Monday, 19 March 2018

On This Day in Math - March 20

Newton Statue in Trinity Chapel, Cambridge UK *R.B.

The mathematical education of the young physicist [Albert Einstein] was not very solid, which I am in a good position to evaluate since he obtained it from me in Zurich some time ago.
~Hermann Minkowski

The 79th day of the year, 78*79 = 6162 (note that the product of consecutive numbers produces a number that is the concatenation of two successive numbers 61 and 62 in ascending order (and 61 is prime).  (Can you find another number, not necessarily prime, so that n(n-1)= a concatenation of consecutive numbers?)

79 = 27 - 72

79 is the smallest number that can not be represented with less than 19 fourth-powers. (Before you read blythly on, there are three more year days that also require the sum of 19 fourth-powers... find one.)

79 = 11 + 31 + 37. Curiously, the sum holds for the reversals: 97 = 11 + 13 + 73, and all are primes.

279 is the smallest power of 2 which is greater than Avogadro's number

1079 has been called the "Universe number" because it is considered a reasonable lower limit estimate for the number of atoms in the observable universe.  *Prime Curios


71 A.D.: A hybrid solar eclipse is noted by the scholar Plutarch from Greece where it was total.  *David Dickinson ‏ @Astroguyz

1664 (1665 NS) Robert Hooke becomes the Gresham Professor of Mathematics.  The failure of many of the professors to give their lectures had caused the College to go into decline. Hooke wrote in his diary that he frequently gave no lecture as “no one attended”.  The College is generally in decline for the next 100-200 years.  Hooke held the position until his death in 1703. 

1732 Laura Maria Caterina Bassi first (and last for a long while) woman elected to Bologna Academy of Science:

The University of Bologna is the oldest university in Europe and at the beginning of the eighteenth century students were still examined by public disputation, i.e. the candidate was expected to orally defend a series of academic theses. At the beginning of 1732 Bassi took part in a private disputation in her home with members of the university faculty in the presence of many leading members of Bolognese intellectual society. As a result of her performance during this disputation she was elected a member of the prestigious Bologna Academy of Science on 20th March. Rumours of this extraordinary young lady quickly spread and on 17th April she defended forty-nine theses in a highly spectacular public disputation. On 12th May following a public outcry she was awarded a doctorate from the university in a grand ceremony in the city hall of Bologna.  Following a further public disputation the City Senate appointed her professor of philosophy at the university, making her the first ever female professor at a European university.

See more at *Thony Christie, The Renaissance Mathematicus

1774 Ben Franklin to Condorcet on capacity of African American Slaves
*Science and the Founding Fathers, I. Bernard Cohen

In 1800, Alessandro Volta dated a letter announcing his invention of the voltaic pile to Sir Joseph Banks, president of the Royal Society, London. “On the electricity excited by the mere contact of conducting substances of different kinds"” described his results of stacking sandwiches of copper and zinc metal discs between pads of moist material. The letter had to pass from Italy, through France, which was then at war with Britain, so Volta sent the message in two parts. When the first pages arrived, Banks showed them to Anthony Carlisle, a London surgeon, who with William Nicholson immediately began trying to repeat Volta's experiments. By 2 May 1800, they stumbled upon electrolysis of water.*TIS
It was an article by Nicholson about the way the Torpedo fish produced it's electric shock that had inspired Volta's latest experiments.  He had been sparring with Galvani about the possibility of mechanical energy for years. In the same letter mentioned above, he credits Nicholson, "The hypothesis of this learned and laborious philosopher …. is indeed very ingenious."
His image, and of the battery named for him, appear on the 10,000 Lira note before Italy converted to the Euro.

1816 John Dalton makes the last entry in his first meteorological notebook. Dalton came to his views on atomism through his interest in meteoroligy.  The volumes contain daily meteorological observations, vol. 1 covering from 1 Apr 1803 to 20 Mar 1816.  He would begin a second volume the next day.

1916 Albert Einstein submitted his general theory of relativity to Annalen der Physik. *A. Hellemans and B. Bunch, The Timetables of Science
Einstein's Theory of General Relativity was titled “Die Grundlagen der allgemeinen Relativitästheorie.” This theory accounted for the slow rotation of the elliptical path of the planet Mercury, which Newtonian gravitational theory failed to do. Fame and recognition came suddenly in 1919, when the Royal Society of London photographed the solar eclipse and publicly verified Einstein's general theory of relativity. In 1921 he was awarded the Nobel Prize for Physics for his photoelectric law and work in the field of theoretical physics, but such was the controversy still aroused by this theories on relativity that these were not specified in the text of the award. *TIS

1997 Cellular Phone Encryption Is "Cracked," Highlighting Privacy Concerns:
Computer security experts announce that they have cracked the code designed to protect the privacy of calls made with digital cellular phones. The breakthrough showed that cellular phone transmissions remained insecure despite recent developments. The National Security Agency, however, cautioned against more advanced encryption that might allow terrorists to conspire by telephone.*chm

2016 Spring officially comes to Possum Trot, Ky. The equinox passed last night in the dark, daffodils are blooming and dogwoods are budding nicely. The word equinox is derived from the Latin words meaning “equal night.” The spring and fall equinoxes are the only dates with equal daylight and dark as the Sun crosses the celestial equator. At the equinoxes, the tilt of Earth relative to the Sun is zero, which means that Earth’s axis neither points toward nor away from the Sun. *Farmer's Almanac

2017 On this day the public schools of the city of Boston, Mass briefly put spherical and projective geometry in the news. On that date the schools began converting their classroom maps from the common Mercator Projection, to the little known Gall-Peters Projection. The Mercator projection makes some areas, Greenland and Alaska, for example, look much larger than other similar sized areas by comparison. The Gall–Peters projectionmaps all areas such that they have the correct sizes relative to each other. Like any equal-area projection, it achieves this goal by distorting most shapes.


1546  Baha ad-din Muhammad ibn Husayn al-Amili (20 Mar 1546; 20 Aug 1622 at age 76)
Syrian-Iranian theologian, mathematician and astronomer, a.k.a. Shaykh Baha'i). He became a very learned Muslim whose genius touched every field of knowledge from mathematics and philosophy to architecture and landscape design. He revived the study of mathematics in Iran. His treatise on the subject, Khulasat al-hisab (“The Essentials of Arithmetic”), and translations from the original Arabic was in use as a textbook until the end of the 19th century. His treatise in astronomy, Tashrihu'l-aflak ("Anatomy of the Heavens") summarised the works of earlier masters. He was born within a year of William Gilbert in England and Tycho Brahe in Denmark, and was still a child when his family left Syria to escape religious persecution.*TIS

1664 Johann Baptist Homann (20 March 1664 – 1 July 1724) was a German geographer and cartographer, who made maps of the Americas.
Homann was born in Oberkammlach near Kammlach in the Electorate of Bavaria.
Homann acquired renown as a leading German cartographer, and in 1715 was appointed Imperial Geographer by Emperor Charles VI. Giving such privileges to individuals was an added right that the Holy Roman Emperor enjoyed. In the same year he was also named a member of the Prussian Academy of Sciences in Berlin. Of particular significance to cartography were the imperial printing privileges (Latin: privilegia impressoria). These protected for a time the authors in all scientific fields such as printers, copper engravers, map makers and publishers. They were also very important as recommendation for potential customers.
In 1716 Homann published his masterpiece Grosser Atlas ueber die ganze Welt (Grand Atlas of all the World). Numerous maps were drawn up in cooperation with the engraver Christoph Weigel the Elder, who also published Siebmachers Wappenbuch.
Homann died in Nuremberg. He was succeeded by the Homann heirs company, in business until 1848. *Wik A beautiful pocket globe he created can be seen at the Vault, Slate's History blog.

1840 Franz Carl Joseph Mertens (20 March 1840 in Schroda, Posen, Prussia (now Środa Wielkopolska, Poland) - 5 March 1927 in Vienna, Austria) Mertens worked on a number of different topics including potential theory, geometrical applications to determinants, algebra and analytic number theory, publishing 126 papers. Bruce C Berndt writes, "Mertens is perhaps best known for his determination of the sign of Gauss sums, his work on the irreducibility of the cyclotomic equation, and the hypothesis which bears his name. "
Many people are aware of Mertens contributions since his elementary proof of the Dirichlet theorem appears in most modern textbooks. However he made many deep contributions including Mertens' theorems, three results in number theory related to the density of the primes. He proved these results using Chebyshev's theorem, a weak version of the prime number theorem. *SAU  
In his youth, Mertens moved to Berlin where he became a student at Berlin
University, and where he studied under Kronecker and Kummer.  Mertens first worked in Krakow, and then moved to Austria. Ernst Fischer and Schrodinger, for instance, were students of Mertens at the University of Vienna. *Julio Gonzalez Cabillon, Historia Matematica Discussions

1856 Frederick Winslow Taylor (20 Mar 1856, 21 Mar 1915 at age 58)  was an American engineer and inventor who is known as the father of scientific management. His system of industrial management has influenced the development of virtually every country enjoying the benefits of modern industry. He introduced a scientific approach (1881) to “time and motion study” while chief engineer at Midvale Steel Company, Philadelphia, Pa. Taylor and his associates used stop-watches to time the laborers as they performed various tasks, counted the number of shovel-loads they each moved, and the load per shovel. Thus he was able to determine an optimum shovel size and length. Such careful observations, aimed at recognizing wasted effort and minimizing time used, increased the efficiency of actions of factory workers.*TIS
The term "scientific management" was coined by US Supreme Court justice Louis Brandeis to describe Taylor's principles, and in 1911, Taylor published his life's work in the book The Principles of Scientific Management. Taylor was an accomplished tennis and golf player. He and Clarence Clark won the inaugural United States National tennis doubles championship at Newport Casino in 1881 Taylor was a lifelong member of the Philadelphia Country Club, and finished fourth in the 1900 Olympic individual golf event. *Wik *Sports Reference

1884  Philipp Frank (20 Mar 1884; 22 Jul 1966 at age 82)  Austrian-American physicist and mathematician whose theoretical work covered a broad range of mathematics, including variational calculus, Hamiltonian geometrical optics, Schrödinger wave mechanics, and relativity. Frank had a deep and lasting interest in the philosophy of science. In a number of writings, he strove to reconcile science and philosophy and “bring about the closest rapprochement between” them. The 1907 paper he wrote analyzing the law of causality caught Einstein's attention, who in 1912 recommended Frank as his successor as professor of theoretical physics at the German University of Prague. He held that position until 1938, when he moved to Harvard University in the U.S., first as visiting lecturer, but remaining there until retirement in 1954. He wrote on misinterpretations of the Theory of Relativity.*TIS

1920 Douglas George Chapman (20 Mar 1920; 9 Jul 1996 at age 76) was a Canadian-born U.S. mathematical statistician  and an expert on wildlife statistics. He was one of the scientific advisors to the International Whaling Commission that warned in the 1960s that the number of whales being taken by the whaling industry was far in excess of what the population could stand, and proposed annual fin whale catch quotas that would permit the depleted populations of this species to recover. His later research on fish farming expanded to include mollusk aquaculture and he directed a program to develop quantitative methods to aid in the management of fisheries resources.*TIS

1938  Sergi Petrovich Novikov (20 Mar 1938,   ) Russian mathematician who was awarded the Fields Medal in 1970 for his work in algebraic topology. His parents were both mathematicians, and Novikov showed his own talent while a youth. In 1960, the year he obtained his first degree, he published a paper on some problems in the topology of manifolds connected with the theory of Thom spaces. In 1965, he proved his famous theorem on the invariance of Pontryagin classes. He was unable receive the Fields Medal in person because Soviet authorities would not permit his travel. Thereafter he pursued an interest in mathematical physics, including the theory of solitons, quantum field theory and string theory. *Tis


Rubens illustration of projection
1617 François d'Aguilon (also d'Aguillon or in Latin Franciscus Aguilonius) (4 January 1567 – 20 March 1617) was a Belgian Jesuit mathematician, physicist and architect.
D'Aguilon was born in Brussels. He became a Jesuit in 1586. In 1611, he started a special school of mathematics, in Antwerp, which was intended to perpetuate mathematical research and study in among the Jesuits. This school produced geometers like André Tacquet and Jean Charles della Faille.
His book, Opticorum Libri Sex philosophis juxta ac mathematicis utiles (Six Books of Optics, useful for philosophers and mathematicians alike), published in Antwerp in 1613, was illustrated by famous painter Peter Paul Rubens. It was notable for containing the principles of the stereographic and the orthographic projections, and it inspired the works of Desargues and Christiaan Huygens. *Wik

1726/7 Isaac Newton  (25 December 1642 – 20 March 1726 [NS: 4 January 1643 – 31 March 1727)  English physicist and mathematician, who made seminal discoveries in several areas of science, and was the leading scientist of his era. His study of optics included using a prism to show white light could be split into a spectrum of colors. The statement of his three laws of motion are fundamental in the study of mechanics. He was the first to describe the moon as falling (in a circle around the earth) under the same influence of gravity as a falling apple, embodied in his law of universal gravitation. As a mathematician, he devised infinitesimal calculus to make the calculations needed in his studies, which he published in Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy, 1687)*TIS
Newton died intestate. Immediately his relatives began to quarrel over the division of his estate, which amounted to a considerable fortune. Thomas Pellet examined Newton’s manuscript holdings in hopes of turning a quick profit. His “thick clumsy annotations ‘Not fit to be printed,’ now seem at once pitiful and ludicrous.” See Whiteside, Newton Works, I, xvii ff for details. *VFR

1878 (Julius) Robert Mayer (25 Nov 1814; 20 Mar 1878) a German physicist. While a ship's doctor sailing to Java, he considered the physics of animal heat. In 1842, he measured the mechanical equivalent of heat. His experiment compared the work done by a horse powering a mechanism which stirred paper pulp in a caldron with the temperature rise in the pulp. He held that solar energy was the ultimate source of all energy on earth, both living and nonliving. Mayer had the idea of the conservation of energy before either Joule or Helmholtz. The prominence of these two scientists, however, diminished credit for Mayer's earlier insights. James Joule presented his own value for the mechanical equivalent of heat. Helmhotlz more systematically presented the law of conservation of energy. *TIS

1895 Ludwig Schläfli (15 Jan 1814 in Grasswil, Bern, Switzerland - 20 March 1895 in Berne, Switzerland) Schläfli is best known for the so-called Schläfli symbols which are used to classify polyhedra. In this work, Theorie der vielfachen Kontinuität (Theory of continuous manifolds), Schläfli introduced polytopes (although he uses the word polyschemes) which he defines to be higher dimensional analogues of polygons and polyhedra. Schläfli introduced what is today aclled the Schläfli symbol. It is defined inductively. {n} is a regular n-gon, so {4} is a square. There {4, 3} is the cube, since it is a regular polyhedron with 3 squares {4} meeting at each vertex. Then the 4 dimensional hypercube is denoted as {4, 3, 3}, having three cubes {4, 3} meeting at each vertex. Euclid, in the Elements, proves that there are exactly five regular solids in three dimensions. Schläfli proves that there are exactly six regular solids in four dimensions {3, 3, 3}, {4, 3, 3}, {3, 3, 4}, {3, 4, 3}, {5, 3, 3}, and {3, 3, 5}, but only three in dimension n where n ≥ 5, namely {3, 3, ..., 3}, {4, 3, 3, ....,3}, and {3, 3, ...,3, 4}.
Most of Schläfli's work was in geometry, arithmetic and function theory. He gave the integral representation of the Bessel function and of the gamma function. His eight papers on Bessel functions played an important role in the preparation of G N Watson's major text Treatise on the theory of Bessel functions (1944). *SAU

1993  Polykarp Kusch (26 Jan 1911; 20 Mar 1993) German-American physicist who shared the Nobel Prize for Physics in 1955 for his accurate determination that the magnetic moment of the electron is greater than its theoretical value. This he deduced from researching the hyperfine structure of the energy levels in certain elements, and in 1947 found a discrepancy of about 0.1% between the observed value and that predicted by theory. Although minute, this anomaly was of great significance and led to revised theories about the interactions of electrons with electromagnetic radiation, now known as quantum electrodynamics. (He shared the prize with Willis E. Lamb, Jr. who performed independent but related experiments at Columbia University on the hyperfine structure of the hydrogen atom.)*TIS

1962 Andrew Ellicott Douglass (5 Jul 1867, 20 Mar 1962 at age 94) American astronomer and archaeologist who coined the name dendrochronology for tree-ring dating, a field he originated while working at the Lowell Observatory, Flagstaff, Ariz. (1894-1901). He showed how tree rings could be used to date and interpret past events. Douglass also sought a connection between sunspot activity and the terrestrial climate and vegetation. The width of tree rings is a record of the rainfall, with implications on the local food supply in dry years. Archaeologist Clark Wissler collaborated in this work by furnishing sections of wooden beams from Aztec Ruin and Pueblo Bonito so Douglass could cross-date the famous sites. Thus the study of tree rings enables archaeologists to date prehistoric remains. *TIS

1983  Ivan Matveyevich Vinogradov (2 Sep 1891, 20 Mar 1983 at age 91) Soviet mathematician known for his contributions to the analytical theory of numbers, including a partial solution of the Goldbach conjecture proving that every sufficiently large odd integer can be expressed as the sum of three odd primes. He described his methods in his most celebrated piece of work Some Theorems Concerning the Theory of Prime Numbers (1937).*TIS

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

On This Day in Math - March 19

Pearls of Sluze, *Mathworld Wolfram

There is no reason why the history and philosophy of science should not be taught in such a way as to bring home to all pupils the grandeur of science and the scope of its discoveries.
~Prince Louis-Victor de Broglie

The 78th day of the year; 78 is the smallest number that can be written as the sum of 4 distinct squares in 3 ways.  *What's Special About This Number

78 is the sum of the first twelve integers, and thus a triangular number.

The cube of 78 is equal to the sum of three distinct cubes, 783 = 393 + 523 + 653
(Historically, it seems Ramanujan was inspired by a much smaller such triplet 63 = 33 + 43 + 53

77 and 78 form the fourth Ruth-Aaron pair, named for the number of home runs hit by Babe Ruth, 714, and the number when Aaron broke the record, 715 (he hit more afterward).  They are consecutive numbers that have the same sums of their prime factors (77 = 7*11, 78 = 2*3*13, and 7+11 = 2+3+13).


In 1474, the Venetian Patent Law, the first of its kind in the world, declared that “each person who will make in this city any new and ingenious contrivance, not made heretofore in our dominion, as soon as it is reduced to perfection... It being forbidden to any other in any territory and place of ours to make any other contrivance in the form and resemblance thereof, without the consent and licence of the author up to ten years.” The law was intended to attract inventors and investors to Venice and stimulate new economic activities. *TIS

*Mark Jardine,
1681 Last observation of C/1680 V1, also called the Great Comet of 1680, Kirch's Comet, and Newton's Comet. It has the distinction of being the first comet discovered by telescope. Discovered by Gottfried Kirch on 14 November 1680, New Style, it became one of the brightest comets of the 17th century--reputedly visible even in daytime--and was noted for its spectacularly long tail. Passing only 0.4 AUs from Earth on 30 November, it sped around an incredibly close perihelion of .006 AU (898,000 km) on 18 December 1680, reaching its peak brightness on 29 December as it rushed outward again. It was last observed on 19 March 1681. As of December 2010 the comet was about 252.1 A.U. from the Sun. While the Kirch Comet of 1680-1681 was discovered and subsequently named for Gottfried Kirch , credit must also be given to the Jesuit, Eusebio Kino, who charted the comet’s course. During his delayed departure for Mexico, Kino began his observations of the comet in Cadíz in late 1680. Upon his arrival in Mexico City, he published his Exposisión astronómica de el [sic] cometa (Mexico City, 1681) in which he presented his findings. Kino’s Exposisión astronómica is among one of the earliest scientific treatises published by a European in the New World. Aside from its brilliance, it is probably most noted for being used by Isaac Newton to test and verify Kepler's laws. *Wik

1706 Advertisement in English Tabloid for William Jones's Synopsis Palmariorum Matheseos, or A New Introduction to the Mathematics. This is the book in which Jones introduces the symbol pi for the ratio of the circumference to diameter of a circle.
*Review of the State of the English Nation (Cumulation) (London, England), Tuesday, March 19, 1706; Issue 34.

1752 Following the death of her father on March 19, 1752, a new phase of Maria Agnesi’s life began that lasted until her death. She restricted her study to theology and gave her time, effort, and money to devotional and charitable activities. Although continuing to live with her family, she kept a separate apartment, where she cared for a few poor, sick people. From 1759 she lived in a rented house with four of her poor people; and when money was needed for her charitable activity, she sold her gifts from the Empress Maria Theresa to a rich Englishman. Besides caring for the sick and indigent, she often taught catechism to working-class people. *Hubert Kennedy, Eight Mathematical Biographies, Pg 8

1791 Prior to 1784, when Jefferson arrived in France, most if not all of his drawings were made in ink. In Paris, Jefferson began to use pencil for drawing, and adopted the use of coordinate, or graph, paper. He treasured the coordinate paper that he brought back to the United States with him and used it sparingly over the course of many years. He gave a few sheets to his good friend David Rittenhouse, the astronomer and inventor:

"I send for your acceptance some sheets of drawing-paper, which being laid off in squares representing feet or what you please, saves the necessity of using the rule and dividers in all rectangular draughts and those whose angles have their sines and cosines in the proportion of any integral numbers. Using a black lead pencil the lines are very visible, and easily effaced with Indian rubber to be used for any other draught."
A few precious sheets of the paper survive today. *
Jefferson was widely interested in Science. For those who wish to know more about his scientific interest, I can recommend this book

1791 Report made to the Paris Academy of Sciences advocating the metric system, including the decimal subdivision of the circle. The committee consisted of J. C. Borda, J. Lagrange, P. S. Laplace, G. Monge, and de Condorcet. [Cajori, History of Mathematics 266] See April 14, 1790. *VFR
A metric system of angles was brought in, with 400 degrees in a full turn (100 degrees in a right angle). Now the earth would rotate 40 degrees in an hour and, since the metre had been designed so that one quarter meridian was 10 million metres, each degree of latitude would be 100 kilometres long. It was certainly a rational system but its introduction would require all watches, all clocks, all trigonometric tables, all charts etc. to be changed. Condorcet proposed that teams of out of work wig makers should be used to recalculate new mathematical tables with the new units. Why, one might ask, were the wig makers out of work? Well they had been employed by the aristocrats who, following the Revolution, no longer required their services! *SAU

1797 The date of the entry in Gauss’s scientific diary showing that he had already discovered the double periodicity of certain elliptic functions. *VFR Gauss was investigating the lemniscate.

1892 E. Hastings Moore, of Northwestern University, was elected professor of mathematics by the Board of Trustees of the new University of Chicago. *T. W. Goodspeed, The Story of the University of Chicago

1918 "An Act to preserve daylight and provide standard time for the United States" was enacted on March 19, 1918. It both established standard time zones and set summer DST to begin on March 31, 1918. *WebExhibits 

1937 John von Neumann gave a popular lecture at Princeton on the game of poker. Game Theory became one of his substantial contributions to mathematics. [A. Hodges, Alan Turing. The Enigma, p. 550]The Book that inspired the movie.

In 1958, Britain's first planetarium, the London Planetarium, opened in the west wing of Madame Tussaud's. It is one of the world's largest. The site used was that of the former Cinema and Restaurant added in 1929, that had been destroyed by a German bomb in 1940.*TIS

1953 Frances Crick writes a letter to his son. "Dear Michael, Jim Watson and I have probably made a most important discovery.” This was only two weeks after Crick solved the DNA puzzle and may well be the first written description of the code. The letter, to be auctioned at Christie’s on April 10, is expected to fetch at least $1 million at auction. *NY Times Science

2016 Spring Equinox. Spring officially comes to Possum Trot, Ky at 11:30 P.M. CDT, this evening. The word equinox is derived from the Latin words meaning “equal night.” The spring and fall equinoxes are the only dates with equal daylight and dark as the Sun crosses the celestial equator. At the equinoxes, the tilt of Earth relative to the Sun is zero, which means that Earth’s axis neither points toward nor away from the Sun. *Farmer's Almanac


1782 Baron Wilhelm von Biela (19 Mar 1782, 18 Feb 1856 at age 73) Austrian astronomer who was known for his measurement (1826) of a previously known comet as having an orbital period of 6.6 years. Subsequently, known as Biela's Comet, it was observed to break in two (1846), and in 1852 the fragments returned as widely separated twin comets that were not seen again. However, in 1872 and 1885, bright meteor showers (known as Andromedids, or Bielids... current Andromedids are only weakly represented by displays of less than three meteors per hour around November 14. ) were observed when the Earth crossed the path of the comet's known orbit. This observation provided the first concrete evidence for the idea that some meteors are composed of fragments of disintegrated comets.*TIS

1799 William Rutter Dawes (19 Mar 1799, 15 Feb 1868 at age 68) English amateur astronomer who set up a private observatory and made extensive measurements of binary stars and on 25 Nov 1850 discovered Saturn's inner Crepe Ring (independently of American William Bond). In 1864, he was the first to make an accurate map of Mars. He was called "Eagle-eyed Dawes" for the keenness of his sight with a telescope (though otherwise, he was very near-sighted). He devised a useful empirical formula by which the resolving power of a telescope - known as the Dawes limit - could be quickly determined. For a given telescope with an aperture of d cm, a double star of separation 11/d arcseconds or more can be resolved, that is, be visually recognized as two stars rather than one. *TIS

1862 Adolf Kneser (19 March 1862 in Grüssow, Mecklenburg, Germany - 24 Jan 1930 in Breslau, Germany (now Wrocław, Poland)) He is remembered most for work mainly in two areas. One of these areas is that of linear differential equations; in particular he worked on the Sturm-Liouville problem and integral equations in general. He wrote an important text on integral equations. The second main area of his work was the calculus of variations. He published Lehrbruch der Variationsrechnung (Textbook of the calculus of variations) (1900) and he gave the topic many of the terms in common use today including 'extremal' for a resolution curve, 'field' for a family of extremals, 'transversal' and 'strong' and 'weak' extremals *SAU

1900 Frederic Joliot-Curie (19 Mar 1900; 14 Aug 1958 at age 58) French physicist and physical chemist who became personal assistant to Marie Curie at the Radium Institute, Paris, and the following year married her daughter Irène (who was also an assistant at the institute). Later they collaborated on research, and shared the 1935 Nobel Prize in Chemistry "in recognition of their synthesis of new radioactive elements." For example, they discovered that aluminium atoms exposed to alpha rays transmuted to radioactive phosphorus atoms. By 1939 he was investigating the fission of uranium atoms. After WW II he supervised the first atomic pile in France. He succeeded his wife as head of the Radium Institute upon her death in 1956. *TIS

1910 Jacob Wolfowitz (March 19, 1910 – July 16, 1981) was a Polish-born American statistician and Shannon Award-winning information theorist. He was the father of former Deputy Secretary of Defense and World Bank Group President Paul Wolfowitz.
While a part-time graduate student, Wolfowitz met Abraham Wald, with whom he collaborated in numerous joint papers in the field of mathematical statistics. This collaboration continued until Wald's death in an airplane crash in 1950. In 1951, Wolfowitz became a professor of mathematics at Cornell University, where he stayed until 1970. He died of a heart attack in Tampa, Florida, where he was a professor at the University of South Florida.
Wolfowitz's main contributions were in the fields of statistical decision theory, non-parametric statistics, sequential analysis, and information theory.*Wik

1910 Jerome Namias (19 Mar 1910, 10 Feb 1997 at age 86) American meteorological researcher most noted for having pioneered the development of extended weather forecasts and who also studied the Dust Bowl of the 1930s and the El Niño phenomenon. *TIS In 1971 he joined the Scripps Institution and established the first Experimental Climate Research Center. His prognosis of warm weather during the Arab oil embargo of 1973 greatly aided domestic policy response.*Wik

1927 Allen Newell (March 19, 1927 – July 19, 1992) was a researcher in computer science and cognitive psychology at the RAND Corporation and at Carnegie Mellon University’s School of Computer Science, Tepper School of Business, and Department of Psychology. He contributed to the Information Processing Language (1956) and two of the earliest AI programs, the Logic Theory Machine (1956) and the General Problem Solver (1957) (with Herbert A. Simon). He was awarded the ACM's A.M. Turing Award along with Herbert A. Simon in 1975 for their basic contributions to artificial intelligence and the psychology of human cognition *Wik

1951 Arthur T. Benjamin (March 19, 1961; ) is an American mathematician who specializes in combinatorics. Since 1989 he has been a Professor of Mathematics at Harvey Mudd College.
He is known for mental math capabilities and mathemagics performances. These have included shows at the Magic Castle and TED. He is also the first mathematician to have been featured on the Colbert Report.
The Mathematical Association of America gave him a regional award for distinguished teaching in 1999 and a national one in 2000. He was the Mathematical Association of America's George Pólya Lecturer for 2006-8. In 2012 he became a fellow of the American Mathematical Society.
Benjamin was one of the performers at the inaugural San Diego Science Festival on April 4, 2009. He also won the American Backgammon Tour in 1997. *Wik A video of his "mathmagic" is here 
And his new book, The Magic of Math: Solving for x and Figuring Out Why, is delightful,


1406 Ibn Khaldūn or Ibn Khaldoun  Al-Ḥaḍrami, May 27, 1332 AD/732 AH – March 19, 1406 AD/808 AH) was a Muslim historiographer and historian who is often viewed as one of the fathers of modern historiography,sociology and economics.
He is best known for his Muqaddimah (known as Prolegomenon in English), which was discovered, evaluated and fully appreciated first by 19th century European scholarship, although it has also had considerable influence on 17th-century Ottoman historians like Ḥajjī Khalīfa and Mustafa Naima who relied on his theories to analyze the growth and decline of the Ottoman Empire. Later in the 19th century, Western scholars recognized him as one of the greatest philosophers to come out of the Muslim world. *Wik

1862 John Edward Campbell (27 May 1862, Lisburn, Ireland – 1 October 1924, Oxford, Oxfordshire, England) is remembered for the Campbell-Baker-Hausdorff theorem which gives a formula for multiplication of exponentials in Lie algebras. *SAU His 1903 book, Introductory Treatise on Lie's Theory of Finite Continuous Transformation Groups, popularized the ideas of Sophus Lie among British mathematicians.
He was elected a Fellow of the Royal Society in 1905, and served as President of the London Mathematical Society from 1918 to 1920. *Wik

1685 René François Walter de Sluse (2 July 1622 in Visé, Principality of Liège (now Belgium) - 19 March 1685 in Liège, Principality of Liège (now Belgium)) a French mathematician, intellectual and clergyman who wrote many books about mathematics and contributed to the development of mathematics.
Plague in Église Saint-Martin

He studied at a university in Rome, and later moved to Liège. His position in the church prevented him from visiting other mathematicians, but he corresponded with the mathematicians and intellectuals of the day.
He studied calculus and his work discusses spirals, tangents, turning points and points of inflection.
There is a family of curves named after him called the Pearls of Sluze: the curves represented by the following equation with positive integer values of m, n and p:
yn = k(a - x)pxm *Wik
This group of curves was studied by de Sluze between 1657 and 1698. It was Blaise Pascal who named the curves after de Sluze.

1922 George Ballard Mathews, FRS (February 23, 1861 — March 19, 1922) was a London born mathematician who specialized in number theory.
After receiving his degree (as Senior Wrangler) from St John's College, Cambridge in 1883, he was elected a Fellow of St John's College. *Wik Mathews also wrote Algebraic equations (1907) which is a clear exposition of Galois theory, and Projective geometry (1914). This latter book develops the subject of projective geometry without using the concept of distance and it bases projective geometry on a minimal set of axioms. The book also treats von Staudt's theory of complex elements as defined by real involutions. The book contains a wealth of information concerning the projective geometry of conics and quadrics. *SAU

1930 Henry Faulds (1 Jun 1843, 19 Mar 1930 at age 86) Scottish physician who, from 1873, became a missionary in Japan, where he worked as a surgeon superintendent at a Tokyo hospital, taught at the local univeristy, and founded the Tokyo Institute for the Blind. In the late 1870s, his attention was drawn to fingerprints of ancient potters remaining on their work that he helped unearth at an archaeological dig site in Japan. He commenced a study of fingerprints, and became convinced that each individual had a unique pattern. He corresponded on the subject with Charles Darwin, and published a paper about his ideas in Nature (28 Oct 1880). When he returned to Britain in 1886, he unsuccessfully offered his fingerprinting identification scheme for forensic uses to Scotland Yard. Undeserved confusion on priority for the discovery with Francis Galton and Sir William J. Herschel lasted until 1917. *TIS

1978 Gaston Maurice Julia (February 3, 1893 – March 19, 1978) was a French mathematician who devised the formula for the Julia set. His works were popularized by French mathematician Benoit Mandelbrot; the Julia and Mandelbrot fractals are closely related.*Wik A report of his bravery during WWI during which he lost his nose:
January 25, 1915, showed complete contempt for danger. Under an extremely violent bombardment, he succeeded despite his youth (22 years) to give a real example to his men. Struck by a bullet in the middle of his face causing a terrible injury, he could no longer speak but wrote on a ticket that he would not be evacuated. He only went to the ambulance when the attack had been driven back. It was the first time this officer had come under fire.
When only 25 years of age, Julia published his 199 page masterpiece Mémoire sur l'iteration des fonctions rationelles which made him famous in the mathematics centres of his day. The beautiful paper, published in Journal de Math. Pure et Appl. 8 (1918), 47-245, concerned the iteration of a rational function f. Julia gave a precise description of the set J(f) of those z in C for which the nth iterate f n(z) stays bounded as n tends to infinity. (These are the Julia Sets popularized by Mandelbrot) *SAU

1984 Richard Ernest Bellman (August 26, 1920 – March 19, 1984) was an American applied mathematician, celebrated for his invention of dynamic programming in 1953, and important contributions in other fields of mathematics. A Bellman equation, also known as a dynamic programming equation, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. Almost any problem which can be solved using optimal control theory can also be solved by analyzing the appropriate Bellman equation. The Bellman equation was first applied to engineering control theory and to other topics in applied mathematics, and subsequently became an important tool in economic theory. The "Curse of dimensionality", is a term coined by Bellman to describe the problem caused by the exponential increase in volume associated with adding extra dimensions to a (mathematical) space.*Wik

1987 Louis Victor Pierre Raymond duc de Broglie (15 Aug 1892,19 Mar 1987 at age 94) was a French physicist best known for his research on quantum theory and for his discovery of the wave nature of electrons. De Broglie was of the French aristocracy - hence the title "duc" (Prince). In 1923, as part of his Ph.D. thesis, he argued that since light could be seen to behave under some conditions as particles (photoelectric effect) and other times as waves (diffraction), we should consider that matter has the same ambiguity of possessing both particle and wave properties. For this, he was awarded the 1929 Nobel Prize for Physics. *TIS
He is buried in the Cimetière de Neuilly-sur-Seine (Ancien),Hauts-de-Seine, Ile-de-France Region, France. (Just outside Paris)

2011 J(ames) Laurie Snell, (January 15th, 1925, Wheaton, Illinois; March 19, 2011, Hanover, New Hampshire) was an American mathematician.
A graduate of the University of Illinois, he taught at Dartmouth College until retiring in 1995. Among his publications was the book "Introduction to Finite Mathematics", written with John George Kemeny and Gerald L. Thompson, first published in 1956 and in multiple editions since.
The Snell envelope, used in stochastics and mathematical finance, is the smallest supermartingale dominating the price process. Snell has published the related theory 1952 in the paper Applications of martingale system theorems.*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

Sunday, 18 March 2018

On This Day in Math - March 18

Steiner eircumellipse *wolfram  alpha

Scientific discovery consists in the interpretation for our own convenience of a system of existence which has been made with no eye to our convenience at all.
~Norbert Wiener

The 77th day of the year; 77 is the only number less than 100 with a multiplicative persistence of 4. Can you find the next? (Multiply all the digits of a number n, repeating with the product until a single digit is obtained. The number of steps required is known as the multiplicative persistence, and the final digit obtained is called the multiplicative digital root of n.) There is not another year day that will have a multiplicative persistence greater than four. [7x7=49, 4x9=36, 3x6=18, 1x8=8]

772 is the smallest square number that can be the sum of consecutive squares greater than 1, \(sum_{k=18}^{28}k^2 = 77^2\)

The concatenation of all palindromes from one up to 77 is prime.

77 is equal to the sum of three consecutive squares, \(4^2 + 5^2 + 6^2= 77\) and also the sum of the first 8 primes. *Prime Curios


2012 The Sunday following March 15 is "Buzzard Sunday" at the Hinckley Reservation (Near Cleveland, Ohio) a family fun day celebrating the buzzards (a common name for the "turkey vulture,"). Every year on March 15 since 1957, the city of Hinckley Ohio has eagerly awaited the return of the buzzards at "Buzzards' Roost" at the Hinckley Reservation, part of the Cleveland Metroparks. *

1973 Comet Kohoutek, formally designated C/1973 E1, 1973 XII, and 1973f, was first discovered on this date while examining photographic plates taken on 7 March 1973 by Czech astronomer Luboš Kohoutek. It attained perihelion on 28 December that same year. Will not be back for a really, really long time.

In 1987, the discovery of "high-temperature" superconductivity was announced to thousands of scientists at a packed meeting of the American Physical Society in New York City. The phenomenon, discovered 1911, was at first known to occur at only 4 degrees above absolute zero, when all electrical resistance in a metal sample disappeared. In 1986, researchers discovered a ceramic material that was a superconductor at a temperature of more than 30 degrees above absolute zero. When published in September of that year, that news stirred the wider scientific community into action. By the time of the APS meeting, further discoveries had been made. The scene of excitement at the meeting was dubbed the "Woodstock of Physics." *TIS

1990 The Mathematische Gesellschaft, the world’s oldest existing mathematical society (founded 1690) began a seven day meeting in Hamburg to celebrate its third centenary. *VFR

2010 It was announced that Grigori Yakovlevich Perelman had met the criteria to receive the first Clay Millennium Prize for resolution of the Poincaré conjecture. On 1 July 2010, he turned down the prize of one million dollars, saying that he considers his contribution to proving the Poincaré conjecture to be no greater than that of Richard Hamilton, who introduced the theory of Ricci flow with the aim of attacking the geometrization conjecture. *Wik

2011 The Pluto-bound New Horizons spacecraft flew past Uranus’ orbit at about 6 p.m. EDT, 1.8 billion miles from Earth. New Horizons is now well over halfway through its journey to Pluto. Motoring along at 57,9000 km/hr (36,000 mph), it will travel more than 4.8 billion km (3 billion miles) to fly past Pluto and its moons Nix, Hydra and Charon in July 2015.The next planetary milestone for New Horizons will be the orbit of Neptune, which it crosses on Aug. 25, 2014, exactly 25 years after Voyager 2 made its historic exploration of that giant planet. *Universe Today (Hat tip to David Dickinson@Astroguyz


1602 Jacques de Billy (18 March 1602 in Compiègne, France - 14 Jan 1679 in Dijon, France) was a French Jesuit. Billy corresponded with Fermat and produced a number of results in number theory which have been named after him. Billy had collected many problems from Fermat's letters and, after the death of his father, Fermat's son appended de Billy's collection under the title Doctrinae analyticae inventum novum (New discovery in the art of analysis) as an annex to his edition of the Arithmetica of Diophantus (1670). *SAU . At the College de Dijon he taught privately Jacques Ozanam, in whom he instilled a love of the calculus. *VFR

1640 Philippe de La Hire (or Lahire or Phillipe de La Hire) (March 18, 1640 – April 21, 1718) was a French mathematician and astronomer. According to Bernard le Bovier de Fontenelle he was an "academy unto himself". La Hire wrote on graphical methods, 1673; on conic sections, 1685; a treatise on epicycloids, 1694; one on roulettes, 1702; and, lastly, another on conchoids, 1708. His works on conic sections and epicycloids were founded on the teaching of Desargues, of whom he was his favourite pupil. He also translated the essay of Manuel Moschopulus on magic squares, and collected many of the theorems on them which were previously known; this was published in 1705. He also published a set of astronomical tables in 1702. La Hire's work also extended to descriptive zoology, the study of respiration, and physiological optics.
Two of his sons were also notable for their scientific achievements: Gabriel-Philippe de La Hire (1677–1719), mathematician, and Jean-Nicolas de La Hire (1685–1727), botanist.
The mountain Mons La Hire on the Moon is named for him. *Wik He was also the first to find the arc length of the cardioid in 1708.

1690 Christian Goldbach (18 Mar 1690, 20 Nov 1764) Russian mathematician whose contributions to number theory include Goldbach's conjecture, formulated in a letter to Leonhard Euler dated 7 Jul 1742. Stated in modern terms it proposes that: "Every even natural number greater than 2 is equal to the sum of two prime numbers." It has been checked by computer for vast numbers - up to at least 4 x 1014 - but still remains unproved. Goldbach made another conjecture that every odd number is the sum of three primes, on which Vinogradov made progress in 1937. (It has been checked by computer for vast numbers, but remains unproved.) Goldbach also studied infinite sums, the theory of curves and the theory of equations. *TIS

1796 Jakob Steiner (18 Mar 1796; 1 Apr 1863 at age 67) Swiss mathematician who was one of the greatest, contributors to projective geometry. He discovered the Steiner surface which has a double infinity of conic sections on it. The Steiner theorem states that the two pencils by which a conic is projected from two of its points are projectively related. He is also known for the Poncelet-Steiner theorem which shows that only one given circle and a straight edge are required for Euclidean constructions. His work included conic sections and surfaces, the theory of second-degree surfaces and centre-of-gravity problems. He developed the principle of symmetrization (1840-41). In 1848 he ws the first to define various polar curves with respect to a given curve, and introduced the “Steiner Curves.” *TIS

1839 Joseph Émile Barbier (18 March 1839 in St Hilaire-Cottes, Pas-de-Calais, France - 28 Jan 1889 in St Genest, Loire, France)
He was offered a post at the Paris Observatory by Le Verrier and Barbier left Nice to begin work as an assistant astronomer. For a few years he applied his undoubted genius to problems of astronomy. He proved a skilled observer, a talented calculator and he used his brilliant ideas to devise a new type of thermometer. He made many contributions to astronomy while at the observatory but his talents in mathematics were also to the fore and he looked at problems in a wide range of mathematical topics in addition to his astronomy work.
As time went by, however, Barbier's behaviour became more and more peculiar. He was clearly becoming unstable and exhibited the fine line between genius and mental problems which are relatively common. He left the Paris Observatory in 1865 after only a few years of working there. He tried to join a religious order but then severed all contacts with his friends and associates. Nothing more was heard of him for the next fifteen years until he was discovered by Bertrand in an asylum in Charenton-St-Maurice in 1880.
Bertrand discovered that although Barbier was clearly unstable mentally, he was still able to make superb original contributions to mathematics. He encouraged Barbier to return to scientific writing and, although he never recovered his sanity, he wrote many excellent and original mathematical papers. Bertrand, as Secretary to the Académie des Sciences, was able to find a small source of income for Barbier from a foundation which was associated with the Académie. Barbier, although mentally unstable, was a gentle person and it was seen that, with his small income, it was possible for him to live in the community. This was arranged and Barbier spent his last few years in much more pleasant surroundings.
Barbier's early work, while at the Observatory, consists of over twenty memoirs and reports. These cover topics such as spherical geometry and spherical trigonometry. We mentioned above his work with devising a new type of thermometer and Barbier wrote on this as well as on other aspects of instruments. He also wrote on probability and calculus.
After he was encouraged to undertake research in mathematics again by Bertrand, Barbier wrote over ten articles between the years 1882 and 1887. These were entirely on mathematical topics and he made worthwhile contributions to the study of polyhedra, integral calculus and number theory. He is remembered for Barbier's theorem, nicely explained here by Alex Bogomolny.*SAU

1870 Agnes Sime Baxter (Hill) (18 March 1870 – 9 March 1917) was a Canadian-born mathematician. She studied at Dalhousie University, receiving her BA in 1891, and her MA in 1892. She received her Ph.D. from Cornell University in 1895; her dissertation was “On Abelian integrals, a resume of Neumann’s ‘Abelsche Integrele’ with comments and applications." *Wik

1891 Walter Andrew Shewhart (March 18, 1891 - March 11, 1967) was an American physicist, engineer and statistician, sometimes known as the father of statistical quality control.
W. Edwards Deming said of him, "As a statistician, he was, like so many of the rest of us, self-taught, on a good background of physics and mathematics. "
His more conventional work led him to formulate the statistical idea of tolerance intervals and to propose his data presentation rules, which are listed below:

Data have no meaning apart from their context.
Data contain both signal and noise. To be able to extract information, one must separate the signal from the noise within the data.
Walter Shewhart visited India in 1947-48 under the sponsorship of P. C. Mahalanobis of the Indian Statistical Institute. Shewhart toured the country, held conferences and stimulated interest in statistical quality control among Indian industrialists

1911 Walter Ledermann (18 March 1911 in Berlin, Germany - 22 May 2009 in London, England) graduated from Berlin but was forced to leave Germany in 1933 to avoid Nazi persecution. He came to St Andrews and studied under Turnbull. He worked at Dundee and St Andrews until after World War II when he moved to Manchester and then to the University of Sussex. He is especially known for his work in homology, group theory and number theory. *SAU

1928 Lennart Axel Edvard Carleson (18 March 1928 in Stockholm, Sweden - ) is a Swedish mathematician who solved one of the most important problems in the theory of Fourier series. He was director of the Mittag-Leffler Institute, Stockholm, from 1968 to 1984, during which time he built the Institute from a small base into one of the leading mathematical research institutes in the world.*SAU


1871 Augustus de Morgan  (born 27 Jun 1806, 18 Mar 1871 at age 64) Born in Madura (now Madurai), India, son of a colonel in the Indian Army. He is best known for his work in Formal Logic. “De Morgan’s Laws”, are contained in his first book (1847), although they were known to Peter of Spain in the fourteenth century. *VFR
In formal logic, De Morgan's laws are rules relating the logical operators "and" and "or" in terms of each other via negation. With two operands A and B:
\overline{A \cdot B} = \overline A + \overline B
\overline{A + B} = \overline {A} \cdot \overline {B}
In another form:
The rules can be expressed in English as:
"The negation of a conjunction is the disjunction of the negations." and
"The negation of a disjunction is the conjunction of the negations."
When he defined and introduced the term "mathematical induction" (1838), he gave the process a rigorous basis and clarity that it had previously lacked. He originated the use of the slash to represent fractions, as in 1/5 or 3/7. In Trigonometry and Double Algebra (1849) he gave a geometric interpretation of complex numbers. *TIS  A nice blog about De Morgan's life and relationships is at The Renaissance Mathematicus.
Teachers might give students the opportunity to find the date of his birth using De Morgan's own clues; “I was x years old in the year x2” *VFR

1907 Pierre-Eugène-Marcellin Berthelot (27 Oct 1827, 18 Mar 1907 at age 79) was a French chemist and science historian and government official whose creative thought and work significantly influenced the development of chemistry in the late 19th century. He helped to found the study of thermochemistry, introduced a standard method for determining the latent heat of steam, measured hundreds of heats of reactions and coined the words exothermic and endothermic. Berthelot systematically synthesized organic compounds, including some not found in nature. His syntheses of many fundamental organic compounds helped to destroy the classical division between organic and inorganic compounds. *TIS

1964 Norbert Wiener (26 Nov 1894; 18 Mar 1964) U.S. mathematician, who established the science of cybernetics, a term he coined, which is concerned with the common factors of control and communication in living organisms, automatic machines, and organizations. He attained international renown by formulating some of the most important contributions to mathematics in the 20th century. His work on generalised harmonic analysis and Tauberian theorems won the Bôcher Prize in 1933 when he received the prize from the American Mathematical Society for his memoir Tauberian theorems published in Annals of Mathematics in the previous year. His extraordinarily wide range of interests included stochastic processes, quantum theory and during WW II he worked on gunfire control. *TIS Cybernetics, published in 1948, was a major influence on later research into artificial intelligence. In the book, Wiener drew on World War II experiments with anti-aircraft systems that anticipated the course of enemy planes by interpreting radar images. Wiener also did extensive analysis of brain waves and explored the similarities between the human brain and a modern computing machine capable of memory association, choice, and decision making.*CHM (Wiener is somewhat revered as the ultimate absent-minded professor. An anecdote I used to share with my classes, almost certainly exaggerated, went something like this: Wiener had moved to a new address, and his wife knowing of his forgetfulness wrote a note with his new address and put it in his coat pocket. During the day struck by a mathematical muse he whipped out the piece of paper and scribbled notes on the back, then realizing his idea had been wrong, he tossed the piece of paper away and went about his day. In the afternoon he returned to his old house out of habit and coming up to the empty house remembered that he had moved, but not where. As he started to leave a young girl walked up and he stopped here. "Young lady, I am the famous mathematician Wiener. Do you know where I live?" The lass replied, "Yes, father, I'll show you the way home."... )
Wiener is buried in Vittum Hill Cemetery in Sandwich, Carroll County, New Hampshire, USA
reader Tom ‏@umacf24 told me that "Before this guy, 'kyber' was an obscure Greek word for 'steering.' " (seems very appropriate root) Thanks Tom.

1989 Sir Harold Jeffreys (22 Apr 1891, 18 Mar 1989 at age 97)English astronomer, geophysicist and mathematician who had diverse scientific interests. In astronomy he proposed models for the structures of the outer planets, and studied the origin of the solar system. He calculated the surface temperatures of gas at less than -100°C, contradicting then accepted views of red-hot temperatures, but Jeffreys was shown to be correct when direct observations were made. In geophysics he researched the circulation of the atmosphere and earthquakes. Analyzing earthquake waves (1926), he became the first to claim that the core of the Earth is molten fluid. Jeffreys also contributed to the general theory of dynamics, aerodynamics, relativity theory and plant ecology.*TIS

2001 Dirk Polder (August 23, 1919, The Hague — March 18, 2001, Iran) was a Dutch physicist who, together with Hendrik Casimir, first predicted the existence of what today is known as the Casimir-Polder force, sometimes also referred to as the Casimir effect or Casimir force. He also worked on the similar topic of radiative heat transfer at nanoscale. *Wik

2013 Mary Ellen Rudin (born December 7, 1924, Hillsboro, Texas - March 18, 2013, Madison, Wisconsin) was an American mathematician.
Born Mary Ellen Estill, she attended the University of Texas, completing her B.A. in 1944 and her Ph.D. in 1949, under Robert Lee Moore. In 1953, she married the mathematician Walter Rudin. Following her mentor Moore, her research centers on point-set topology. She was appointed as Professor of Mathematics at the University of Wisconsin in 1971, and is currently a Professor Emerita there. She served as vice-president of the American Mathematical Society, 1980–1981. In 1984 she was selected to be a Noether Lecturer. She is an honorary member of the Hungarian Academy of Sciences (1995).
Rudin is best known in topology for her constructions of counterexamples to well-known conjectures. Most famously, she was the first to construct a Dowker space, thus disproving a conjecture of Dowker's that had stood, and helped drive topological research, for more than twenty years. She also proved the first Morita conjecture and a restricted version of the second. Her latest major result is a proof of Nikiel's conjecture. Rudin's Erdős number is 1.
"Reading the articles of Mary Ellen Rudin, studying them until there is no mystery takes hours and hours; but those hours are rewarded, the student obtains power to which few have access. They are not hard to read, they are just hard mathematics, that's all." (Steve Watson)
She lived in Madison, Wisconsin, in the Rudin House, a home designed by architect Frank Lloyd Wright, and died at the age of 88. *SAU

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 & Campbel

Saturday, 17 March 2018

On This Day in Math - March 17


St. Patrick’s Day. The equation of the day is the four-leaved rose r = sin(2θ). Work on this curve was first published by the Italian priest Guido Grandi in 1723. *VFR

"Spirit of '76" by Archibald McNeal Willard, 189

The 76th day of the year; 76 is an automorphic number because the square of 76 ends in 76. (5 and 6 are automorphic because 52 ends in five and 62 ends in six).
There is one other two digit automorphic number (it should be easy to find) but can you find the three digit ones?

76= 8 + 13 + 21 + 34 the sum of four consecutive Fibonacci numbers

76 is the number of 6 X 6 symmetric permutation matrices.


1694 L’Hospital hires his former tutor Johann Bernoulli to “work on what I shall ask you ... and also to communicate to me your discoveries, with the request not to mention them to others.” The first calculus text resulted in 1696. It contained the famous “L’Hospital’s rule,” which, we now know, is the work of Bernoulli. [Eves, Circles, 208◦] VFR
(Because L'Hospital is so often discredited by Intro Calculus teachers for his role, I wanted to add more detail in the hopes they will share a more enlightened presentation of his work.)
In a letter from March 17, 1694, l'Hôpital made the following proposal to Johann Bernoulli: in exchange for an annual payment of 300 Francs, Bernoulli would inform L'Hôpital of his latest mathematical discoveries, withholding them from correspondence with others, including Varignon. Bernoulli's immediate response has not been preserved, but he must have agreed soon, as the subsequent letters show. L'Hôpital may have felt fully justified in describing these results in his book, after acknowledging his debt to Leibniz and the Bernoulli brothers, "especially thle younger one" (Johann). Johann Bernoulli grew increasingly unhappy with the accolades bestowed on l'Hôpital's work and complained in private correspondence about being sidelined. After l'Hôpital's death, he publicly revealed their agreement and claimed credit for the statements and portions of the text of Analyse, which were supplied to l'Hôpital in letters. Over a period of many years, Bernoulli made progressively stronger allegations about his role in the writing of Analyse, culminating in the publication of his old work on integral calculus in 1742: he remarked that this is a continuation of his old lectures on differential calculus, which he discarded since l'Hôpital had already included them in his famous book. For a long time, these claims were not regarded as credible by many historians of mathematics, because l'Hôpital's mathematical talent was not in doubt, while Bernoulli was involved in several other priority disputes. For example, both H. G. Zeuthen and Moritz Cantor, writing at the cusp of the 20th century, dismissed Bernoulli's claims on these grounds. However, in 1921 Paul Schafheitlin discovered a manuscript of Bernoulli's lectures on differential calculus from 1691–1692 in the Basel University library. The text showed remarkable similarities to l'Hôpital's writing, substantiating Bernoulli's account of the book's origin.
L'Hôpital's pedagogical brilliance in arranging and presenting the material remains universally recognized. Regardless of the exact authorship (one should also note that the book was first published anonymously), Analyse was remarkably successful in popularizing the ideas of differential calculus stemming from Leibniz. *Wik

1856 Joseph Lacomme, a French well-sinker, and illiterate laborer who asked a mathematics professor to tell him the amount of stone needed to cover the bottom of a circular cistern, and unsatisfied with the reply that it would be impossible to tell him exactly, set about experimenting and determined the "True" ratio of the circumference to diameter of a circle. Teaching himself arithmetic and writing to confirm the results he obtained by experimentation he shared his computation with the commissioner of police in Paris. The commissioner introduced Lacomme to his father, who presented him to the Academie and after consideration by a committee, Lacomme received a silver medal from the French Academie for his discovery of the true ratio of diameter to circumfrence of a circle. He would later receive three more medals from other societies for his value of 3 1/8. *Augustus DeMorgan, A Budget of Paradoxes, pgs 46-47
The Kindle edition of A Budget of Paradoxes, Volume I is currently free.

1889 A political cartoon in the New York World lampooned President Benjamin Harrison's advisers and cabinet members showing the group sitting around playing the game, Pigs in Clover which had recently been invented by Charles Martin Crandall. The caption read "Will Mr. Harrison be able to get all these hungry pigs in the official pen?"
The events which prompted the story were related in a New York Tribune's March 13, 1889 issue:
Senator William M. Evarts purchased one from a street fakir in order to get rid of him. He took the puzzle home and worked it for hours. The following morning he brought it with him into senate chambers where Senator George Graham Vest stopped by Evarts' desk, borrowed the puzzle and took it to a cloak room. Soon thereafter he was joined by Senators James L. Pugh, James B. Eustis, Edward C. Walthall and John E. Kenna. A page was sent out to buy five of the puzzles and upon his return, the group engaged in a "pig driving contest". About 30 minutes later, Senator Vest announced his accomplishment of driving the last pig in the pen.
*Antique Toy Collectors of America *Wik (Will negotiate trade of my off-spring or other not-to-valuable property for a imageof this cartoon. )

1905 Albert Einstein submits his paper "On a Heuristic Point of View Concerning the Production and Transformation of Light" to the Annalen der Physik. In this revolutionary paper he proposes that light can be conceived both as waves and as discrete quanta (later to be called photons) which are localized at points in space. This paper was the primary reason for his Nobel Prize.

1914 Ramanujan boarded the S.S. Nevasa on 17 March 1914, and at 10 o'clock in the morning, the ship departed from Madras. He arrived in London on 14 April, with E. H. Neville waiting for him with a car. A tweet from @amanicdroid pointed out that, "this was significant for him culturally as a high-caste Hindu as crossing the ocean was taboo. "

1941 The National Gallery of Art opened its doors on the mall in Washington D.C. The gallery was a gift of Pittsburgh financier Andrew W. Mellon. His personal collection of 152 masterpieces has grown to 80,000 priceless works today. Today it is a good place to see some mathematics, from the lack of perspective in its medieval works, to The Lady in the Red Hat with its camera obscura technique, to the geometric starkness of the East Wing. *VFR

1988 Apple Computer sues Microsoft Corporation for copyright infringement in its Windows design. After Apple developed a highly successful graphical user interface for its Macintosh computer released in 1984, Microsoft fought back with an operating system of its own, called "Windows." In 1995, Apple lost the lawsuit, in which it claimed that the similarities of the Windows and Macintosh environments extended too far.*CHM

2013 Flash of Meteor hitting moon visible to naked eye. Scientists monitoring the moon for meteorite impacts spotted the biggest impact event to date: a space rock the size of a basketball slammed into the lunar surface at a speed of 56,000 miles per hour (90,000 km/hr), creating a new crater around 20 meters wide.
The flash was impressive — it unleashed the equivalent energy of 5 tons of TNT exploding and would have been visible to anyone casually looking at the moon, no telescope required. *NASA The impact hit almost exactly on a crater already present. This animated gif shows before and after shots of the site.

1733 Carsten Niebuhr(March 17, 1733 Lüdingworth – April 26, 1815 Meldorf, Dithmarschen), German mathematician, cartographer, and explorer in the service of Denmark. Niebuhr's first book, Beschreibung von Arabien, was published in Copenhagen in 1772, the Danish government providing subsidies for the engraving and printing of its numerous illustrations. This was followed in 1774 and 1778 by the two volumes of Niebuhr's Reisebeschreibung von Arabien und anderen umliegenden Ländern. These works (particularly the one published in 1778), and most specifically the accurate copies of the cuneiform inscriptions found at Persepolis, were to prove to be extremely important to the decipherment of cuneiform writing. Before Niebuhr's publication, cuneiform inscriptions were often thought to be merely decorations and embellishments, and no accurate decipherments or translations had been made up to that point. Niebuhr demonstrated that the three trilingual inscriptions found at Persepolis were in fact three distinct forms of cuneiform writing (which he termed Class I, Class II, and Class III) to be read from left to right. His accurate copies of the trilingual inscriptions gave Orientalists the key finally crack the cuneiform code, leading to the discovery of Old Persian, Akkadian, and Sumerian. *Wik

1876 Ernest Benjamin Esclangon (March 17, 1876 – January 28, 1954) was a French astronomer and mathematician. During World War I, he worked on ballistics and developed a novel method for precisely locating enemy artillery. When a gun is fired, it initiates a spherical shock wave but the projectile also generates a conical wave. By using the sound of distant guns to compare the two waves, Escaglon was able to make accurate predictions of gun locations.
After the armistice, Esclangon became director of the Strasbourg Observatory and professor of astronomy at the university the following year. In 1929, he was appointed director of the Paris Observatory and of the International Time Bureau, and elected to the Bureau des Longitudes in 1932. In 1933, he initiated the talking clock telephone service in France. He was elected to the Académie des Sciences in 1939.
Serving as director of the Paris Observatory throughout World War II and the German occupation of Paris, he retired in 1944. He died in Eyrenville, France.
The binary asteroid 1509 Esclangona and the lunar crater Esclangon are named after him.*Wik

1915 Wolfgang Döblin, known in France as Vincent Doblin, (17 March 1915 – 21 June 1940) was a German-French mathematician. Wolfgang was the son of the Jewish-German novelist, Alfred Döblin. His family escaped from Nazi Germany to France where he became a citizen. Studying probability theory at the Institute Henri Poincaré under Fréchet, he quickly made a name for himself as a gifted theorist. He became a doctor at age 23. Drafted in November 1938, after refusing to be exempted of military service, he had to stay in the active Army when World War II broke out in 1939, and was quartered at Givet, in the Ardennes, as a telephone operator. There, he wrote down his latest work on the Chapman-Kolmogorov equation, and sent this as a "pli cacheté" (sealed envelope) to the French Academy of Sciences. His company, sent to the sector of the Saare on the ligne Maginot in April 1940, was caught in the German attack in the Ardennes in May, withdrew to the Vosges, and capitulated on June 22, 1940. On June 21, Doblin had committed suicide in Housseras (a small village near to Epinal), at the moment where German troops came in sight of the place. In his last moments, he burned his mathematical notes.
The sealed envelope was opened in 2000, revealing that Döblin was ahead of his time in the development of the theory of Markov processes. In recognition of his results, Itō's lemma is now referred to as the Itō–Doblin Theorem.
His life was recently the subject of a movie by Agnes Handwerk and Harrie Willems, A Mathematician Rediscovered. *Wik

1972 Kalpana Chawla (March 17, 1962 – February 1, 2003) was an American astronaut and the first indian woman in space. She first flew on Space Shuttle Columbia in 1997 as a mission specialist and primary robotic arm operator. In 2003, Chawla was one of the seven crew members killed in the Space Shuttle Columbia disaster. *Wik

1652 Benjamin Bramer (15 Feb 1588 in Felsberg, Germany - 17 March 1652 in Ziegenhain, Germany) was an architect who published work on the calculation of sines. He was tutored by Jost Bürgi in a wide range of subjects but it was mathematics that he loved and he passed this love on to Bramer. (Bramer married Bürgi's daughter) Bramer followed Alberti (1435), Dürer (1525) and Bürgi (1604) when in 1630 he constructed a device that enabled one to draw accurate geometric perspective. The instrument had been described in a 1617 publication Trigonometrica planorum mechanica oder Unterricht und Beschreibung eines neuen und sehr bequemen geometrischen Instrumentes zu allerhand Abmessung. Bramer designed several other mathematical instruments, for example a description of the pantograph appears in the same 1617 publication. The instrument is designed to copy a geometric shape and reproduce it at a reduced or enlarged scale. It consists of an assemblage of rigid bars adjustably joined by pin joints; as the point of one bar is moved over the outline to be duplicated, the motion is translated to a point on another bar, which makes the desired copy according to the predetermined scale. Bramer has not been recognised as the inventor of the pantograph, this distinction going to the Jesuit Christoph Scheiner who describes a similar instrument in his 1631 publication Pantographice seu acre delineandi res quaslibet by parallelogrammum linear seu cavum mechanicum, mobile. Although Scheiner's publication did much to spread knowledge of the pantograph, the instrument he describes is technically inferior to the earlier instrument as described by Bramer. *SAU

1767 George Parker (born 1697, 17 Mar 1764) [2nd Earl of Macclesfield] English astronomer who was instrumental in changing the computation of current chronology, subsequently enacted as the British Calendar Act of 1751 which co-authored and co-promoted. (Shortly thereafter, he was elected President of the Royal Society, 1752-1764). Since 1582, the new calendar of Pope Gregory XIII had been used in most of Europe. In England the new calendar was rejected as popish. By 1750, the old calendar became 11 days out of sequence with the position of the Earth in its orbit due to its lack of leap years. Parker was assisted in these calculations by his friend James Bradley, the astronomer royal, and received influential support from Philip Dormer Stanhope, 4th Earl of Chesterfield. *TIS

1771 Chester Moor Hall, (Dec. 9, 1703, Leigh, Essex, Eng.— March 17, 1771, Sutton, Surrey), English jurist and mathematician who invented the achromatic lens, which he utilized in building the first refracting telescope free from chromatic aberration (colour distortion).
Convinced from study of the human eye that achromatic lenses were feasible, Hall experimented with different kinds of glass until he found (1729) a combination of crown glass and flint glass that met his requirements. In 1733 he built several telescopes with apertures of 2.5 inches (6.5 cm) and focal lengths of 20 inches (50 cm).*

1782 Daniel Bernoulli (29 January 1700 (8 Feb new style), 8 March 1782) was a Dutch-Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. Bernoulli's work is still studied at length by many schools of science throughout the world. The son of Johann Bernoulli (one of the "early developers" of calculus), nephew of Jakob Bernoulli (who "was the first to discover the theory of probability"), and older brother of Johann II, He is said to have had a bad relationship with his father. Upon both of them entering and tying for first place in a scientific contest at the University of Paris, Johann, unable to bear the "shame" of being compared as Daniel's equal, banned Daniel from his house. Johann Bernoulli also plagiarized some key ideas from Daniel's book Hydrodynamica in his own book Hydraulica which he backdated to before Hydrodynamica. Despite Daniel's attempts at reconciliation, his father carried the grudge until his death.
He was a contemporary and close friend of Leonhard Euler. He went to St. Petersburg in 1724 as professor of mathematics, but was unhappy there, and a temporary illness in 1733 gave him an excuse for leaving. He returned to the University of Basel, where he successively held the chairs of medicine, metaphysics and natural philosophy until his death.
In May, 1750 he was elected a Fellow of the Royal Society. He was also the author in 1738 of Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk), in which the St. Petersburg paradox was the base of the economic theory of risk aversion, risk premium and utility.
One of the earliest attempts to analyze a statistical problem involving censored data was Bernoulli's 1766 analysis of smallpox morbidity and mortality data to demonstrate the efficacy of vaccination. He is the earliest writer who attempted to formulate a kinetic theory of gases, and he applied the idea to explain Boyle's law. He worked with Euler on elasticity and the development of the Euler-Bernoulli beam equation. *Wik

1846 Friedrich Wilhelm Bessel (22 Jul 1784, 17 Mar 1846 at age 61). He is noted for the special class of functions that have become an indispensable tool in applied mathematics. This, like all of his mathematical work, was motivated by his work in astronomy. *VFR In 1809, at the age of 26, Bessel was appointed director of Frederick William III of Prussia's new Königsberg Observatory and professor of astronomy, where he spent the rest of his career. His monumental task was determining the positions and proper motions for about 50,000 stars, which allowed the first accurate determination of interstellar distances. Bessel's work in determining the constants of precession, nutation and aberration won him further honors. Other than the sun, he was the first to measure the distance of a star, by parallax, of 61 Cygni (1838). In mathematical analysis, he is known for his Bessel function. *TIS

1853 Christian Doppler (29 Nov 1803; 17 Mar 1853) Austrian physicist who first described how the observed frequency of light and sound waves is affected by the relative motion of the source and the detector, known as the Doppler effect. In 1845, to test his hypothesis, Doppler used two sets of trumpeters: one set stationary at a train station and one set moving on an open train car, all holding the same note. As the train passed the station, it was obvious that the frequency of the notes from the two groups didn't match. Sound waves would have a higher frequency if the source was moving toward the observer and a lower frequency if the source was moving away from the observer. Edwin Hubble used the Doppler effect of light from distant stars to determine that the universe is expanding.*TIS

1922 Heinrich Suter (4 January 1848, Hedingen near Zurich, Switzerland – 17 March 1922) was a historian of science specializing in Islamic mathematics and astronomy.*Wik

1956 Irène Joliot-Curie (12 Sep 1897; 17 Mar 1956) French physicist and physical chemist, wife of Frédéric Joliot-Curie, who shared the 1935 Nobel Prize for Chemistry "in recognition of their synthesis of new radioactive elements." For example, in their joint research they discovered that aluminium atoms exposed to alpha rays transmuted to radioactive phosphorus atoms. She was the daughter of Nobel Prize winners Pierre and Marie Curie. From 1946, she was director of the Radium Institute, Paris, founded by her mother. She died of leukemia, like her mother, resulting from radiation exposure during research.*TIS

1956 Henry Frederick Baker FRS (3 July 1866 – 17 March 1956) was a British mathematician, working mainly in algebraic geometry, but also remembered for contributions to partial differential equations (related to what would become known as solitons), and Lie groups.
Baker was born in Cambridge, England and educated at The Perse School before winning a scholarship to St John's College, Cambridge in October 1884. Baker graduated as Senior Wrangler in 1887, bracketed with 3 others.
Baker was elected Fellow of St John's in 1888 where he remained for 68 years.
In June, 1898 he was elected a Fellow of the Royal Society. In 1911, he gave the presidential address to the London Mathematical Society.
In January 1914 he was appointed Lowndean Professor of Astronomy. *Wik
In the 1920's and 30's before the war Baker's graduate students would meet at what they called Professor Baker’s "Tea Party". They met each Saturday to discuss the areas of research in which they were working. It was to one of these meetings that a young Donald Coxeter brought his "Aunt Alice", the 69 year old Alicia Boole to co-present on the subject of Polytopes in higher dimensions.

1962 Wilhelm Blaschke (13 Sep 1885; 17 Mar 1962) German mathematician whose major contributions to geometry concerned kinematics and differential geometry. Kinetic mapping (important later in the axiomatic foundations of various geometries) he both discovered and established it as a tool in kinematics. He also initiated topological differential geometry (the study of invariant differentiable mappings)*TIS

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