## Wednesday, 7 February 2018

### On This Day in Math - February 7

 The Frenet-Serret Frame, *Wik

A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. Beauty is the first test: there is no permanent place in the world for ugly mathematics.
~Godfrey Harold Hardy

Vincent Pantaloni pointed out that this year 2/7/18 should be called "e day". He also noticed a nice approximation to e correct to 9 dp.

(Student's might want to expand the result to more decimal places to see how it works.)

The 38th day of the year; 31415926535897932384626433832795028841 is a prime number.  BUT, It’s also the first 38 digits of pi.

38 is the largest even number so that every partition of it into two odd integers must contain a prime.

38 is the sum of squares of the first three primes $2^2 + 3^2 + 5^2 = 38$. *Prime Curios

At the beginning of the 21st Century there were 38 known Mersenne Primes. As of this writing, there are 50, the last being discovered in Dec of 2017..

38 is also the magic constant in the only possible magic hexagon which utilizes all the natural integers up to and including 19. It was discovered independently by Ernst von Haselberg in 1887, W. Radcliffe in 1895, and several others. Eventually it was also discovered by Clifford W. Adams, who worked on the problem from 1910 to 1957. He worked on the problem throughout his career as a freight-handler and clerk for the Reading Rail Road by trial and error and after many years arrived at the solution which he transmitted to Martin Gardner in 1963. Gardner sent Adams' magic hexagon to Charles W. Trigg, who by mathematical analysis found that it was unique disregarding rotations and reflections.

 *Wik

EVENTS

In 1812, the third day of powerful earthquakes struck, this one with an epicenter near New Madrid, Missouri, part of a three-month series in the central Mississippi River valley, known as the New Madrid earthquakes that began on 16 Dec 1811. The first two had happened on that December day, six hours apart, each with an epicenter in northeastern Arkansas, and were felt hundreds of miles away. Another followed on 23 Jan 1812, with epicenter in the far southeast corner of Missouri. All were powerful, about magnitude 7-7.5, with many aftershocks. Contemporary accounts tell of houses damaged, chimneys toppled, remarkable geological phenomena and landscapes changed. They remain among the most powerful earthquakes in the United States. The New Madrid fault remains a concern. *TIS (especially to those of us who live not far away in Possum Trot, Ky.)

1885 Hilbert promoted to Ph.D. He defended Kant's statement that man possesses, beyond logic and experience, certain a priori knowledge * Constance Reid, Hilbert, p. 16

In 1896, radiology began in England when X-rays were first used to discover the location of a bullet in a 12-yr-old boy's wrist who shot himself the previous month. When the pellet could not be found on probing, surgeon Sir Robert Jones had been consulted. Jones, having heard about the recently discovered X-rays, asked Oliver Lodge, head of the physics department at Liverpool University, if he could help with the new X-rays. On this day, the boy was brought to Lodge's laboratory. The pellet was identified embedded in the third carpo-metacarpal joint. Jones and Lodge reported the case in The Lancet on 22 Feb 1896. Charles Thurstan Holland who had been in attendance subsequently pioneered in clinical radiological examinations.*TIS

In 1932, the "neutron" was described in an article in the journal Nature by its discoverer, James Chadwick, who coined the name for this neutral particle he discovered present in the nucleus of atoms. He was an English physicist who studied at Cambridge, and in Berlin under Geiger, then worked at the Cavendish Laboratory with Ernest Rutherford, where he investigated the structure of the atom. He worked on the scattering of alpha particles and on nuclear disintegration. By bombarding beryllium with alpha particles, Chadwick discovered the neutron for which he received the Nobel Prize for Physics in 1935. He led the UK's work on the atomic bomb in WW II, and was knighted in 1945.*TIS

In 1935, Monopoly was first marketed by Charles Darrow, with the symbol of Rich Uncle Pennybags. He had invented the game on 7 Mar 1933. (See Note Below) A patent was issued for the game 31 Dec 1935, assigned to Parker Brothers, Inc.(No. 2,026,082). The patent described a "Board Game Apparatus... intended primarily to provide a game of barter, thus involving trading and bargaining" in which "much of the interest in the game lies in trading and in striking shrewd bargains." Illustrations showed the playing board, pieces, 22 "Title cards of the respective Real Estate holdings," Utilities, Chance and Community Chest cards, and scrip money. On the throw of the dice, the players may move onto Real Estate locations which may be acquired.*TIS
The history of the board game Monopoly can be traced back to the early 20th century. The earliest known design was by the American Elizabeth Magie created in 1903. A series of board games was developed from 1906 through the 1930s that involved the buying and selling of land and the development of that land. By 1934, a board game had been created much like the version of Monopoly sold by Parker Brothers and its parent companies through the rest of the 20th century, and into the 21st. Several people, mostly in the Midwestern United States and near the East Coast, contributed to the game's design and evolution.
By the 1970s, the idea that the game had been created solely by Charles Darrow had become popular folklore: it was printed in the game's instructions and even in the 1974 book The Monopoly Book: Strategy and Tactics of the World's Most Popular Game by Maxine Brady.*Wik

1956 Doug Ross Presents Gestalt Programming at the Western Joint Computer Conference in Los Angeles. Ross had experimented with the programming while working for the Air Force and Emerson Electric Co. *CHM

1975 Hungary issued a stamp commemorating the bicentenary (they were two days early) of the birth of Farkas Bolyai (1775–1856). [Scott #2347] *VFR

2015 A Mathematician wins an Oscar, FOR MATH. Robert Bridson, an adjunct professor in computer science at the University of British Columbia, was recognized for "early conceptualization of sparse-tiled voxel data structures and their application to modelling and simulation,".

BIRTHS

1816 Jean Frenet (7 Feb 1816 in Périgueux, France - 12 June 1900 in Périgueux, France) was a French mathematician best remembered for the Serret-Frenet formulas for a space-curve *SAU (Vector notation and linear algebra notation currently used to write these formulas was not yet in use at the time of their discovery.)

1824 Sir William Huggins (7 Feb 1824; 12 May 1910 at age 86) English astronomer who explored the spectra of stars, nebulae and comets to interpret their chemical composition, assisted by his wife Margaret Lindsay Murray. He was the first to demonstrate (1864) that whereas some nebulae are clusters of stars (with stellar spectral characteristics, ex. Andromeda), certain other nebulae are uniformly gaseous as shown by their pure emission spectra (ex. the great nebula in Orion). He made spectral observations of a nova (1866). He also was first to attempt to measure a star's radial velocity. He was one of the wealthy 19th century private astronomers that supported their own passion while making significant contributions. At age only 30, Huggins built his own observatory at Tulse Hill, outside London *TIS

1877 Godfrey Harold "G. H." Hardy FRS (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis.
He is usually known by those outside the field of mathematics for his essay from 1940 on the aesthetics of mathematics, A Mathematician's Apology, which is often considered one of the best insights into the mind of a working mathematician written for the layman.
Starting in 1914, he was the mentor of the Indian mathematician Srinivasa Ramanujan, a relationship that has become celebrated. Hardy almost immediately recognized Ramanujan's extraordinary albeit untutored brilliance, and Hardy and Ramanujan became close collaborators. In an interview by Paul Erdős, when Hardy was asked what his greatest contribution to mathematics was, Hardy unhesitatingly replied that it was the discovery of Ramanujan. He called their collaboration "the one romantic incident in my life."
Hardy preferred his work to be considered pure mathematics, perhaps because of his detestation of war and the military uses to which mathematics had been applied. He made several statements similar to that in his Apology:
"I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world."

However, aside from formulating the Hardy–Weinberg principle in population genetics, his famous work on integer partitions with his collaborator Ramanujan, known as the Hardy–Ramanujan asymptotic formula, has been widely applied in physics to find quantum partition functions of atomic nuclei (first used by Niels Bohr) and to derive thermodynamic functions of non-interacting Bose-Einstein systems. Though Hardy wanted his maths to be "pure" and devoid of any application, much of his work has found applications in other branches of science.*Wik

1883 Eric Temple Bell (7 Feb 1883; 21 Dec 1960 at age 77) Scottish-American mathematician and writer who contributed to analytic number theory (in which he found several inportant theorems), Diophantine analysis and numerical functions. In addition to about 250 papers on mathematical research, he also wrote for the layman in Men of Mathematics (1937) and Mathematics, Queen and Servant of Science (1951) among others. Under the name of John Taine, he also wrote science fiction. *TIS Although he was a well known mathematician in his day, he is best remembered for his popular Men of Mathematics. This book is hated by historians of mathematics for its exagerations and inaccuracies, but it is loved by high school students, and has motivated many mathematicians to become mathematicians. If you have not read it, do! *VF

1897 Maxwell Herman Alexander "Max" Newman, FRS (7 February 1897 – 22 February 1984) was a British mathematician and codebreaker. After WWII he continued to do research on combinatorial topology during a period when England was a major center of activity, notably Cambridge under the leadership of Christopher Zeeman. Newman made important contributions leading to an invitation to present his work at the 1962 International Congress of Mathematicians in Stockholm at the age of 65, and proved a Generalized Poincaré conjecture for topological manifolds in 1966. He died in Cambridge.*Wik

1898 Charles Wilderman Trigg,(Feb 7, 1898 Baltimore, Md; June 28, 1989 San Diego, Ca.) American engineer, mathematician and educator. Educated in engineering, mathematics and education at University of Pittsburgh, University of Southern California and University of California at Los Angeles. Worked as an industrial chemist and engineer, 1917-1943, and as an educator and administrator, 1946-1963. Served in the United States Navy during World War II. Book review editor of the Journal of Recreational Mathematics. Considered one of the foremost recreational mathematicians of the twentieth century. *U of Calgary Archives

1899 Hans Jenny (7 Feb 1899; 9 Jan 1992 at age 92) Swiss agricultural chemist and pedologist (soil scientist) who developed numerical functions to describe soil in terms of five interacting factors in his book Factors of Soil Formation (1941). These related Climate (temperature and moisture); Organisms (those living on the soil and in the soil, vegetation and animals, fungi algae and bacteria, decay of organic matter, humus); Relief (topography, and geomorphic landscape); Parent Material (bedrock or sediment type); and Time (ranging from 100's to 1000's of years while maturity or equilibrium of soil development is attained). He moved to the U.S. in 1926. After retirement, he studied the soil relationships in the unusual ecological community of the Pygmy Forest in California, known for its stunted and twisted confers. *TIS

1905 Lucien Alexandre Charles René de Possel (Feb 7, 1905– ?, 1974) was a French mathematician, one of the founders of the Bourbaki group, and later a pioneer computer scientist, working in particular on optical character recognition.
He had the conventional background for a member of Bourbaki: the École Normale Supérieure, agrégation, and then study in Germany. He left Bourbaki at an early stage: there was an obvious personal matter intruding between him and André Weil who had married De Possel's ex-wife Eveline following her divorce from De Possel in 1937.
De Possel published an early book on game theory in 1936 (Sur la théorie mathématique des jeux de hasard et de réflexion). His later research work in computer science at the Institut Blaise Pascal was in a position of relative isolation, as the subject strove for independence and to move away from the imposed role of service provider in the field of numerical analysis. *Wik

DEATHS

1736 Stephen Gray (December 1666 – 7 February 1736) was an English dyer and amateur astronomer, who was the first to systematically experiment with electrical conduction, rather than simple generation of static charges and investigations of the static phenomena.
Gray was born in Canterbury, Kent and after some basic schooling, he was apprenticed to his father (and later his elder brother) in the cloth-dyeing trade. His interests lay with natural science and particularly with astronomy, and he managed to educate himself in these developing disciplines, mainly through wealthy friends in the district who gave him access to their libraries and scientific instruments.
Stephen Gray produced a long series of experiments with electricity. In producing charge on a long glass tube, he discovered in 1729 that he could communicate the electrical effect to other objects by direct connection. Using string, he could charge an object over 50 feet from the rubbed tube, but oddly enough some other substances, such as silk thread, would not carry charge. Brass wire would transmit charge even better. These experiments with charged strings and glass tubes revealed the properties of conduction, insulation, and transmission. From these experiments came an understanding of the role played by conductors and insulators (names applied by John Desaguliers).
Despite the importance of his discoveries (it can be argued that he was the inventor of electrical communications) he received little credit at the time because of the factional dispute in the Royal Society, and the dominance of Newtonianism (which became the Masonic 'ideology'). By the time his discoveries were publicly recognised, experiments in electricity had moved rapidly on and his past discoveries tended to look trivial. For this reason, some historians tend to overlook his work.

There is no monument to Gray, and little recognition of what he achieved, against all odds, in his scientific discoveries. He is believed to be buried in a common grave in an old London cemetery, in an area reserved for pauper pensioners from the Charterhouse. *Wik *Yovisto
 In a famous experiment Stephen Gray demonstrated static electricity by charging a boy suspended by insulating strings in 1744 *Yovisto

1897 Galileo Ferraris (31 Oct 1847 - 7 Feb 1897 at age 49) Italian physicist who studied optics, acoustics and several fields of electrotechnics, but his most important discovery was the rotating magnetic field. He produced the field with two electromagnets in perpendicular planes, and each supplied with a current that was 90º out of phase. This could induce a current in a incorporated copper rotor, producing a motor powered by alternating current. He produced his first induction motor (with 4 poles) in May-Jun 1885. Its principles are now applied in the majority of today's a.c. motors, yet he refused to patent his invention, and preferred to place it at the service of everyone. *TIS

1948 Poul Heegaard (2 Nov 1871 in Copenhagen, Denmark - 7 Feb 1948 in Oslo, Norway) was a Danish mathematician who (with Max Dehn) was the first to classify compact surfaces.*SAU His 1898 thesis introduced a concept now called the Heegaard splitting of a 3-manifold. Heegaard's ideas allowed him to make a careful critique of work of Henri Poincaré. Poincaré had overlooked the possibility of the appearance of torsion in the homology groups of a space.
He later co-authored, with Max Dehn, a foundational article on combinatorial topology, in the form of an encyclopedia entry.
Heegaard studied mathematics at the University of Copenhagen, from 1889 to 1893 and following years of traveling, and teaching mathematics, he was appointed professor at University of Copenhagen in 1910.
Following a dispute with the faculty over, among other things, the hiring of Harald Bohr (The Brother of Niels Bohr, and Olmpic Soccer medalist) as professor at the University (Heegaard was against it); Heegaard accepted a professorship at Oslo in Norway, where he worked till his retirement in 1941.*Wik

1969 Hans Rademacher (3 April 1892 in Wandsbeck (part of Hamburg), Schleswig-Holstein, Germany - 7 Feb 1969 in Haverford, Pennsylvania, USA) It was philosophy that he intended to take as his main university subject when he entered the university of Göttingen in 1911, but he was persuaded to study mathematics by Courant after having enjoyed the excellent mathematics teaching of Hecke and Weyl. He is remembered for the system of orthogonal functions (now known as Rademacher functions) which he introduced in a paper published in 1922. Berndt writes "Since its discovery, Rademacher's orthonormal system has been utilised in many instances in several areas of analysis." Rademacher's early arithmetical work dealt with applications of Brun's sieve method and with the Goldbach problem in algebraic number fields. About 1928 he began research on the topics for which he is best known among mathematicians today, namely his work in connection with questions concerning modular forms and analytic number theory. Perhaps his most famous result, obtained in 1936 when he was in the United States, is his proof of the asymptotic formula for the growth of the partition function (the number of representations of a number as a sum of natural numbers). This answered questions of Leibniz and Euler and followed results obtained by Hardy and Ramanujan. Rademacher also wrote important papers on Dedekind sums and investigated many problems relating to algebraic number fields. *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 & Campbell