Saturday, 28 March 2015

On This Day in Math - March 28

*George W. Hart, Sculpture

 `The introduction of the cipher 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps ...'.
in a letter in 1982 to Ronald Brown

The 87th day of the year; the sum of the squares of the first four primes is 87. \(87 = 2^2 + 3^2 + 5^2 + 7^2 \)

87 = 3 * 29, \(87^2 + 3^2 + 29^2 and 87^2 - 3^2 - 29^2 \)are both primes

Among Australian cricket players, it seems, 87 is an unlucky score and is referred to as "the devil's number", supposedly because it is 13 runs short of 100.

In 1747, the fascination with electricity upon reaching the American colonies was the subject of Benjamin Franklin's first of the famous series of letters in which he described his experiments on electricity to Peter Collinson, Esq., of London. He thanked Collison for his “kind present of an electric tube with directions for using it” with which he and others did electrical experiments. “For my own part I never was before engaged in any study that so totally engrossed my attention and my time as this has lately done; for what with making experiments when I can be alone, and repeating them to my friends and acquaintances, who, from the novelty of the thing, come continually in crowds to see them, I have, during some months past, had little leisure for anything else.”*TIS

1764 In a second trial of John Harrison his son William departed for Barbados aboard the Tartar. As with the first trial, William used H4 to predict the ship's arrival at Madeira with extraordinary accuracy. The watch's error was computed to be 39.2 seconds over a voyage of 47 days, three times better than required to win the maximum reward of £20,000. *Royal Museum Greenwich
1802 Olbers, while observing the constellation Virgo, had observed a "star" of the seventh-magnitude not found on the star charts. Over the following week he would observe the motion and determined that it was a planet. In early April he sent the data to Gauss to compute the orbit. On the 18th of April, Gauss computed the orbit in only three hours, placing the orbit between Mars and Jupitor. Olbers named the new planetoid Pallas, and predicted there would be others found in the same area. John Herschel dismissed this speculation as "dreams in which astronomers... indulge" but over 1000 such planetoids have been observed. *Dunnington, Gray, & Dohse; Carl Friedrich Gauss: Titan of Science

1809 Gauss finished work on his Theoria Motus. It explains his methods of computing planetary orbits using least squares. [Springer’s 1985 Statistics Calendar] *VFR

In 1946, the Census Bureau and the National Bureau of Standards met to discuss the purchase of a computer. The agencies agreed to buy UNIVAC, the world's first general all-purpose business computer, from Presper Eckert and John Mauchly for a mere $225,000. Unfortunately, UNIVAC cost far more than that to develop. Eckert and Mauchly's venture floundered as the company continued to build and program UNIVACs for far less than the development cost. Eventually, the company was purchased by Remington Rand. *TIS

1949 The phrase "Big Bang" is created. Shortly after 6:30 am GMT on BBC's The Third Program, Fred Hoyle used the term in describing theories that contrasted with his own "continuous creation" model for the Universe. "...based on a theory that all the matter in the universe was created in one big bang ... ". *Mario Livio, Brilliant Blunders

1959 Germany issued a stamp commemorating the 400th anniversary of the death of Adam Riese [Scott #799] *VFR I understand that the German expression "nach Adam Riese", is still used today. It means "according to Adam Ries" and it is used in saying something is exactly correct.

In 2006, a substantial "lost" book of manuscripts by Robert Hooke in his own handwriting was bought for the Royal Society by donations of nearly £1 million. The book was just minutes before going on the auction block when a last-minute purchase agreement was made and kept the precious document in Britain. Hooke is now often overlooked, except for his law of elasticity, although in his time, he was a prolific English scientist and contributed greatly to planning the rebuilding of London after the Great Fire of 1666. The document of more than 520 pages of manuscripts included the minutes of the Royal Society from 1661-82. It had been found in a cupboard in a private house by an antiques expert there to value other items. *TIS

2012 First day of the baseball season. The exact width of home plate is irrational: 12 times the square root of two. History: The plate was originally a circle of diameter one, then a square of the same size(!), which, by mistake was a one-by-one square. Then the corners were filled in to make the current pentagonal plate. *VFR Home plate is an irregular pentagon. The front is 17 inches wide, faces the pitcher, and defines the width of the strike zone. Then parallel sides 8.5 inches long connect to the foul lines. Finally 12 inch sides run down the foul lines, connecting where the foul lines meet.
It can be thought of as a 17 inch square with the parts that would be in foul territory removed. The figure described in the official rules of MLB, as well as above, is technically impossible. One of two things must be true to make it possible:

the parallel sides of 8.5" are in reality approximately 8.5295" (the square root of 71.75)
the 12" sides that run along the foul lines are approximately 12.0208" (square root of 144.5)
The latter is more likely the case, as it would produce the angle measurements of 90º at the base and rear point and 135º at the sides.

1847 Gyula Farkas (28 March 1847 in Sárosd, Fejér County, Hungary - 27 Dec 1930 in Pestszentlorinc, Hungary) He is remembered for Farkas theorem which is used in linear programming and also for his work on linear inequalities. In 1881 Gyula Farkas published a paper on Farkas Bolyai's iterative solution to the trinomial equation, making a careful study of the convergence of the algorithm. In a paper published three years later, Farkas examined the convergence of more general iterative methods. He also made major contributions to applied mathematics and physics, particularly in the areas of mechanical equilibrium, thermodynamics, and electrodynamics.*SAU

1923 Israel Nathan Herstein (March 28, 1923, Lublin, Poland – February 9, 1988, Chicago, Illinois) was a mathematician, appointed as professor at the University of Chicago in 1951. He worked on a variety of areas of algebra, including ring theory, with over 100 research papers and over a dozen books.
He is known for his lucid style of writing, as exemplified by the classic and widely influential Topics in Algebra, an undergraduate introduction to abstract algebra that was published in 1964, which dominated the field for 20 years. A more advanced classic text is his Noncommutative Rings in the Carus Mathematical Monographs series. His primary interest was in noncommutative ring theory, but he also wrote papers on finite groups, linear algebra, and mathematical economics.*Wik

1928 Alexander Grothendieck (28 Mar 1928-13 November 2014) In 1966 he won a Fields Medal for his work in algebraic geometry. He introduced the idea of K-theory and revolutionized homological algebra. Within algebraic geometry itself, his theory of schemes is used in technical work. His generalization of the classical Riemann-Roch theorem started the study of algebraic and topological K-theory. His construction of new cohomology theories has left consequences for algebraic number theory, algebraic topology, and representation theory. His creation of topos theory has appeared in set theory and logic.
One of his results is the discovery of the first arithmetic Weil cohomology theory: the ℓ-adic étale cohomology. This result opened the way for a proof of the Weil conjectures, ultimately completed by his student Pierre Deligne. To this day, ℓ-adic cohomology remains a fundamental tool for number theorists, with applications to the Langlands program.
Grothendieck influenced generations of mathematicians after his departure from mathematics. His emphasis on the role of universal properties brought category theory into the mainstream as an organizing principle. His notion of abelian category is now the basic object of study in homological algebra. His conjectural theory of motives has been behind modern developments in algebraic K-theory, motivic homotopy theory, and motivic integration. *Wik

1678 Claude François Milliet Dechales (1621 in Chambéry, France - 28 March 1678 in Turin, Italy) Dechales is best remembered for Cursus seu mundus mathematicus published in Lyons in 1674, a complete course of mathematics. Topics covered in this wide ranging work included practical geometry, mechanics, statics, magnetism and optics as well as topics outwith the usual topics of mathematics such as geography, architecture, astronomy, natural philosophy and music. In 1678 he published in Lausanne his edition of Euclid, The Elements of Euclid Explained in a New but Most Easy Method: Together with the Use of Every Proposition through All Parts of the Mathematics, written in French by That Most Excellent Mathematician, F Claude Francis Milliet Dechales of the Society of Jesus. This work covers Books 1 to 6, together with Books 11 and 12, of Euclid's Elements. A second edition was published in 1683, then an edition revised by Ozanam was published in Paris in 1753. An English translation was published in London by M Gillyflower and W Freeman, the translation being by Reeve Williams. A second edition of this English translation appeared in 1696. Schaap writes, "Dechales's separate edition of Euclid, long a favourite in France and elsewhere on the Continent, never became popular in England." *SAU

1794 Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (17 September 1743 – 28 March 1794), known as Nicolas de Condorcet, was a French philosopher, mathematician, and early political scientist whose Condorcet method in voting tally selects the candidate who would beat each of the other candidates in a run-off election. Unlike many of his contemporaries, he advocated a liberal economy, free and equal public education, constitutionalism, and equal rights for women and people of all races. His ideas and writings were said to embody the ideals of the Age of Enlightenment and rationalism, and remain influential to this day. He died a mysterious death in prison after a period of being a fugitive from French Revolutionary​ authorities.*Wik
Condorcet committed suicide by poisoning while in jail so that the republican terrorists could not take him to Paris. *VFR (The St Andrews site has the date of his death one day later.)

1840 Simon Antoine Jean Lhuilier (24 April 1750 in Geneva, Switzerland - 28 March 1840 in Geneva, Switzerland) His work on Euler's polyhedra formula, and exceptions to that formula, were important in the development of topology. Lhuilier also corrected Euler's solution of the Königsberg bridge problem. He also wrote four important articles on probability during the years 1796 and 1797. His most famous pupil was Charles-François Sturm who studied under Lhuilier during the last few years of his career in Geneva. *SAU

1850 Bernt Michael Holmboe (23 March 1795 – 28 March 1850) was a Norwegian mathematician. Holmboe was hired as a mathematics teacher at the Christiania Cathedral School in 1818, where he met the future renowned mathematician Niels Henrik Abel. Holmboe's lasting impact on mathematics worldwide has been said to be his tutoring of Abel, both in school and privately. The two became friends and remained so until Abel's early death. Holmboe moved to the Royal Frederick University in 1826, where he worked until his own death in 1850.
Holmboe's significant impact on mathematics in the fledgling Norway was his textbook in two volumes for secondary schools. It was widely used, but faced competition from Christopher Hansteen's alternative offering, sparking what may have been Norway's first debate about school textbooks. *Wik

1874 Peter Andreas Hansen (8 Dec 1795; 28 Mar 1874) Danish astronomer whose most important work was the improvement of the theories and tables of the orbits of the principal bodies in the solar system. At Altona observatory he assisted in measuring the arc of meridian (1821). He became the director (1825) of Seeberg observatory, which was removed to Gotha in a new observatory built for him (1857). He worked on theoretical geodesy, optics, and the theory of probability. The work in celestial mechanics for which he is best known are his theories of motion for comets, minor planets, moon and his lunar tables (1857) which were in use until 1923. He published his lunar theory in Fundamenta ("Foundation") in 1838, and Darlegung ("Explanation") in 1862-64.*TIS

1950 Ernst David Hellinger (0 Sept 1883 in Striegau, Silesia, Germany (now Strzegom, Poland) - 28 March 1950 in Chicago, Illinois, USA) introduced a new type of integral: the Hellinger integral . Jointly with Hilbert he produced an important theory of forms. From 1907 to 1909 he was an assistant at Göttingen and, during this time, he ".. edited Hilbert's lecture notes and Felix Klein's influential Elementarmathematik vom höheren Standpunkte aus (Berlin, 1925) which was translated into English (New York, 1932). Years later the story is told that,
Shortly after his arrival at Northwestern, one of the professors in describing Northwest's mathematics program to him remarked that in the honours course Felix Klein's 'Elementary mathematics from an advanced standpoint' was used as a text and "perhaps Hellinger was familiar with it". At this Hellinger ... replied "familiar with it, I wrote it!".

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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