Friday 6 April 2018

On This Day in Math - April 6

Abel Statue at Univ of Oslo, *Monuments on Mathematicians

Niels Henrik Abel
1802 - 1829
mathematician, famed due to
epoch-making works in
theory of equations, [theory of] infinite series
and elliptic functions

Science can amuse and fascinate us all, but it is engineering that changes the world.
~Isaac Asimov

The 96th day of the year; 96 is the smallest number that can be written as the difference of 2 squares in 4 ways. *What's So Special About This Number?  
(students are encouraged to find them all...Is there a smaller number that can be so expressed in 3 ways?)

The sum of 96 consecutive squared integers is a square number ( \( x^2 + (x+1)^2 + (x+2)^2 +(x+3)^2 + \dotsm + (x+95)^2 = y^2 \) ) can be solved with eight sets of 96 consecutive year days. One solution is \( 13^2 + 14^2 + \dotsm + 108^2 = 652^2 \) *Ben Vitale

Ninety Six, South Carolina. There is much confusion about the mysterious name, "Ninety-Six," and the true origin may never be known. Speculation has led to the mistaken belief that it was 96 miles to the nearest Cherokee settlement of Keowee; to a counting of creeks crossing the main road leading from Lexington, SC, to Ninety-Six; to an interpretation of a Welsh expression, "nant-sych," meaning "dry gulch." Pitcher Bill Voiselle of the Boston Braves was from Ninety Six, South Carolina, and wore uniform number 96.

648 B.C. First Greek record of a total solar eclipse is made. See June 4, 780 B.C., and October 13, 2128 B.C. *VFR
"Zeus, the father of the Olympic Gods, turned mid-day into night,
hiding the light of the dazzling Sun; and sore fear came upon men."
"Nothing can be surprising any more or impossible or miraculous,
now that Zeus, father of the Olympians has made night out of noonday,
hiding the bright sunlight, and . . . fear has come upon mankind.
After this, men can believe anything, expect anything.
~ Archilochus, Greek poet
*Ted Pedas, Eclipse History web site.

1741 Euler's First paper on partitions is given. (This may be where generating functions are first used). On September 4, 1740, Philip Naudé the younger (1684-1747) wrote Euler from Berlin to ask “how many ways can the number 50 be written as a sum of seven different positive integers?” The problem seems to have captured Euler’s imagination. Euler gave his first answer on April 6, 1741, in a paper he read at the weekly meeting of the St. Petersburg Academy. That paper was published ten years later and is number 158 on Eneström’s index. (Ed Sandifer, "How Euler Did It") [E158 can be downloaded in English from Euler Project]

1841 William Thompson, the future Lord Kelvin, age 16, was formally entered at St. Peter's (or Peterhouse) Cambridge as a student of the college. His father, Professor James Thompson, may have urged him to enter Peterhouse because of the college's mathematical coach, Hopkins, whom Professor Kelvin admired. It would become the college of choice for many young Scots for a while. Tait went there, and Maxwell began there but later transferred to Trinity. *Silvanus Phillips Thompson, The life of Lord Kelvin

1852, Edward Sabine announced that the 11 year sunspot cycle was "absolutely identical" with the geomagnetic cycle. Later, using a larger dataset, Rudolf Wolf confirmed this fact. Since Newton's explanation of the effect of the sun's gravity on earth, this was the first new phenomenon of the sun interacting with the earth. Thus began continuing studies of the solar-terrestrial activity. Sabine was an Irish geophysicist, astronomer, and explorer, who made extensive pendulum measurements to determine the shape of the earth, and established magnetic observatories to relate sunspot activity with disturbances in terrestrial magnetism. Sabine was knighted in 1869.

In 1869, the American Museum of Natural History in New York City was officially created with the signing of a bill by the Governor of New York, John Thompson Hoffman. The museum began from the efforts of Albert Smith Bickmore, one-time student of Harvard zoologist Louis Agassiz, who was successful in his proposal to create a natural history museum in Central Park, New York City, with the support of William E. Dodge, Jr., Theodore Roosevelt, Sr., Joseph Choate, and J. Pierpont Morgan. It opened to the public 27 Apr 1871. With a series of exhibits, the Museum's collection went on view for the first time in the Central Park Arsenal, the Museum's original home, on the eastern side of Central Park. *TIS

1909 Ernst Zermelo (1871–1953) liked to argue that it is impossible for anyone ever to reach the North Pole, because the amount of whiskey needed to reach any latitude is proportional to the tangent of that latitude. Unaware of this argument, Robert E. Peary wrote in his diary on this date. “The Pole at last!!! The prize of 3 centuries, my dream & ambition for 23 years. Mine at last. I cannot bring myself to realize it. It all seems so simple ... .” Peary, his remarkable Black associate, Matthew Henson, and four Eskimos were the first humans to reach the North Pole. See The National Geographic Society. 100 Years of Adventure and Discovery (1987), pp. 53 & 59. [Reid, Hilbert, p. 97.]*VFR

1922 Emmy Noether named “unofficial associate professor” at Gottingen. This purely honorary position reveals the strong prejudice of the day against women. [DSB 10, 138 and A. Dick, xiii.] Thony Christie sent me a note that says "In 1922 Emmy Noether was appointed 'außerordentliche Professur' which is not an 'unofficial associate professor' but is an official professorial post without a chair. " Thanks, Thony

1929 To celebrate the centenary of the Death of Neils Henrik Abel, Norway issued a set of stamps in his honor. This is the first set of stamps honoring a mathematician in Philatelic history.

1938 DuPont researcher Roy Plunkett and his assistant, Jack Rebok, discovered polytetrafluoroethy­lene, the slipperiest man-made substance. Teflon became a household word in 1960 when Teflon-coated frying pans were introduced. The Manhattan Project used it in producing Uranium-235, for it was the only gasket material that would contain the corrosive hexaflouride.

In 1955, a report that Jupiter emitted radio waves was the subject of a page-length column of the New York Times. Discovered by Bernard F. Burke and Kenneth L. Franklin, astronomers at the Carnegie Institution in Washington, the waves resembled short bursts of static, similar to the interference on home radios caused by lightning. This was the first time radio waves were detected from any planet in our solar system. The astronomers announced their find at the semi-annual meeting of the American Astronomical Society in Princeton, N.J. Discovered at first by chance, it took several weeks to pinpoint Jupiter as the origin, rather than any local source on Earth.*TIS

1956 The first circular office building, the Capital Tower, at Hollywood and Vine in Los Angeles, was dedicated. The building has a diameter of 92 feet and a height of 150 feet. Above the 13 floors was a 90 foot spire from which a beacon flashed the word “Hollywood” in Morse code. *FFF

1963 Watson-Watt is remembered as the inventor of Radar, for which he received a patent on April 2, 1935. Twenty-eight years later he read a poem in a science meeting in San Francisco about the strange twist of Technological Karma that led to his getting a speeding ticket in Canada in 1956. Reportedly he told the officer who stopped him, "If I knew what you were going to do with it, I would never have invented it." The poem reads:
Pity Sir Watson-Watt,
strange target of this radar plot
and thus, with others I can mention,
the victim of his own invention.
His magical all-seeing eye
enabled cloud-bound planes to fly
but now by some ironic twist
it spots the speeding motorist
and bites, no doubt with legal wit,
the hand that once created it.

Oh Frankenstein who lost control
of monster man created whole,
with fondest sympathy regard
one more hoist with his petard.
As for you courageous boffins
who may be nailing up your coffins,
particularly those whose mission
deals in the realm of nuclear fission,
pause and contemplate fate's counter plot
and learn with us what's Watson-Watt.

1967 Spain issued a stamp picturing Averroes (1126–1198) physician and philosopher. [Scott #1461] *VFR

1972 Cray Research is an American supercomputer manufacturer based in Seattle, Washington. The company's predecessor, Cray Research, Inc. (CRI), was founded in 1972 by computer designer Seymour Cray.

1992 Microsoft Releases Windows 3.1:
Microsoft Corporation releases Windows 3.1, an operating system that provided IBM and IBM-compatible PCs with a graphical user interface (though Windows was not the first such interface for PCs). Retail price was $149.00. In replacing the previous DOS command line interface with its Windows system, however, Microsoft created a program similar to the Macintosh operating system, and was sued by Apple for copyright infringement. (Microsoft later prevailed in this suit).
Windows 3.1 added multimedia extensions allowing support for sound cards, MIDI, and CD Audio, Super VGA (800 x 600) monitors, and increased the speed of modem it would support to 9600 bps. It also finally abandoned "Real Mode," a vestigial environment dating back to the 8086 CPU. It provided scalable fonts and trapped the "three finger salute" (CTRL-ALT-DEL), prompting the user to avoid inadvertent re-boots. It also refined its OLE (Object Linking and embedding) concept, allowing users to cut and paste between applications.*CHM

1995 Stephen Hawking, in response to a request for a "time travel equation" from the editors of THE FACE magazine, sent the following fax: "Thank you for your recent fax. I do not have any equations for time travel. If I had, I would win the National Lottery every week."  *Letters of Note web site

1749 Samuel Vince (6 April 1749; Fressingfield – 28 November 1821; Ramsgate) was an English clergyman, mathematician and astronomer at the University of Cambridge.
The son of a plasterer, Vince was admitted as a sizar to Caius College, Cambridge in 1771. In 1775 he was Senior Wrangler, and Winner of the Smith Prize at Cambridge. Migrating to Sidney Sussex College in 1777, he gained his M.A. in 1778 and was ordained a clergyman in 1779.
He was awarded the Copley Medal in 1780 and was Plumian Professor of Astronomy and Experimental Philosophy at Cambridge from 1796 until his death.
As a mathematician, Vince wrote on many aspects of his expertise, including logarithms and imaginary numbers. His Observations on the Theory of the Motion and Resistance of Fluids and Experiments upon the Resistance of Bodies Moving in Fluids had later importance to aviation history. He was also author of the influential A Complete System of Astronomy (3 vols. 1797-1808).
Vince also published the pamphlet The Credibility of Christianity Vindicated, In Answer to Mr. Hume's Objections; In Two Discourses Preached Before the University of Cambridge by the Rev. S. Vince. In this work, Vince made an apology of the Christian religion and, like Charles Babbage, sought to present rational arguments in favor of the belief in miracles, against David Hume's criticism. *Wik

1801 William Hallowes Miller (6 Apr 1801; 20 May 1880 at age 79) Welsh minerologist known for his Millerian indices built on his system of reference axes for crystals by which the different systems of crystal forms can be designated using a a set of three integers for each crystal face. When he published this scheme in A Treatise on Crystallography (1839), he provided an alternative to the existing confusion due to the many different descriptive systems previously in use. In his early career he published successful textbooks for hydrostatics and hydrodynamics (1831) and differential calculus (1833). Miller also prepared new standards in 1843 to replace the National Standards of weight and length that had been lost in the 1834 fire that destroyed the Parliament buildings. *TIS For an interesting story about how mathematics was related to the fire, read here.

1890 André-Louis Danjon (6 Apr 1890; 21 Apr 1967 at age 76) French astronomer who devised a now standard five-point scale for rating the darkness and colour of a total lunar eclipse, which is known as the Danjon Luminosity Scale. He studied Earth's rotation, and developed astronomical instruments, including a photometer to measure Earthshine - the brightness of a dark moon due to light reflected from Earth. It consisted of a telescope in which a prism split the Moon's image into two identical side-by-side images. By adjusting a diaphragm to dim one of the images until the sunlit portion had the same apparent brightness as the earthlit portion on the unadjusted image, he could quantify the diaphragm adjustment, and thus had a real measurement for the brightness of Earthshine.*TIS

1903 Harold Eugene Edgerton (6 Apr 1903; 4 Jan 1990 at age 86) was an American engineer and ultra-high-speed photographer who, as a graduate at the Massachusetts Institute of Technology (1926), used a strobe light in his studies, which,. by 1931, he applied the strobe to ultra-high-speed photography. He formed a company (1947) to specialize in electronic technology, which led to inventing the Rapatronic camera, capable of photographing US nuclear bomb test explosions from a distance of 7 miles. Throughout his career he applied high-speed photography as a tool in various scientific applications. He also developed sonar to study the ocean floor. Using side-scan sonar, in 1973, he helped locate the sunken Civil War battleship USS Monitor, lost since 1862, off Cape Hatteras, NC. *TIS

1947 Michael Worboys (born April 6, 1947, ) is a British mathematician and computer scientist. He is professor of spatial informatics and director of the School of Computing and Information Science at the University of Maine.
Worboys is mostly known for his research on the computational and mathematical foundations of Geographic Information Science (GIS). In 1993 he founded the GIS Research UK (GISRUK) conference series, which is still held annually. With Matt Duckham, he wrote the well-known text book GIS: a computing perspective.*Wik

1528 Albrecht Durer (21 May 1471, 6 April 1528)
German artist who published a book on geometric constructions (1535) using a straight-edge and compass. Although designed to enable artists better represent a natural three-dimensional scene on a canvas, Dürer included careful proofs to establish the validity of the constructions. In this respect, it could be regarded as the oldest surviving text on applied mathematics. He also wrote on the proportions of the human body.*TIS

1829 Niels Henrik Abel, age 26, died of tuberculosis. In 1929 Norway issued four stamps for the centenary of his death. [Scott #145–148] Neils Henrik Abel was born at Fomm¨oy, a small island near Stavanger in Norway. Before going to the university in 1821 he attacked, with the vigor and immodesty of youth, the problem of the solution of the quintic equation. He submitted a solution for publication but found an error before it was published. In 1823 he proved the impossibility of a solution involving radicals that solves fifth or higher degree equations. *VFR
He developed the concept of elliptic functions independently of Carl Gustav Jacobi, and the theory of Abelian integrals and functions became a central theme of later 19th-century analysis. He had difficulty finding an academic position, was troubled by poverty, and died in poverty in his late twenties.*TIS
I love Abel's commet on Gauss' writing style, "He is like the fox, who effaces his tracks in the sand with his tail."
The early death of this talented mathematician, of whom Adrien-Marie Legendre said "quelle tête celle du jeune Norvégien!" ("what a head the young Norwegian has"), cut short a career of extraordinary brilliance and promise. Under Abel's guidance, the prevailing obscurities of analysis began to be cleared, new fields were entered upon and the study of functions so advanced as to provide mathematicians with numerous ramifications along which progress could be made. His works, the greater part of which originally appeared in Crelle's Journal, were edited by Bernt Michael Holmboe and published in 1839 by the Norwegian government, and a more complete edition by Ludwig Sylow and Sophus Lie was published in 1881. The adjective "abelian", derived from his name, has become so commonplace in mathematical writing that it is conventionally spelled with a lower-case initial "a" (e.g., abelian group, abelian category, and abelian variety). (Wikipedia)

1963 Otto Struve (12 Aug 1897, 6 Apr 1963 at age 65) Russian-American astronomer who was a fourth generation astronomer, the great-grandson of Friedrich Struve. He made detailed spectroscopic investigations of stars, especially close binaries and peculiar stars, the interstellar medium (where he discovered H II regions), and gaseous nebulae. He contributed to the understanding of the broadening of spectral lines due to stellar rotation, electric fields, and turbulence and worked to separate these effects from each other and from chemical abundances. He was a pioneer in the study of mass transfer in closely interacting binary stars. Struve emigrated to the USA (1921) and joined the Yerkes Observatory, Wisconsin, becoming its director in 1932. *TIS

1992 Isaac Asimov (2 Jan 1920; 6 Apr 1992) American author and biochemist, who was a prolific writer of science fiction and of science books for the layperson. Born in Petrovichi, Russia, he emigrated with his family to New York City at age three. He entered Columbia University at the age of 15 and at 18 sold his first story to Amazing Stories. After earning a Ph.D., he taught biochemistry at Boston University School of Medicine after 1949. By 18 Mar 1941, Asimov had already written 31 stories, sold 17, and 14 had been published. As an author, lecturer, and broadcaster of astonishing range, he is most admired as a popularizer of science (The Collapsing Universe; 1977) and a science fiction writer (I, Robot;1950). He coined the term "robotics." He published about 500 volumes.*TIS

1993 John Charles Burkill FRS (1 February 1900 Holt, Norfolk, England – 6 April 1993 Sheffield, England) was an English mathematician who worked on analysis and introduced the Burkill integral. He was elected a fellow of the Royal Society in 1953*Wik

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

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