## Tuesday, 19 April 2016

### On This Day in Math - April 19

 The White Bridge, across from my home in Elk Rapids, Mi.
People must understand that science is inherently neither a potential for good nor for evil. It is a potential to be harnessed by man to do his bidding.
~Glenn T. Seaborg

The 110th day of the year; The sum of the first 110 primes has only two prime factors. 2+3+5+7+....+599 + 601 = 29897 = 7 X 4271

110 is the average of first fifty-three primes.

110 is the side of the smallest square that can be tiled with distinct integer-sided squares (see image below). There are 3 distinct Simple Perfect Squared Squares with this property. Two 110's with 22 squares were discovered in 1978, one by Duijvestijn using computer search, the second by Willcocks, who transformed Duijvestijns 110 into a different second 110, and one more 110 with 23 squares was discovered in 1990 by Duijvestijn. It was Gambini who proved 110 is the minimal square. *http://www.archimedes-lab.org

110 = 52 + 62 + 72 (3 consecutive squares)
= 11^2 - 11^1 (difference between powers of the same number)

110 hertz is the standard frequency of the musical note A or La.

110 is also known as "eleventy" according to the number naming system invented by J. R. R. Tolkien.

EVENTS
1739  John Winthrop (12 Dec 1714-1779) of Cambridge, Mass., the first astronomer of note in the U.S. began sunspot observations and continued over the next two days. No observations were possible on 21 Apr due to cloudy weather. His observations exist as one-page reports in the University Archives of Harvard University, though they were never published. In 1761, he went on an expedition to St. John’s, Newfoundland, to observe the transit of Venus across the sun on 6 Jun 1761, which measurements could be used to compute the distance between the sun and the Earth. He also observed the transit of 1769 from Cambridge.*TIS

1760 Euler writes the first of many “Letters to a German Princess”.. Madam, The hope of having the honor to communicate, in person, to your Highness, my lessons in geometry, becoming more and more distant, which is a very sensible mortification to me, I feel myself impelled to supply personal instruction by writing, as far as the nature of the objects can permit.” Thus begins the letter on “of maginitude or extension” . the letters will continue, two or more per week, for the next three years. *VFR

1879 “A red letter day in Massachusetts. On that day the second circular which launched the Harvard ‘Annex’, later Radcliﬀe College, was sent out ... ” Mathematics 2 dealt with plane geometry and algebra through quadratics. [Scripta Mathematica, 11(1945), p. 260] *VFR

1957 First FORTRAN program run.[The first FORTRAN program (other than internal IBM testing) runs at Westinghouse, producing a missing comma diagnostic. A successful attempt followed.*CHM] I think the first actual program run of Fortran is described here. It was a calculation using gamma function.

1958 France issued a stamp to honor Jean Cavailles (1903–1944) as a hero of the French Underground during World War II. [Scott #879] *VFR He was a French philosopher and mathematician, specialized in philosophy of science. He took part in the French Resistance within the Libération movement and was shot by the Gestapo on February 17, 1944. *Wik

1975 India’s ﬁrst scientiﬁc satellite was successfully launched from a Soviet cosmodrome with the help of the Soviet rocket carrier at 1300 hours Indian standard time. The satellite was named Aryabhata, after the famous Indian astronomer and mathematician, who was born in Kusuma­pura, near present-day Patna, in A.D. 476. [Eves, Return to Mathematical Circles,7◦]*VFR

1977 The German Democratic Republic issued a stamp commemorating the 200th anniversary of Gauss’s birth, 30 April 1777. Besides a portrait of Gauss there is a geometric construction (dealing with the constructible regular polygons?). Why wasn’t it issued on the anniversary day? [Scott #1811] *VFR I found a different stamp than the one Professor Rickey describews issued for the same reason showing complex plane. (pb) also found this anecdote about Gauss recently, "Such was his admiration of Karl Friedrich Gauss that the German mathematician Peter Dirichlet is said to have slept with Gauss's Disquisitiones Arithmeticae under his pillow. [The admiration was mutual: "The total number of Dirichlet's publications is not large," Gauss once remarked. "Jewels are not weighed on a grocery scale." (Gauss's motto? "Few, but ripe.")] *anecdotatge web site and one more note for students.. To understand a little more about "constuctable" see this post by Alexander Bogomolny at "Cut the Knot".

1984 In the early 1980's, examination of the fossil record led some archeologists to suggest that there was a pattern of extinctions of species on the earth every 26 million years. On this date, two articles appeared in the same edition of the journal article to explain this. "It is proposed that periodic extinction events are triggered by an unseen companion to the sun traveling in a moderately eccentric orbit which at its closest approach passes through the 'Oort cloud' of comets which surrounds the sun. During each passage this unseen solar companion perturbs the orbits of these comets, sending a large number of them into paths which reach the inner solar system. Several of these hit the earth, on average, in the following million years. At present the unseen companion should be approximately at its maximum distance from the sun, about 2.4 light years, and it will present no danger to the earth until about 15 million years from now." The proposed brown or red dwarf companion to the earth was nicknamed Nemisis, for "Greek goddess of vengeance, personification of divine wrath,". *Nature, *Wik
1988 In an article entitled “Hot hands phenomenon: A myth?” the New York Times (pp. 23, 25) reported on work of the Stanford Psychologist A. Iversky. Most fans believe that a player who has made a string of baskets is likely to succeed on the next try. By examining thousands of shots of the Philadelphia 76ers over a season and a half, Iversky has shown otherwise: Outcomes of successive shots are independent. [Mathematics Magazine 61 (1988), p. 268].*VFR [The article is here (pb)]

BIRTHS
1748 D'Amondans Charles de Tinseau (19 April 1748 in Besançon, France - 21 March 1822 in Montpellier, France) wrote on the theory of surfaces, working out the equation of a tangent plane at a point on a surface, and he generalised Pythagoras's theorem proving that the square of a plane area is equal to the sum of the squares of the projections of the area onto mutually perpendicular planes. He continued Monge's study of curves of double curvature and ruled surfaces, being in a sense Monge's first follower. Taton writes that Tinseau's works, "... deal with topics in the theory of surfaces and curves of double curvature: planes tangent to a surface, contact curves of circumscribed cones or cylinders, various surfaces attached to a space curve, the determination of the osculatory plane at a point of a space curve, problems of quadrature and cubature involving ruler surfaces, the study of properties of certain special ruled surfaces (particularly conoids), and various results in the analytic geometry of space." Two papers were published in 1772 on infinitesimal geometry Solution de quelques problèmes relatifs à la théorie des surfaces courbes et des lignes à double courbure and Sur quelques proptiétés des solides renfermés par des surfaces composées des lignes droites. He also wrote Solution de quelques questions d'astronomie on astronomy but it was never published. He did publish further political writings, as we mentioned above, but other than continuing to correspond with Monge on mathematical topics, he took no further part in mathematics. *SAU

1801 Gustav Theodor Fechner (19 Apr 1801; 18 Nov 1887 at age 86) German physicist and philosopher who was a key figure in the founding of psychophysics, the science concerned with quantitative relations between sensations and the stimuli producing them. He formulated the rule known as Fechner’s law, that, within limits, the intensity of a sensation increases as the logarithm of the stimulus. He also proposed a mathematical expression of the theory concerning the difference between two stimuli, advanced by E. H. Weber. (These are now known to be only approximately true. However, as long as the stimulus is of moderate intensity, then the laws will give us a good estimate.) Under the name “Dr. Mises” he also wrote humorous satire. In philosophy he was an animist, maintaining that life is manifest in all objects of the universe. *TIS

1880 Evgeny Evgenievich Slutsky (19 April 1880 in Novoe, Yaroslavl guberniya, Russia - 10 March 1948 in Moscow, USSR) Slutsky was important in the application of mathematical methods in economics. Slutsky introduced stochastic concepts of limits, derivatives and integrals between 1925 to 1928 while he worked at the Conjuncture Institute. In 1927 he showed that subjecting a sequence of independent random variables to a sequence of moving averages generated an almost periodic sequence. This work stimulated the creation of stationary stochastic processes. He also studied correlations of related series for a limited number of trials. He obtained conditions for measurability of random functions in 1937. He applied his theories widely, in addition to economics mentioned above he also studied solar activity using data from 500 BC onwards. Other applications were to diverse topics such as the pricing of grain and the study of chromosomes. *SAU

1883 Richard von Mises (19 Apr 1883; 14 Jul 1953 at age 70.) Austrian-American mathematician and aerodynamicist who notably advanced statistics and the theory of probability. Von Mises' contributions range widely, also including fluid mechanics, aerodynamics, and aeronautics. His early work centred on aerodynamics. He investigated turbulence, making fundamental advances in boundary-layer-flow theory and airfoil design. Much of his work involved numerical methods and this led him to develop new techniques in numerical analysis. He introduced a stress tensor which was used in the study of the strength of materials.Von Mises' primary work in statistics concerned the theory of measure and applied mathematics. His most famous, yet controversial, work was in probability theory *TIS

1912 Glenn T. Seaborg (19 Apr 1912; - 25 Feb 1999 at age 86) American nuclear chemist. During 1940-58, Seaborg and his colleagues at the University of California, Berkeley, produced nine of the transuranic elements (plutonium to nobelium) by bombarding uranium and other elements with nuclei in a cyclotron. He coined the term actinide for the elements in this series. The work on elements was directly relevant to the WW II effort to develop an atomic bomb. It is said that he was influential in determining the choice of plutonium rather than uranium in the first atomic-bomb experiments. Seaborg and his early collaborator Edwin McMillan shared the 1951 Nobel Prize for chemistry. Seaborg was chairman of the US Atomic Energy Commission 1962-71. Element 106, seaborgium (1974), was named in his honor. *TIS

1966 Brett J. Gladman (April 19, 1966 - ) is a Canadian astronomer and a full professor at the University of British Columbia's Department of Physics and Astronomy in Vancouver, British Columbia. He holds the Canada Research Chair in Planetary Astronomy.
Gladman is best known for his work in dynamical astronomy in the Solar System. He has studied the transport of meteorites between planets, the delivery of meteoroids from the main asteroid belt, and the possibility of the transport of life via this mechanism, known as panspermia. He also studies planet formation, especially the puzzle of how the giant planets came to be.
He is discoverer or co-discoverer of many astronomical bodies in the solar system, asteroids, Kuiper Belt comets, and many moons of the giant planets:

Uranus: Caliban, Sycorax, Prospero, Setebos, Stephano, and Ferdinand
Saturn: A dozen satellites in several groups, each named after a theme of Canadian Inuit gods, French deities, and Norse gods
Neptune: The satellite Neso
Jupiter: Discovery and co-discovery of 6 moons

Gladman is a member of the Canada France Ecliptic Plane Survey (CFEPS), which has detected and tracked the world's largest sample of well-understood Kuiper Belt comets, including unusual objects like Buffy = 2004 XR190 and Drac. *Wik

DEATHS
1567  Michael Stifel (1487 in Esslingen, Germany - 19 April 1567 in Jena, Germany). This number mystic (for his “beasting” of Pope Leo X, see Eves, History,p. 199) became the greatest German algebraist of the sixteenth century. He died on the same date in 1567. [Muller] *VFR His most important work is "Arithmetica integra" (1544) contained important innovations in mathematical notation. It has the first use of multiplication by juxtaposition (with no symbol between the terms) in Europe. He is the first to use the term "exponent". The book contains a table of integers and powers of 2 that some have considered to be an early version of a logarithmic table. In 1532 Stifel published anonymously his "Ein Rechenbuchlin vom EndChrist. Apocalyps in Apocalypsim" (A Book of Arithmetic about the AntiChrist. A Revelation in the Revelation). This predicted that Judgement Day the world would end at 8am on October 19, 1533. When this prediction failed, he did not make any other predictions. *Wik (Some sources say he was also born on April 19)
Here is a clip from Louis Karpinski's Unified Mathematics about Stifel's contribution to logarithms:

1739 Nicholas Saunderson died of scurvy at age 56. At age 1 he became blind from smallpox. This did not prevent him from learning Greek, Latin and French and “hearing” the works of Euclid, Archimedes, and Diophantus in the original, learning some parts by heart. He created a “palpable arithmetic,” a nailboard for doing arithmetic and forming diagrams with silk threads—the forerunner of the geoboard. He became Lucasian professor at Cambridge in 1711 and earned a reputation as an excellent teacher.*VFR Would love to have an image of one of these he actually used... anyone?
According to Stephen M. Stigler, he may have been the earliest discoverer of Bayes theorem

1791 Richard Price (23 February 1723 – 19 April 1791) was a British moral philosopher and preacher in the tradition of English Dissenters, and a political pamphleteer, active in radical, republican, and liberal causes such as the American Revolution. He fostered connections between a large number of people, including writers of the Constitution of the United States. He spent most of his adult life as minister of Newington Green Unitarian Church, where possibly the congregant he most influenced was early feminist Mary Wollstonecraft, who extended his ideas on the egalitarianism inherent in the spirit of the French Revolution to encompass women's rights as well. In addition to his work as a moral and political philosopher, he also wrote on issues of statistics and finance, and was inducted into the Royal Society for these contributions. Price was a friend of the mathematician and clergyman Thomas Bayes. He edited Bayes' most famous work "An Essay towards solving a Problem in the Doctrine of Chances" which contains Bayes' Theorem, one of the most fundamental theorems of probability theory, and arranged for its posthumous publication. Price wrote an introduction to Bayes' paper which provides some of the philosophical basis of Bayesian statistics.
Besides the above-mentioned, Price wrote an Essay on the Population of England (2nd ed., 1780) which directly influenced Thomas Robert Malthus.*Wik

1882 Charles Robert Darwin (12 Feb 1809, 19 Apr 1882 at age 73) was an English naturalist who presented facts to support his theory of the mode of evolution whereby favourable variations would survive which he called "Natural Selection" or "Survival of the Fittest," and has become known as Darwinism. His two most important books were On the Origin of Species by Means of Natural Selection (1859) and The Descent of Man, and Selection in Relation to Sex.

1889 Warren De la Rue (15 Jan 1815, 19 Apr 1889 at age 74)English astronomer who pioneered in astronomical photography, the method by which nearly all modern astronomical observations are made. *TIS In 1854 he turned his attention to solar physics, and for the purpose of obtaining a daily photographic representation of the state of the solar surface he devised the photoheliograph, described in his report to the British Association, On Celestial Photography in England (1859), and in his Bakerian Lecture (Phil. Trans. vol. clii. pp. 333–416). Regular work with this instrument, inaugurated at Kew by De la Rue in 1858, was carried on there for fourteen years; and was continued at the Royal Observatory, Greenwich, from 1873 to 1882. The results obtained in. the years 1862–1866 were discussed in two memoirs, entitled Researches on Solar Physics, published by De la Rue, in conjunction with Professor Balfour Stewart and Mr B Loewy, in the Phil. Trans. *Wik

1906 Pierre Curie (15 May 1859, 19 Apr 1906 at age 46)French physical chemist and cowinner of the Nobel Prize for Physics in 1903. His studies of radioactive substances were made together with his wife, Marie Curie, whom he married in 1895. They were achieved under conditions of much hardship - barely adequate laboratory facilities and under the stress of having to do much teaching in order to earn their livelihood. Together, they discovered radium and polonium in their investigation of radioactivity by fractionation of pitchblende (announced in 1898). Later they did much to elucidate the properties of radium and its transformation products. Their work in this era formed the basis for much of the subsequent research in nuclear physics and chemistry. *TIS

1933 Ernest William Hobson FRS (27 October 1856 – 19 April 1933) was an English mathematician, now remembered mostly for his books, some of which broke new ground in their coverage in English of topics from mathematical analysis. He was Sadleirian Professor at the University of Cambridge from 1910 to 1931. He was the brother of the economist John A. Hobson. He became a Fellow of Christ's almost immediately after graduation. He made his way into research mathematics only gradually, becoming an expert in the theory of spherical harmonics. His 1907 work on real analysis was something of a watershed in the British mathematical tradition; and was lauded by G. H. Hardy. It included material on general topology and Fourier series that was topical at the time; and included mistakes that were picked up later (for example by R. L. Moore).*Wik He fought against “the superstition that it is impossible to be ‘rigorous’ without being dull.” “Althouth he lived to be seventy-six he was active almost up to his death; his last book (and perhaps in some ways his best) was published when he was seventy-four. He was a singular exception to the general rule that good mathematicians do their best work when they are young.” See The Mathematical Intelligencer, 6(1984), no. 2, p. 9. *VFR

1914 Charles Sanders Peirce (10 Sep 1839, 19 Apr 1914 at age 74)American scientist, logician, and philosopher who is noted for his work on the logic of relations and on pragmatism as a method of research. He was the first modern experimental psychologist in the Americas, the first metrologist to use a wave-length of light as a unit of measure, the inventor of the quincuncial projection of the sphere, the first known conceiver of the design and theory of an electric switching-circuit computer, and the founder of "the economy of research." He is the only system-building philosopher in the Americas who has been both competent and productive in logic, in mathematics, and in a wide range of sciences. *TIS Charles Sanders Peirce was the son of Sarah Hunt Mills and Benjamin Peirce, himself a professor of astronomy and mathematics at Harvard University, perhaps the first serious research mathematician in America. At 12 years of age, Charles read an older brother's copy of Richard Whately's Elements of Logic, then the leading English-language text on the subject. Thus began his lifelong fascination with logic and reasoning. *Wik

1974 Alexander Dinghas (February 9, 1908 – April 19, 1974) was a Turkish mathematician. He is known for his work in different areas of mathematics including differential equations, functions of a complex variable, functions of several complex variables, measure theory and differential geometry. His most important contribution was his work in function theory, in particular Nevanlinna theory and the growth of subharmonic functions.*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