Thursday, 5 January 2017

On This Day in Math - January 5

If God has made the world a perfect mechanism, He has at least conceded so much to our imperfect intellect that in order to predict little parts of it, we need not solve innumerable differential equations, but can use dice with fair success.

~Max Born

The fifth day of the year; five is the number of Platonic Solids. Five is also the smallest number of queens needed to attack every square on a standard chess board. (can you demonstrate such a board ?)

The sum of the first five integers raised to their own power, is prime, \(1^1 + 2^2 + 3^3 + 4^4 + 5^5 = 3413 \) (and so is the sum of the first six)

One of math's perplexing mysteries.  A sphere in five dimensional space has a larger volume (\( \frac{8 \pi ^2}{15} \) ) than in any other dimension for a unit radius.  From two dimensions up to five the volume increases, then decreases forever after.

In 1845, Gabriel Lame proved a remarkable theorem involving the number 5.  "The number of steps (i.e., divisions) in an application of the Euclidean algorithm never exceeds 5 times the number of (decimal) digits in the lesser."  Donald Knuth (1969) extended this to show that, this was related to the Fibonacci numbers (and \( \sqrt{5} \) ).

and from Jim Wilder : 1084 is the smallest integer whose spelling, one thousand eighty-four, contains the 5 vowels (a, e, i, o, u) in order.


1665 The first volume of the Journal des Savants appeared in Paris. The Journal des sçavans (later renamed Journal des savants), founded by Denis de Sallo, was the earliest academic journal published in Europe, that from the beginning also carried a proportion of material that would not now be considered scientific, such as obituaries of famous men, church history, and legal reports. The first edition appeared as a twelve page quarto pamphlet on Monday, 5 January 1665. This was shortly before the first appearance of the Philosophical Transactions of the Royal Society, on 6 March 1665. *Wik

1769 On January 5, 1769, James Watt finally received the patent for his steam engine: patent 913 A method of lessening the consumption of steam in steam engines-the separate condenser. *yovisto

1853 "First derivative" first used as a noun in English in "On the General Law of the Transformation of Energy" by William John Macquorn Rankine, a paper read before the Philosophical Society of Glasgow

1874 In a letter to Dedekind, Cantor asks if the points in a square can be put in one-to-one correspondence with those on a line. “Methinks that answering this question would be no easy job, despite the fact that the answer seems so clearly to be ‘no’ that proof appears almost unnecessary.” It was three years before Cantor could prove the answer was “yes”. *VFR

In 1892, the first successful auroral photograph was made by the German physicist Martin Brendel. Although it was limited to a blurred, low-contrast picture, it did convey some sense of the shape of the aurora. The task was not easy because the auroral light itself was generally feeble and flickering while photographic materials of the time required a long exposure, and was little sensitive to the deep reds in the aurora. One of his photographs, taken on 1 Feb 1892 was published in the Century Magazine of Oct 1897. Brendel had traveled to Alten Fiord, Lapland, to spend several months studying auroral displays and magnetic disturbances. The first colour pictures were not taken until about 1950, and Life magazine published colour aurora photographs in 1953.*TIS

In 1896, an Austrian newspaper, Wiener Presse, published the first public account of a discovery by German physicist Wilhelm Roentgen, the form of radiation that became known as X-rays.*TIS

1900 Minkowski responds to Hilbert who had asked his opinion about several potential topics for Hilbert's address at the Second International Conference of Mathematicians in Paris, in the summer. Minkowski responds that, "Most alluring would be the attempt at a look into the future and a listing of the problems on which mathematicians should try themselves during the coming century. With such a lecture you could have people talking about your lecture decades later." *Reid, Hilbert, pg 69

1902 In a letter to his mother, Earnest Rutherford writes, “I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies... “ — 1st Baron Rutherford of Nelson Ernest Rutherford * Quoted in A. S. Eve, Rutherford: Being the Life and Letters of the Rt. Hon. Lord Rutherford (1939), 80.

1962 The first reference to Simula in writing is made. This early object-oriented language was written by Kristen Nygaard and Ole-John Dahl of the Norwegian Computing Center in Oslo. Simula grouped data and instructions into blocks called objects, each representing one facet of a system intended for simulation. *CHM

1974 The famous grasshopper weather vane atop Faneuil Hall in Boston was removed by thieves, but later recovered. When a weather vane was fashioned for this famous trading hall of colonial Boston, the grasshopper was chosen as it appears on the crest of Sir Thomas Gresham, founder of England’s Royal Exchange. He also founded the earliest professorship of mathematics in Great Britain, the chair in Geometry at Gresham College London.*VFR

1723 Nicole-Reine Lepaute (5 Jan 1723 in Paris, France - 6 Dec 1788 in Saint-Cloud, France) was a French noblewoman who helped Lalande with astronomical calculations. In June 1757 Lalande decided that he would like to attempt to calculate a precise date for the return of Halley's comet. It was known to have been seen in 1305, 1380, 1456, 1531, 1607 and 1682 and Halley, taking into account perturbations to the orbit caused by the gravitational effects of Jupiter, had predicted that the comet would return reaching perihelion in December 1758. However the only way to get a more accurate prediction of its date of return was to calculate the perturbations to the orbit caused by the gravitational effects of both Jupiter and Saturn. Lalande approached Alexis Clairaut for help and Clairaut provided a basic programme of work requiring an extraordinary amount of computation. Lalande then asked Nicole-Reine Lepaute to assist him in the computations. Lalande wrote, "During six months we calculated from morning to night, sometimes even at meals. ... The assistance of Mme Lepaute was such that, without her I should never have been able to undertake the enormous labour, in which it was necessary to calculate the distance of each of the two planets Jupiter and Saturn from the comet, separately for each successive degree for 150 years. *SAU

1838 Camille Jordan (5 Jan 1838; 20 Jan 1922) French mathematician and engineer who prepared a foundation for group theory and built on the prior work of Évariste Galois (died 1832). As a mathematician, Jordan's interests were diverse, covering topics throughout the aspects of mathematics being studied in his era. The topics in his published works include finite groups, linear and multilinear algebra, the theory of numbers, topology of polyhedra, differential equations, and mechanics. *TIS

1871 Federigo Enriques born in Leghorn, Italy. In 1907 he and Severi received the Bordin Prize from the Paris Academy for their work on hyperelliptical surfaces. *VFR Now known principally as the first to give a classification of algebraic surfaces in birational geometry, and other contributions in algebraic geometry.*SAU

1871 Gino Fano (5 Jan 1871 in Mantua, Italy - 8 Nov 1952 in Verona, Italy) He was a pioneer in finite geometries. He created a finite geometry that is now a common classroom example. *VFR

1884 Arnaud Denjoy ( 5 January 1884, 21 January 1974) was a French mathematician. Denjoy was born in Auch, Gers. His contributions include work in harmonic analysis and differential equations. His integral was the first to be able to integrate all derivatives. Among his students is Gustave Choquet.Denjoy died in Paris in 1974.*Wik

1909 Stephen Cole Kleene (5 Jan 1909; 25 Jan 1994) American mathematician and logician whose research was on the theory of algorithms and recursive functions. He developed the field of recursion theory with Church, Gödel, Turing and others. He contributed to mathematical Intuitionism which had been founded by Brouwer. His work on recursion theory helped to provide the foundations of theoretical computer science. By providing methods of determining which problems are soluble, Kleene's work led to the study of which functions can be computed. *TIS

1943 George Washington Carver (1861?, 5 Jan 1943)American agricultural chemist, agronomist, and experimenter who helped revolutionize the agricultural economy of the South. Carver demonstrated to farmers how fertility could be restored to their land by diversification, especially by planting peanuts and sweet potatoes, to replenish soil impoverished by the regular growth of cotton and tobacco. He showed that peanuts contained several different kinds of oil, and peanut butter was another of his innovations. In all he is reported to have developed over 300 new products from peanuts and over 100 from sweet potatoes. For most of his career he taught and conducted research at the Tuskegee Institute, Alabama where he stayed despite lucrative offers to work for such magnates as Henry Ford and Thomas Edison. *TIS

1951 Joseph Fels Ritt (August 23, 1893–January 5, 1951) was an American mathematician at Columbia University in the early 20th century.
He is known for his work on characterizing the indefinite integrals that can be solved in closed form, for his work on the theory of ordinary differential equations and partial differential equations, for beginning the study of differential algebraic groups,[1][2] and for the method of characteristic sets used in the solution of systems of polynomial equations.*Wik

1970 Max Born (11 Dec 1882, 5 Jan 1970) German physicist who shared the Nobel Prize for Physics in 1954 (with Walther Bothe), for his statistical formulation of the behavior of subatomic particles. Born's studies of the wave function led to the replacement of the original quantum theory, which regarded electrons as particles, with a mathematical description.*TIS (I was not aware until Thony Christie advised me that his granddaughter is Grammy winner Olivia Newton-John)

1971 Columbus O'D Iselin (25 Sept 1904, 5 Jan 1971) Columbus O'D(onnell) Iselin was an American oceanographer, born in New Rochelle, N.Y. As director of the Woods Hole Oceanographic Institution (1940-50; 1956-57) in Massachusetts, he expanded its facilities 10-fold and made it one of the largest research establishments of its kind in the world. He developed the bathythermograph and other deep-sea instruments responsible for saving ships during World War II. He made major contributions to research on ocean salinity and temperature, acoustics, and the oceanography of the Gulf Stream. *TIS

1987 Josif Zakharovich Shtokalo (16 Nov 1897 in Skomorokhy, Sokal, Galicia (now Ukraine) - 5 Jan 1987 in Kiev, Ukraine) Shtokalo worked mainly in the areas of differential equations, operational calculus and the history of mathematics.  Shtokalo's work had a particular impact on linear ordinary differential equations with almost periodic and quasi-periodic solutions. He extended the applications of the operational method to linear ordinary differential equations with variable coefficients.
He is regarded as one of the founders of the history of Soviet mathematics and particularly of the history in Ukraine and articles about M Ostrogradski and H Voronoy, he edited the three volume collections of Voronoy's (1952-3) and Ostrogradski's works (1959-61), a Russian-Ukrainian mathematical dictionary (1960) and approximately eighteen other Russian-Ukrainian terminology dictionaries. *SAU

1994 Sir David Robert Bates, FRS(18 November 1916, Omagh, County Tyrone, Ireland – 5 January 1994) was an Irish mathematician and physicist.
During the Second World War he worked at the Admiralty Mining Establishment where he developed methods of protecting ships from magnetically activated mines.
His contributions to science include seminal works on atmospheric physics, molecular physics and the chemistry of interstellar clouds. He was knighted in 1978 for his services to science, was a Fellow of the Royal Society and vice-president of the Royal Irish Academy. In 1970 he won the Hughes Medal. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1974.
The Mathematics Building at Queens University Belfast, is named after him. *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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