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. He had invented the game on 7 Mar 1933, though it was preceded by other real-estate board games. *TIS

1987 The last minute (UT) of the last hour of the last day of the year 1987 carried an extra second, a leap second. This was to coordinate the slowdown in rotation of the Earth on its axis, or Solar Time, with the more precise atomic time. The one-second insertion was made at 6:59:59 P.M. at the Naval Observatory in Washington D.C. Just exactly when the proverbial man-in-the¬street choose to insert this second was his own business, but in New York’s Times Square it was done with much hoopla at midnight. *U.S. Naval Observatory's “Stargazing Notes for December 1987.” *VFR

1999 Millenium memorial puzzle at Luppitt. It is made of fine grained granite, which is an exceptionally hard stone. It was unveiled on 31st December 2000 - Just in time for the true Millennium. The puzzles on the site, as described at the puzzle's website:
The puzzles include a wordsearch concealing over 30 local placenames, a three way anamorphic illusion, a completely new idea based on the Tinner's Rabbits, an ancient maze from a French church, a modern Railway Maze (specially designed by Professor Sir Roger Penrose), a Word Anagram, a Letter misplacement puzzle, a traditional Word square puzzle, cryptarithms, hidden mice, and other curiosities and puzzles.

1999 Professor Andrew Wiles is knighted. The Princeton mathematician found fame in October 1994 when he succeeded in proving Fermat's Last Theorem. This was an amazing achievement that had eluded some of the greatest minds since Pierre Fermat conjured up his theory in the 1630s. His work has received every major honour and he had the pleasure in 1999 of seeing some of his former pupils crack another of mathematics' great puzzles: The Shimura-Taniyama-Weil conjecture. *BBC

1999 Alan Sugar, the man who founded Amstrad some 30 years ago and now runs Tottenham Hotspur football club, has been knighted.
So too has Maurice Wilkes, who developed the world's first practical stored-program computer in 1949.
"I'm tickled pink by the news," said Mr Sugar, whose company launched the world's first mass-market word processor built with low-cost components from the Far East.
At the height of its success, Amstrad was worth £1.5bn on the FTSE-100 index. Mr Sugar eventually broke Amstrad up, spinning off Viglen Technology, its personal computer business, of which he is now chairman.
Maurice Wilkes led the Cambridge University team that developed the Edsac - Electronic Delay Storage Automatic Calculator. It was a huge contraption that could carry out just 650 instructions per second. Nevertheless, it went down in history as the first truly programmable computer. *BBC

1864 Robert Grant Aitken (31 Dec 1864; 29 Oct 1951) American astronomer who specialized in the study of double stars, of which he discovered more than 3,000. He worked at the Lick Observatory from 1895 to 1935, becoming director from 1930. Aitken made systematic surveys of binary stars, measuring their positions visually. His massive New General Catalogue of Double Stars within 120 degrees of the North Pole allowed orbit determinations which increased astronomers' knowledge of stellar masses. He also measured positions of comets and planetary satellites and computed orbits. He wrote an important book on binary stars, and he lectured and wrote widely for the public.*TIS

1896 Carl Ludwig Siegel (December 31, 1896 – April 4, 1981) was a mathematician specializing in number theory and celestial mechanics. He was one of the most important mathematicians of the 20th century.
Among his teachers were Max Planck and Ferdinand Georg Frobenius, whose influence made the young Siegel abandon astronomy and turn towards number theory instead. His best student was Jürgen Moser, one of the founders of KAM theory (Kolmogorov-Arnold-Moser), which lies at the foundations of chaos theory.
Siegel's work on number theory, diophantine equations, and celestial mechanics in particular won him numerous honours. In 1978, he was awarded the Wolf Prize in Mathematics, one of the most prestigious in the field.
Siegel's work spans analytic number theory; and his theorem on the finiteness of the integer points of curves, for genus greater than 1, is historically important as a major general result on diophantine equations, when the field was essentially undeveloped. He worked on L-functions, discovering the (presumed illusory) Siegel zero phenomenon. His work derived from the Hardy-Littlewood circle method on quadratic forms proved very influential on the later, adele group theories encompassing the use of theta-functions. The Siegel modular forms are recognised as part of the moduli theory of abelian varieties. In all this work the structural implications of analytic methods show through.
André Weil, without hesitation, named Siegel as the greatest mathematician of the first half of the 20th century. In the early 1970s Weil gave a series of seminars on the history of number theory prior to the 20th century and he remarked that Siegel once told him that when the first person discovered the simplest case of Faulhaber's formula then, in Siegel's words, "Es gefiel dem lieben Gott." (It pleased the dear Lord.) Siegel was a profound student of the history of mathematics and put his studies to good use in such works as the Riemann-Siegel formula.*Wik

1929 Jeremy Bernstein (31 Dec 1929, ) American physicist, educator, and writer widely known for the clarity of his writing for the lay reader on the major issues of modern physics. He was a staff writer for the New Yorker for over 30 years until 1993. He has held appointments at the Institute for Advanced Study, Brookhaven National Laboratory, CERN, Oxford, the University of Islamabad, and the Ecole Polytechnique. Berstein has written over 50 technical papers as well as his books popularizing science including Albert Einstein; Cranks, Quarks, and the Cosmos and A Theory for Everything. His passion for science was launched after he entered Harvard University, thereafter combining it with a talent as a writer. *TIS

1930 Jaime Alfonso Escalante Gutierrez (December 31, 1930 — March 30, 2010) was a Bolivian educator well-known for teaching students calculus from 1974 to 1991 at Garfield High School, East Los Angeles, California. Escalante was the subject of the 1988 film Stand and Deliver, in which he is portrayed by Edward James Olmos.*Wik

1945 Leonard Max Adleman (December 31, 1945, ) is an American theoretical computer scientist and professor of computer science and molecular biology at the University of Southern California. He is known for being a co-inventor of the RSA (Rivest-Shamir-Adleman) cryptosystem in 1977, and of DNA computing. RSA is in widespread use in security applications. *Wik

1952 Vaughan Frederick Randal Jones (31 Dec 1952, ) is a New Zealand mathematician who was awarded the Fields Medal in 1990 for his study of functional analysis and knot theory. In 1984, Jones discovered a relationship between von Neumann algebras and geometric topology. As a result, he found a new polynomial invariant for knots and links in 3-space. It was a complete surprise because his invariant had been missed completely by topologists, in spite of intense activity in closely related areas during the preceding 60 years.*TIS

1610 Ludolph van Ceulen, a German mathematician who is famed for his calculation of π to 35 places. In Germany π used to be called the Ludolphine number. Because van Ceulen could not read Greek, Jan Cornets de Groot, the burgomaster of Delft and father of the jurist, scholar, statesman and diplomat, Hugo Grotius​, translated Archimedes' approximation to π for Van Ceulen. This proved a significant point in Van Ceulen's life for he spent the rest of his life obtaining better approximations to π using Archimedes' method with regular polygons with many sides.*SAU He has Pi on his memorial stone.

1679 Giovanni Alfonso Borelli (28 Jan 1608; 31 Dec 1679) Italian mathematician, physiologist and physicist sometimes called “father of biomechanics.” He was the first to apply the laws of mechanics to the muscular action of the human body. In De motu animalium (Concerning Animal Motion, 1680), he correctly described the skeleton and muscles as a system of levers, and explained the mechanism of bird flight. He calculated the forces required for equilibrium in various joints of the body well before the mechanics of Isaac Newton. In 1649, he published a work on malignant fevers. He repudiated astrological causes of diseases and believed in chemical cures. In 1658, he published Euclidus restitutus. He made anatomical dissections, drew a diver's rebreather, investiged volcanoes, was first to suggest a parabolic path for comets, and considered Jupiter had an attractive influence on its moons.*TIS

1719 John Flamsteed (19 Aug 1646; 31 Dec 1719)English astronomer who established the Greenwich Observatory. Science Historian/blogger Thony Christie writes:
" Observational astronomy only produced three significant star catalogues in the two thousand years leading up to the 18th century. The first, the Greek catalogue from Hipparchus and Ptolemaeus published by Ptolemaeus in the 2nd century CE, which contained just over 1000 stars mapped with an accuracy that was astounding for the conditions under which it was produced. The second, containing somewhat more that 700 stars plus another 300 borrowed from the Ptolemaeus catalogue, was produced by the Danish astronomer Tycho Brahe in the last quarter of the 16th century, with an accuracy many factors better than his Greek predecessors. Both of these catalogues were produced with naked eye observations. The first catalogue to be produced using telescopic sights on the measuring instruments was that of John Flamsteed published posthumously in 1725, which contains more than 3000 stars measured to a much higher degree of accuracy than that of Tycho."
He then goes on to correct some misconceptions about Flamsteed's life that are commonly repeated, (he did NOT take part in talking Charles II into creating the observatory) and gives a nice description of a complex man. *Renaissance Mathematicus

1894 Thomas Jan Stieltjes, who did pioneering work on the integral. *VFR Thomas Stieltjes worked on almost all branches of analysis, continued fractions and number theory. *SAU

1913 Seth Carlo Chandler, Jr. (17 Sep 1846, 31 Dec 1913) was an American astronomer best known for his discovery (1884-85) of the Chandler Wobble, a complex movement in the Earth's axis of rotation (now referred to as polar motion) that causes latitude to vary with a period of 14 months. His interests were much wider than this single subject, however, and he made substantial contributions to such diverse areas of astronomy as cataloging and monitoring variable stars, the independent discovery of the nova T Coronae, improving the estimate of the constant of aberration, and computing the orbital parameters of minor planets and comets. His publications totaled more than 200. *TIS

1962 Charles G Darwin was the grandson of the famous biologist and graduated from Cambridge. He lectured on Physics at Manchester and after service in World War I and a period back at Cambridge he became Professor of Physics at Edinburgh. He left eventually to become head of a Cambridge college. He worked in Quantum Mechanics and had controversial views on Eugenics. *SAU

1982 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

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

Friday, 30 December 2011

On This Day in Math - Dec 30

It requires a very unusual mind to undertake the analysis of the obvious.
~Alfred North Whitehead

The 364th day of the year; 364 is the total number of gifts in the Twelve Days of Christmas song: 1+(2+1) + (3+2+1) ... which is a series of triangular numbers.  The sum of the first n triangular numbers can be expressed as (n+2 Choose 3).

In 1873, the American Metrological Society was formed in New York City to improve systems of weights, measures and money. Its activities eventually extended with a committee considering units of force and energy, and another concerned with the adoption of Standard Time for the U.S. On 30 Dec 1884, at the meeting of the American Metrological Society at Columbia College in New York City, Charles S. Peirce read a paper on the determination of gravity. He also participated in a discussion of the adequacy of the standards of weight and measure in the United States and pointed out some of the deficiencies in the current system. As a result of his revelations, the Society passed a resolution recommending the appointment of a committee to advise Congress on the need for establishing an efficient bureau of standards. *TIS

1881 The “Four Fours” problem was first published in Knowledge a magazine of popular science edited by the astronomer Richard Proctor. The problem is to express whole numbers using exactly four fours and various arithmetical signs. For example 52 = 44 + 4 + 4. This can be done for the integers from 1 to 112, but 113 is a problem. Variations of the game allow use of factorials, square roots, decimal points (such as .4) etc. A good source for further study is here.

1902 Leornard Eugene Dickson married Susan Davis. Later he often said of his honeymoon: “It was a great success, except that I only got two research papers written.” In all he published 18 books and hundreds of articles.*VFR

In 1924, Edwin Hubble announced the existence of another galactic system in addition to the Milky Way. He had found at least one "island universe," or galaxy of stars, lies outside our own Milky Way. Until then, scientists were not certain whether certain fuzzy clouds of light called "nebulae" that had been seen with telescopes were small clusters of clouds within the Milky Way or separate galaxies. Hubble measured the distance to the Andromeda nebula and showed it to be a hundred thousand times as far away as the nearest stars. This proved it was a separate galaxy, as large as our own Milky Way, but very far away. More galaxies have been found, some a spiral form like the Milky Way; others spheroidal, others without the spiral arms, or of irregular shape.
1952 Harvard mathematician Andrew Gleason received the Newcomb Cleveland Prize, a $1000 financial award, for his contributions toward the solution of Hilbert's Fifth Problem about Lie Groups.

In 1982, a second full moon of the month was visible. Known as a "blue moon," the name does not refer to its color, but it is a rare event, giving rise to the expression, "once in a blue moon" came from. This blue blue moon was more special as a total lunar eclipse also occurred (U.S.). Although there were 41 blue moons in the twentieth century, this was one of four during an eclipse of the moon, and the only total eclipse of a blue moon in the twentieth century. A blue moon happens every 2.7 years because of a disparity between our calendar and the lunar cycle. The lunar cycle is the time it takes for the moon to revolve around the earth, is 29 days, 12 hours, and 44 minutes. *TIS The next blue moon will occur on Setember 30 of 2012.

1985 Version 3.2 of the IBM PC​-DOS operating system is announced
PC-DOS, IBM's version of the DOS operating system used on the IBM PC, released Version 3.2 on this date. The system required 128KB RAM and was available on either one 720KB disk or two 51/4” disks. DOS has remained in use since the introduction of the IBM PC in 1981, with PC-DOS 200 being the latest release in 1998. *CHM

1850 John Milne (30 Dec 1850; 30 Jul 1913) English seismologist who invented the horizontal pendulum seismograph (1894) and was one of the European scientists that helped organize the seismic survey of Japan in the last half of the 1800's. Milne conducted experiments on the propagation of elastic waves from artificial sources, and building construction. He spent 20 years in Japan, until 1895, when a fire destroyed his property, and he returned home to the Isle of Wight. He set up a new laboratory and persuaded the Royal Society to fund initially 20 earthquake observatories around the world, equipped with his seismographs. By 1900, Milne seismographs were established on all of the inhabited continents and he was recognized as the world's leading seismologist. He died of Bright's disease.*TIS

1897 Stanisław Saks (December 30, 1897 – November 23, 1942) was a Polish mathematician and university tutor, known primarily for his membership in the Scottish Café circle, an extensive monograph on the Theory of Integrals, his works on measure theory and the Vitali-Hahn-Saks theorem.*wIK

1931 Sir John (Theodore) Houghton (30 Dec 1931, ) Welsh metereologist who began in the late 1960's drawing attention to the buildup of carbon dioxide in the earth's atmosphere and its result of global warming, now known as the greenhouse effect. As director-general (1983) of the British Meteorological Office, he began tracking changing climate patterns. In 1990, he co-chaired a team of scientists working for the United Nations that produced the first comprehensive report on the science of climate change. This led to the 1997 U.N. Conference on Climate Change, in Kyoto, Japan. The Kyoto Protocol that resulted there was a treaty among industrialized and developed nations to combat global warming by voluntarily adhering to progressively stiffening emissions-reduction standards.*TIS

1934 John N. Bahcall (30 Dec 1934, ) American astrophysicist who pioneered the development of neutrino astrophysics in the early 1960s. He theorized that neutrinos (subatomic particles that have no charge and exceedingly weak interaction with matter) can be used to understanding how stars shine. They are emitted by the sun and stars during the fusion energy creation process, and most are able to pass through the Earth without being stopped. He calculated the expected output of neutrinos from the sun, which created an experimental challenge to explain the unexpected result. He won the National Medal of Science (1998) for both his contributions to the planning and development of the Hubble Space Telescope and his pioneering research in neutrino astrophysics.*TIS

1691 Robert Boyle (25 Jan 1627, 30 Dec 1691) Anglo-Irish chemist and natural philosopher noted for his pioneering experiments on the properties of gases and his espousal of a corpuscular view of matter that was a forerunner of the modern theory of chemical elements. He was a founding member of the Royal Society of London. From 1656-68, he resided at Oxford where Robert Hooke, who helped him to construct the air pump. With this invention, Boyle demonstrated the physical characteristics of air and the necessity of air for combustion, respiration, and the transmission of sound, published in New Experiments Physio-Mechanical, Touching the Spring of the Air and its Effects (1660). In 1661, he reported to the Royal Society on the relationship of the volume of gases and pressure (Boyle's Law).*TIS

1695 Sir Samuel Morland (born 1625, 30 Dec 1695) English mathematician and inventor of mechanical calculators. His first machine added and subtracted English money using eight dials that were moved by a simple stylus. Another could multiply and divide using 30 discs with numbers marked around the edge - circular versions of Napier's linear bones. Five more discs handled finding square and cube roots. His third machine made trigonometric calculations. Morland built a speaking trumpet (1671) he claimed would allow a conversation to be conducted over a distance of 3/4 mile. By 1675, he had developed various pumps for domestic, marine and industrial applications, such as wells, draining ponds or mines, and fire fighting. He also designed iron stoves for marine use, and improved barometers. *TIS

1883 John Henry Dallmeyer (6 Sep 1830, 30 Dec 1883) German-born British inventor and manufacturer of lenses and telescopes. He introduced improvements in both photographic portrait and landscape lenses, in object glasses for the microscope, and in condensers for the optical lantern. Dallmeyer made photoheliographs (telescopes adapted for photographing the Sun) for Harvard observatory (1864), and the British government (1873). He introduced the "rapid rectilinear" (1866) which is a lens system composed of two matching doublet lenses, symmetrically placed around the focal aperture to remove many of the aberrations present in more simple constructions. He died on board a ship at sea off New Zealand. *TIS

1932 Eliakim Hastings Moore (January 26, 1862 – December 30, 1932) was an American mathematician. He discovered mathematics through a summer job at the Cincinnati Observatory while in high school. When the University of Chicago opened its doors in 1892, Moore was the first head of its mathematics department, a position he retained until his death in 1931. His first two colleagues were Bolza and Maschke. The resulting department was the second research-oriented mathematics department in American history, after Johns Hopkins University.
Moore first worked in abstract algebra, proving in 1893 the classification of the structure of finite fields (also called Galois fields). Around 1900, he began working on the foundations of geometry. He reformulated Hilbert's axioms for geometry so that points were the only primitive notion, thus turning Hilbert's primitive lines and planes into defined notions. In 1902, he further showed that one of Hilbert's axioms for geometry was redundant. Independently, the twenty year old R.L. Moore (no relation) also proved this, but in a more elegant fashion than E. H. Moore used. When E. H. Moore heard of the feat, he arranged for a scholarship that would allow R.L. Moore to study for a doctorate at Chicago. E.H. Moore's work on axiom systems is considered one of the starting points for metamathematics and model theory. After 1906, he turned to the foundations of analysis. The concept of closure operator first appeared in his 1910 Introduction to a form of general analysis. He also wrote on algebraic geometry, number theory, and integral equations.
At Chicago, Moore supervised 31 doctoral dissertations, including those of George Birkhoff, Leonard Dickson, Robert Lee Moore (no relation), and Oswald Veblen. Birkhoff and Veblen went on to forge and lead the first-rate departments at Harvard and Princeton, respectively. Dickson became the first great American algebraist and number theorist. Robert Moore founded American topology. According to the Mathematics Genealogy Project, as of January 2011, E. H. Moore had over 14,900 known "descendants."
Moore convinced the New York Mathematical Society to change its name to the American Mathematical Society, whose Chicago branch he led. He presided over the AMS, 1901–02, and edited the Transactions of the American Mathematical Society, 1899–1907. He was elected to the National Academy of Sciences, the American Academy of Arts and Sciences, and the American Philosophical Society.
The American Mathematical Society established a prize in his honor in 2002. *Wik

1947 Alfred North Whitehead (15 Feb 1861, 30 Dec 1947) English mathematician and philosopher, who worked in logic, physics, philosophy of science and metaphysics. He is best known for his work with Bertrand Russell on one of probably the most famous books of the century, Principia Mathematica (1910-13) to demonstrate that logic is the basis for all mathematics. In physics (1910-24) his best known work was a theory of gravity, that competed with Einstein's general relativity for many decades. In his later life from 1924 onward at Harvard, he worked on more general issues in philosophy rather than mathematics, including the development of a comprehensive metaphysical system which has come to be known as process philosophy. *TIS

1956 Heinrich Scholz (December 17 1884 in Berlin , December 30 1956 in Muenster, Westphalia ) was a German logician, philosopher and theologian. *Wik

1982 Philip Hall (11 April 1904 in Hampstead, London, England - 30 Dec 1982 in Cambridge, Cambridgeshire, England) Hall was the main impetus behind the British school of group theory and the growth of group theory to be one of the major mathematical topics of the 20th Century was largely due to him.*SAU

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

Thursday, 29 December 2011

Repost of assorted interesting tidbits from Futility Closet

I really enjoyed the following from Greg Ross at the Futility closet.... 

Things you probably didn't know:

Greg Ross Dec 28, 2011 5:53 PM - Show original item
  • Canada’s coastline is six times as long as Australia’s.
  • Rudyard Kipling invented snow golf.
  • Can you see your eyes move in a mirror?
  • 26364 = 263 × 6/4
  • “If a man who cannot count finds a four-leaf clover, is he entitled to happiness?” — Stanislaw Lec
The last reminds me of the question, "If a man says something that no woman is present to hear, is he still wrong?"

And one from dy/dan that makes me think I knew this teacher once: