Wednesday, 1 March 2017

On This Day in Math - March 1

section of Van Dyke's portrait of della Faille showing mathematical tools *Wik

The role of the teacher is to create the conditions for invention rather than provide ready-made knowledge.
~Seymour Papert

The 60th day of the year; 60 is the smallest composite number which is the order of a simple group.

7! is the smallest # with 60 divisors.

There are four Archimedean solids with 60 vertices , : the truncated icosahedron, (shown) the rhombicosidodecahedron, the snub dodecahedron, and the truncated dodecahedron.

Oh, and Pi day is coming up in a couple of weeks, so ... suppose you were scrolling through the digits of pi and wondered how long it would take until you found a string of ten digits that had all ten of 0 through nine in it... Benjamin Vitale ‏@BenVitale thought to find out and :

You can arrange the whole numbers from 1 to 60 into pairs so that the sum of the numbers in each pair is a perfect square; in fact, you can do it in   4,366,714 ways. Here is one of those presented in a pretty fashion using only five squares for the sums. *Gordon Hamilton, Kiran S. Kedlaya, and Henri Picciotto; Square–Sum Pair Partitions(Won the George Polya Prize from MAA for 2016)


1774 William Herschel begins to keep an astronomical journal, and records observations of Saturn's rings. Herschel's music led him to an interest in mathematics and lenses. His interest in astronomy grew stronger after he made the acquaintance of the English Astronomer Royal Nevil Maskelyne. He started building his own reflecting telescopes and would spend up to 16 hours a day grinding and polishing the speculum metal primary mirrors. He "began to look at the planets and the stars" in May, 1773 and on 1 March 1774 began an astronomical journal by noting his observations of Saturn's rings and the Great Orion Nebula(M4).*Wik

1790 On March 1, Congres ordered the first US Census to be taken, to begin on the first Monday in August.
the marshals of the several judicial districts of the United States were required to
cause the number of the inhabitants within their respective districts
to be taken, omitting Indians not taxed, and distinguishing free persons,
including those bound to service for a term of year, from all
others. This separation in itself was sufficient to meet all the constitutional
requirements of the enumeration, but the act also required
the marshals to distinguish the sex and color of free persons and free
males of 16 years and upward from those under that age; in the latter
case, undoubtedly, for the purpose of ascertaining the military and
industrial strength of the country.
*The history and growth of the United States census,

Even at this time there was opposition t0 a Census for fear of invoking "The Sin of David." In earlier attempts to enumerate the population of the colonies, there had been strong religious opposition. In 1712, in a letter to the Lord of Trade, the Governor of New York blamed the imperfections of the census of 1712 on the fear of God's wrath and, in a report, claimed that an earlier count had been followed by excessive sickness in the colony.

In 1813, Michael Faraday was appointed at the Royal Institution as Chemical Assistant to Humphry Davy, whom he succeeded as Professor of Chemistry in 1820. Since age 14, in 1805, while an apprentice bookbinder, Faraday had educated himself about science. In 1810, he joined the City Philosophical Society to attend lectures and discuss scientific matters. A turning point in his life happened in 1812. A client of the bookbindery gave him four tickets to hear Humphry Davy lecturing at the Royal Institution. Fascinated by the scientific topics, He took notes, which he took with him later to show Davy when he later asked for a position. Davy interviewed him, but there was no opening at the time. When a vacancy occurred in 1813, Davy recalled him and Faraday was hired.*TIS His The Chemical History of a Candle is free from Amazon on Kindle (and quite inexpensive on paper)

1847 On March 1, 1847, Gabriel Lamé announced that he believed that he had found a full proof for Fermat's Last Theorem. He presented to the Paris Academy the outline of what he believed was a complete proof. Earlier he had succeeded in the first proof for x7 + y7 = z7.. The error was later pointed out by Liouville and by Kummer. The error hinged on the assumption of the unique factorization of the roots of unity. Kummer's work on this assumption led to his discovery that unique factorization could be "saved" by using "ideal complex numbers." Kummer's ideal complex numbers would turn out to be a major breakthrough in the generalization of Fermat's Last Theorem. It would also turn out to be the foundation for what is today known as algebraic number theory. *Larry Freeman web page on FLT

1896 Henri Becquerel re-discovers radioactivity. In 1903, together with the Curies, he received the Nobel Prize in Physics for this work. Becquerel thought that phosphorescent materials, such as some uranium salts, might emit penetrating x-ray-like radiation when illuminated by bright sunlight. His first experiments appeared to show this. He presented a paper describing them to the French Academy of Sciences on 24 February 1896
. Then he began to doubt his theory. "I kept the apparatuses prepared and returned the cases to the darkness of a bureau drawer, leaving in place the crusts of the uranium salt. Since the sun did not come out in the following days, I developed the photographic plates on the 1st of March, expecting to find the images very weak. Instead the silhouettes appeared with great intensity.." *Wik

1953 On this date in 1953, Watson and Crick solved the structure of DNA. What better day to lay to rest a few myths about it? *genotopoia Seuagenerian-double-helix

1960 John McCarthy's LISP Programmer's Manual Released :
The first LISP Programmer's Manual is released. Considered the mother tongue of Artificial Intelligence (AI), LISP is older than most other high-level languages still in use today. Its inventor, John McCarthy, created the recursive and symbolic language. *CHM

In 1966, the mission of the Soviet Union's unmanned spacecraft Venera 3 (Venus 3) was a partial success when it reached Venus and automatically released a small landing capsule intended to explore the planet's atmosphere during a parachute descent. However, contact had been lost since 16 Feb 1966. Although no data was returned before the capsule impacted, it became the first man-made object to touch the surface of another planet. The Soviet Union issued a commemorative stamp to mark the achievement. Venera 3 was launched on 16 Nov 1965. The landing capsule (0.9-m diam., about 300-kg) had been designed to collect data on pressure, temperature, and composition of the Venusian atmosphere. Failure is believed due to overheating of internal components and the solar panels.*TIS

1980 It was on this date that Benoit B Mandelbrot first saw an image of the set that would eventually bear his name. On 1 March 1980, at IBM's Thomas J. Watson Research Center in Yorktown Heights, New York, Benoit Mandelbrot first saw a visualization of the set. This fractal was first defined and drawn in 1978 by Robert W. Brooks and Peter Matelski as part of a study of Kleinian groups. Mandelbrot studied the parameter space of complex quadratic polynomials in an article that appeared in 1980. The mathematical study of the Mandelbrot set really began with work by the mathematicians Adrien Douady and John H. Hubbard, who established many of its fundamental properties and named the set in honor of Mandelbrot.

1984 The Vatican newspaper, L’Observatore Romano, stated, “The so-called heresy of Galileo does not seem to have any foundation, neither theologically nor under canon law.” In 1822 the church lifted the ban on the works of Galileo and by 1979 Pope John Paul II selected a commission to investigate. On March 1, 1984, the result appeared in the Vatican Newspaper. But it still took until Oct 31, 1992, before Pope John Paul II declared that the church may have been mistaken in condemning Galileo. *Wik

1597 Jan-Karel della Faille or Jean Charles de La Faille (1 March 1597 in Antwerp, Belgium - 4 Nov 1652 in Barcelona, Spain) was a Flemish Jesuit who was the first to determine the center of gravity of the sector of a circle. He proved that the centers of gravity of a sector of a circle, of a regular figure inscribed in it, of a segment of a circle, or of an ellipse lie on the diameter of the figure. These theorems are founded on a postulate from Luca Valerio's De centro gravitatis solidorum (1604). ... La Faille ended his work with four corollaries which revealed his ultimate goal: an examination of the quadrature of the circle. *SAU

1611 John Pell (1 March 1611 in Southwick, Sussex, England - 12 Dec 1685 in Westminster, London, England) Malcolm wrote, "The mathematician John Pell is a significant figure in the intellectual history of 17th century England - significant, however, more because of his activities, contacts and correspondence than because of his published work. His few publications are, nevertheless, valuable sources of information about his intellectual biography.
Pell worked on algebra and number theory. He gave a table of factors of all integers up to 100000 in 1668.
 Pell's equation \( y^2 = ax^2 + 1 \), where a is a non-square integer, was first studied by Brahmagupta and Bhaskara II. Its complete theory was worked out by Lagrange, not Pell. It is often said that Euler mistakenly attributed Brouncker's work on this equation to Pell. However the equation appears in a book by Rahn which was certainly written with Pell's help: some say entirely written by Pell. Perhaps Euler knew what he was doing in naming the equation. *SAU He introduced the division sign (obelus, ÷) into England. The obelus was first used by Johann Rahn (1622-1676) in 1659 in Teutsche Algebra. Rahn's book was interpreted into English and published, with additions made by John Pell. According to some sources, John Pell was a key influence on Rahn and he may be responsible for the development of the symbol. The word obelus comes from a Greek word meaning a "roasting spit." The symbol wasn't new. It had been used to mark passages in writings that were considered dubious, corrupt or spurious.*TIS

1879 Robert Daniel Carmichael (1 March 1879 in Goodwater, Coosa County, Alabama, USA - 2 May 1967 in Merriam, Northeast Johnson County, Kansas, USA) Carmichael is known for his mathematical research in what are now called the Carmichael numbers (numbers satisfying properties of primes described by Fermat's Little Theorem although they are not primes- see below), Carmichael's theorem, and the Carmichael function, all significant in number theory and in the study of the prime numbers. Carmichael might have been the first to describe the Steiner system S(5,8,24), a structure often attributed to Ernst Witt. While at Indiana University Carmichael was involved with special theory of relativity. *Wik Fermat had proved that if n is prime then xn-1 = 1 mod n for every x coprime to n. A 'Carmichael number' is a non-prime n satisfying this condition for any x coprime to n. It was given this name since Carmichael discovered the first such number, 561, in 1910 (there are several base ten Carmichael numbers below 561 for the interested student to search for). For many years it was an open problem as to whether there were infinitely many Carmichael numbers, but this was settled in 1994 by W R Alford, A Granville, and C Pomerance in their paper There are infinitely many Carmichael numbers. *SAU

1914 I. Bernard Cohen (1 March 1914 – 20 June 2003) was the Victor S. Thomas Professor of the history of science at Harvard University and the author of many books on the history of science and, in particular, Isaac Newton.
Cohen was the first American to receive a Ph.D. in history of science, was a Harvard undergraduate ('37) and then a Ph.D. student and protégé of George Sarton who was the founder of Isis and the History of Science Society. Cohen taught at Harvard from 1942 until his death, and his tenure was marked by the development of Harvard's program in the history of science. *Wik

1928 Seymour Papert (1 Mar 1928, )American computer scientist who invented the Logo computer programming language, an educational computer programming language for children. He studied under Piaget, absorbing his educational theories. He has studied ways to use mathematics to understand better how children learn and think, and about the ways in which computers can aid in a child's learning. With Marvin Minsky, he co-founded the Artificial Intelligence Lab at MIT. In the mid-80's he worked in Costa Rica to develop a nationwide program of intensive computer use throughout the public education system. Costa Rica, which now has the highest literacy rate in the Americas, continues to serve as a model for large-scale deployment of computer technology in education.*TIS

1862 Peter Barlow (13 Oct 1776 Norwich, UK; 1 Mar 1862) English mathematician and engineer who invented two varieties of achromatic (non-colour-distorting) telescope lenses. In 1819, Barlow began work on the problem of deviation in ship compasses caused by the presence of iron in the hull. For his method of correcting the deviation by juxtaposing the compass with a suitably shaped piece of iron, he was awarded the Copley Medal. In 1822, he built a device which is to be considered one of the first models of an electric motor supplied by continuous current. He also worked on the design of bridges, in particular working (1819-26) with Thomas Telford on the design of the bridge over the Menai Strait, the first major modern suspension bridge. Barlow was active during the period of railway building in Britain.*TIS His New Mathematical Tables (1814) later known as Barlow’s Tables, gave the factors, squares, cubes, square roots, reciprocals, and natural logarithms of all numbers from 1 to 10,000. It was so accurate that it was reprinted numerous times, the last being 1947. *VFR

1884 Isaac Todhunter (23 Nov 1820 in Rye, Sussex, England - 1 March 1884 in Cambridge, England) Todhunter is best known for his textbooks and his writing on the history of mathematics. Among his textbooks are Analytic Statics (1853), Plane Coordinate Geometry (1855), Examples of Analytic geometry in Three Dimensions (1858). He also wrote some more elementary texts, for example Algebra (1858), Trigonometry (1859), Theory of Equations (1861), Euclid (1862), Mechanics (1867) and Mensuration (1869).
Among his books on the history of mathematics are A History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace (1865, reprinted 1965) and History of the Mathematical Theories of Attraction (1873). No mathematical treatises on elementary subjects probably ever attained so wide a circulation; and, being adopted by the Indian government, they were translated into Urdu and other Oriental languages.
Todhunter received many awards for his contributions to mathematics. In addition to the fellowship of the Royal Society he served on its Council in 1874, the same year in which he was awarded the Adams Prize for his work Researches on the calculus of variations.*SAU

1908 Heinrich Maschke (24 October 1853 in Breslau, Germany (now Wrocław, Poland) – 1 March 1908 Chicago, Illinois, USA) was a German mathematician who proved Maschke's theorem, a theorem in group representation theory that concerns the decomposition of representations of a finite group into irreducible pieces.*Wik

1913 Mario Pieri (22 June 1860 in Lucca, Italy - 1 March 1913 in S Andrea di Compito (near Lucca), Italy) Pieri's main area was projective geometry and he is an important member of the Italian School of Geometers. However, after he moved to Turin, Pieri became influenced by Peano at the University and Burali-Forti who was a colleague at the Military Academy. This influence led Pieri to study the foundations of geometry.
In 1895 he set up an axiomatic system for projective geometry with three undefined terms, namely points, lines and segments. He improved on results of Pasch and Peano and then, in 1905, Pieri gave the first axiomatic definition of complex projective geometry which does not build on real projective geometry.
In 1898 Pieri published the memoir The principles of the geometry of position through the Academy of Sciences of Turin. Russell was impressed by this memoir and wrote, in his Principia, "This is, in my opinion, the best work on the present subject." *SAU

1978 Kiyoshi Oka (April 19, 1901 – March 1, 1978) was a Japanese mathematician who did fundamental work in the theory of several complex variables. He was born in Osaka. He went to Kyoto Imperial University in 1919, turning to mathematics in 1923 and graduating in 1924.
He was in Paris for three years from 1929, returning to Hiroshima University. He published solutions to the first and second Cousin problems, and work on domains of holomorphy, in the period 1936–1940. These were later taken up by Henri Cartan and his school, playing a basic role in the development of sheaf theory. Oka continued to work in the field, and proved Oka's coherence theorem in 1950.
He was professor at Nara Women's University from 1949 to retirement at 1964. He received many honours in Japan.*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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