## Monday, 16 April 2012

### On This Day in Math - April 16

Predictability: Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?
~Edward Lorenz
Title of paper presented at the 139th Annual Meeting of the American Association for the Advancement of Science (29 Dec 1979)*TIS

The 107th day of the year; There is no integer N such that N! has exactly 107 zeros in it. The same is true if we replace 107 by the primes 3, 31, or 43.*Prime Curios (This seems a most remarkable set of facts to me.)
Interestingly, the sum of the first 107 digits of pi is prime, and the sum of the first 107 digits of e is prime. This is trivially true for the first digit of each, but can you find the one (I believe) other number between 1 and 107 for which the sum of the digits of e and pi are both prime?

EVENTS
1178BC Homer records the events of a solar eclipse. This may have marked the return of Odysseus, legendary King of Ithaca, to his kingdom after the Trojan War. The date is surmised from a passage in Homer's Odyssey, which reads, "The Sun has been obliterated from the sky, and an unlucky darkness invades the world." This happens in the context of a new moon and at noon, both necessary preconditions for a full solar eclipse. In 2008, to investigate, Dr Marcelo O. Magnasco, an astronomer at Rockefeller University, and Constantino Baikouzis, of the Observatorio Astrónomico de La Plata in Argentina, looked for more clues. Within the text, they interpreted three definitive astronomical events: there was a new moon on the day of the slaughter (as required for a solar eclipse); Venus was visible and high in the sky six days before; and the constellations Pleiades and Boötes were both visible at sunset 29 days before. Since these events recur at different intervals, this particular sequence should be unique: the doctors found only one occurrence of this sequence while searching between 1250 and 1115 BC, the 135-year spread around the putative date for the fall of Troy. It coincided with the eclipse of April 16, 1178 BC.*Wik
837 Comet Halley passed 3.2 million miles from Earth, About 13x the lunar distance. *David Dickinson ‏ @Astroguyz (This is the closest to Earth in history. It is recorded widely, and was almost certainly an event in every culture on the planet.)
1673 “I conjecture that Mr. Collins himself does not speak of these summations of inﬁnite series because he brings forward the example of the series 1/2, 1/3, 1/4, 1/5, 1/6, ... which if it is continued to inﬁnity cannot be summed because the sum is not ﬁnite, like the sum of the triangular numbers, but inﬁnite. But now I am cramped by the space of my paper.” Leibniz to Oldenburg, indicating some hint of a distinction between convergent and divergent series. [The Correspondence of Henry Oldenburg, 9, pp. 599–600.] *VFR

1705 Newton knighted by Queen Anne at Trinity College. [DSB 10, 83] *VFR

1866 “At the meeting held April 16th, 1866, Prof. Cayley called attention to the theorem, that the diﬀerence between two consecutive prime numbers may exceed any given number N − 1 whatever. For if a, b, c, . . . k are the prime numbers not greater than N, then abc . . . k + 1, and abc . . . k +1+ N may be one or both of them prime, but all the intermediate numbers are composite; that is, the diﬀerence of the two successive primes is = N at least.” *Proc. London Math. Soc., vol. 2 (1866-69)

1938 The ﬁrst William Lowell Putnam competition was held. It was won by the team of three from the University of Toronto. Irving Kaplansky was one of the team members. For the history of this now famous exam for undergraduates, see AMM, 72(1965), p. 474. *VFR

1959 "LISP" Language Unveiled:
The programming language that provided the basis for work in artificial intelligence, LISP, has its first public presentation. Created by John McCarthy, LISP offers programmers flexibility in organization and it or its descendants are still used in the AI development environment.*CHM

BIRTHS
1495 Peter Apian (16 Apr 1495; 21 Apr 1552 at age 56)German astronomer and geographer, also known as Petrus Apianus, whose major work was Instrumentum sinuum sivi primi mobilis (1534), in which he gave tables of his calculations of sines for every minute, with a decimal division of the radius. *TIS Apian remained in Ingolstadt until his death. Although he neglected his teaching duties, the university evidently was proud to host such an esteemed scientist. Apian's work included in mathematics—in 1527 he published a variation of Pascal's triangle, and in 1534 a table of sines— as well as astronomy. In 1531, he observed a comet and discovered that a comet's tail always point away from the sun. (Girolamo Fracastoro also detected this in 1531, but Apian's publication was the first to also include graphics.) He designed sundials, published manuals for astronomical instruments and crafted volvelles ("Apian wheels"), measuring instruments useful for calculating time and distance for astronomical and astrological applications.*Wik

1660 Sir Hans Sloane (16 Apr 1660; 11 Jan 1753 at age 92) (Baronet) British physician and naturalist whose collection of books, manuscripts, and curiosities formed the basis for the British Museum in London. By the time he died, Sloane had amassed one of the world's largest and most varied collections of natural history specimens. His passion for the collection and his concern for its future upkeep after his death led him to write a will which clearly stated that it must "remain together and not be separated." He offered it to the British nation, requesting in return a sum of £20,000 for his heirs. Parliament accepted, and King George II gave his royal assent 7 Jun 1753. Thus the British Museum was created and eventually its sister institution, the British Museum of Natural History. *TIS

1682 John Hadley (16 Apr 1682; 14 Feb 1744 at age 61) British mathematician and inventor who perfected methods for grinding and polishing telescope lenses. Hadley improved the reflecting telescope (first introduced by Newton in 1668) and produced the first of its kind having sufficient accuracy and power to be useful in astronomy. It had a 6 inch mirror. He is also known for the reflecting octant (1730) used at sea to measure the altitude of the Sun or a celestial body above the horizon to within one second of arc. It was the ancestor of the modern nautical sextant. He was a prominent member of the Royal Society, of which he was vice-president from 21 Feb 1728. John Hadley was the older brother of George Hadley.*TIS

1728 Joseph Black (16 Apr 1728; 6 Dec 1799 at age 71)Scottish chemist and physicist who experimented with "fixed air" (carbon dioxide), discovered bicarbonates and identified latent heat. He lectured in chemistry, anatomy at the University of Glasgow, while also a physician. From heated magnesia alba (magnesium carbonate), Black collected a gas, carbon dioxide, different from common air. He published Experiments Upon Magnesia Alba, Quicklime, and Some Other Alcaline Substances (1756). Carbon dioxide was also released by fermentation, respiration, and burning charcoal so he assumed it was in the atmosphere. He also observed that ice melts without change of temperature, due to heat that becomes "hidden" - latent heat - and determined "specific heat" for heated of materials.*TIS

1823 Ferdinand Gotthold Max Eisenstein (16 Apr 1823; 11 Oct 1852 at age 29)
German mathematician whose work covered a range of topics including the theory of elliptic functions, and quadratic and cubic forms, which led to cyclotomy, the reciprocity theorem for cubic residues, and also theorems for quadratic and biquadratic residues from partition of prime numbers. *TIS Gauss said of him, "There have been only three epoch-making mathematicians, Archimedes, Newton, and Eisenstein."

1894 Jerzy Neyman (16 Apr 1894; 5 Aug 1981 at age 87) Russian-American mathematician who was one of the principal architects of modern theoretical statistics. His papers on hypothesis testing (1928-33) helped establish the subject. During 1934-38, he gave a theory of confidence intervals (important in the analysis of data); extended statistical theory to contagious distributions, (for interpretation of biological data); wrote on sampling stratified populations (which led to such applications as the Gallup Poll); and developed the model for randomised experiments (widely relevant across the fields of science, including agriculture, biology, medicine, and physical sciences). His later research applied statistics to meteorology and medicine. In 1968 he was awarded the prestigious National Medal of Science.*TIS

DEATHS
1446 Sometimes given as the date of the Death of the architect Filippo Brunelleschi, who helped develop a systematic theory of mathematical perspective. He is especially noted for his design of the Duomo in Florence. More Commonly given date is the 15th

1756 Jacques Cassini (18 Feb 1677; 16 Apr 1756 at age 79) French astronomer whose direct measurement of the proper motions of the stars (1738) disproved the ancient belief in the unchanging sphere of the stars. He also studied the moons of Jupiter and Saturn and the structure of Saturn's rings. His two major treatises on these subject appeared in 1740: Elements of Astronomy and Astronomical Tables of the Sun, Moon, Planets, Fixed Stars, and Satellites of Jupiter and Saturn. He also wrote about electricity, barometers, the recoil of firearms, and mirrors. He was the son of astronomer, mathematician and engineer Giovanni Cassini (1625-1712) with whom he made numerous geodesic observations. Eventually, he took over his father's duties as head of the Paris Observatory.*TIS Cassini was born at the Paris Observatory and died at Thury, near Clermont. Admitted at the age of seventeen to membership of the French Academy of Sciences, he was elected in 1696 a fellow of the Royal Society of London, and became maître des comptes in 1706. *Wik

1788 Comte Georges-Louis Leclerc de Buffon (7 Sep 1707, 16 Apr 1788 at age 80) French naturalist who formulated a crude theory of evolution and was the first to suggest that the earth might be older than suggested by the Bible. In 1739 he was appointed keeper of the Jardin du Roi, a post he occupied until his death. There he worked on a comprehensive work on natural history, for which he is remembered, Histoire naturelle, générale et particulière. He began this work in 1749, and it dominated the rest of his life. It would eventually run to 44 volumes, including quadrupeds, birds, reptiles and minerals. He proposed (1778) that the Earth was hot at its creation and, from the rate of cooling, calculated its age to be 75,000 years, with life emerging some 40,000 years ago.*TIS He is remembered in mathematics for a question he asked more than any questions he answered. Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon:

Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle onto the floor. What is the probability that the needle will lie across a line between two strips?

Buffon's needle was the earliest problem in geometric probability to be solved; it can be solved using integral geometry. The solution, in the case where the needle length is not greater than the width of the strips, can be used to design a Monte Carlo-style method for approximating the number π. *Wik

1901 Henry Augustus Rowland (27 Nov 1848, 16 Apr 1901 at age 52) American physicist who invented the concave diffraction grating, which replaced prisms and plane gratings in many applications, and revolutionized spectrum analysis--the resolution of a beam of light into components that differ in wavelength. His first major research was an investigation of the magnetic permeability of iron, steel and nickel, work which won the praise of Maxwell. Another experiment was the first to conclusively demonstrate that the motion of charged bodies produced magnetic effects. In the late 1870s, he established an authoritative figure for the absolute value of the ohm, and redetermined the mechanical equivalent of heat in the early 1880s, demonstrating that the specific heat of water varied with temperature. *TIS

1914 George William Hill (3 Mar 1838, 16 Apr 1914 at age 76)U.S. mathematical astronomer considered by many of his peers to be the greatest master of celestial mechanics of his time. Hill joined the Nautical Almanac Office in 1861. He computed the orbit of the moon while making original contributions to the three body problem. He introduced infinite determinants, a concept which later found application in many fields of mathematics and physics. When Simon Newcomb took over the Nautical Almanac in 1877 and began a complete recomputation of all solar system motions, Hill was assigned the difficult problem of the orbits of Jupiter and Saturn. After completing the enormous labor in ten years, he returned to his farm, where he continued his research in celestial mechanics.*TIS

1958 Rosalind Elsie Franklin (25 Jul 1920, 16 Apr 1958 at age 37) was an English physical chemist and X-ray crystallographer who contributed to the discovery of the molecular structure of deoxyribonucleic acid (DNA), a constituent of chromosomes that serves to encode genetic information. Beginning in 1951, she made careful X-ray diffraction photographs of DNA, leading her to suspect the helical form of the molecule, at least under the conditions she had used. When James Watson saw her photographs, he had confirmation of the double-helix form that he and Francis Crick then published. She never received the recognition she deserved for her independent work, but had died of cancer four years before the Nobel Prize was awarded to Crick and Watson. *TIS

2008 Edward Lorenz (23 May 1917, 16 Apr 2008 at age 90)American mathematician and meteorologist known for pointing out the "butterfly effect" whereby chaos theory predicts that "slightly differing initial states can evolve into considerably different states." In his 1963 paper in the Journal of Atmospheric Sciences, he cited the flapping of a seagull's wings as changing the state of the atmosphere in even such a trivial way can result in huge changes in outcome in weather patterns. Thus very long range weather forecasting becomes almost impossible. He determined this unexpected result in 1961 while running a computer weather simulation that gave wildly different results from even tiny changes in the input data. *TIS

Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*SAU=St Andrews Univ. Math History
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell