Sunday 11 September 2011

On This Day in Math - Sep 11

We have already considered with disfavour the possibility of the universe having been planned by a biologist or an engineer; from the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician.
~Sir James Jeans

The 254th day of the year; 254 is the maximum number of pieces a flat pizza could be cut into with n straight lines.... find n. (for help, see bottom of this post, a good quadratic problem)

1789 Alexander Hamilton appointed the first secretry of the U.S. Treasury. It is because of him that we did not adopt the English system of counting money, but a decimal system instead. *VFR

1820 André Marie AMPÈRE (1775-1836) was professor of mathematics at the École Polytechnique from 1809. On 11 September 1820 he heard of H. C. Ørsted's discovery that a magnetic needle is acted on by a voltaic current. Only a week later, on 18 September, Ampère presented a paper to the Academy containing a much more complete exposition of that and kindred phenomena. On the same day, Ampère also demonstrated before the Academy that parallel wires carrying currents attract or repel each other, depending on whether currents are in the same (attraction) or in opposite directions (repulsion). This laid the foundation of electrodynamics.*Wik

In 1822, it was announced by the College of Cardinals that henceforth "the printing and publication of works treating of the motion of the earth and the stability of the sun, in accordance with the opinion of modern astronomers, is permitted." When two weeks pope Pius VII ratified the Cardinals' decree, the Catholic Church finally officially accepted the Copernican principle that on 22 Jun 1633 Italian scientist Galileo had been imprisoned for championing. It was not until 1835 that the Vatican removed Galileo's Dialogue Concerning the Two Chief World Systems from its list of banned books. Finally 31 Oct 1992, the Catholic Church admitted that Galileo had been correct. *TIS

In 1831, Charles Darwin and Captain Robert Fitzroy travelled from London to Plymouth to inspect the Beagle. This was Darwin's first sight of the ship on which he would sail on a voyage of discovery leading to his famous theory of evolution. *TIS

1831 After a four hour disputation in Latin, Jacobi was appointed professor at the University of K¨onigsburg. While there he inaugurated what was then a complete novelty in mathematics— research seminars—assembling the more advanced students and interested colleagues. [DSB 7, 50] *VFR

1893 Edgeworth sends greetings to Karl Pearson, "I hope that you flourish in Probabilities." *The History of Statistics: The Measurement of Uncertainty Before 1900
By Stephen M. Stigle
1940 The first remote computation -- from Dartmouth College to AT&T Bell Laboratories -- is demonstrated during a meeting of the American Mathematical Association. At Dartmouth, George Stibitz​ set up a terminal that allowed attendees to perform remote calculation by telegraph wire with the Complex Calculator in New York City. *CHM

1981 NBC Magazine broadcasts a story about Rubik's cube on TV. The cube had begun production in 1977 in Hungary and after a couple of years began to sweep across Europe. In 1981, the rage hit the US. In November of 1981, the US would hold 1st American Rubik's Cube Championships. *Mark Longridge, A Rubik's Cube Chronology
In 1997, the Mars Global Surveyor, launched in Nov 1996, went into an elliptical orbit around Mars. To drop into a lower orbit the original mission plan was to use a braking effect by dipping into the upper Martian atmosphere. The lower orbit was a better position for mapping purposes. However, the aerobraking method originally planned was suspended for several weeks to give engineers time to develop more gentle manoeuvers to protect the craft when a solar array failed to deploy correctly, and was flexing excessively. It was to spend two years mapping the surface of Mars. *TIS

1623 Stephano Angeli was an Italian mathematician who worked on infinitesimals and used them to study spirals, parabolas and hyperbolas.(James)Gregory studied with Angeli in Padua from 1664 to 1668 and learnt from him about series expansions of functions. *SAU

1798 Franz Ernst Neumann born. He formulated the law of electromagnetic induction
1847 Mary Watson Whitney (11 Sep 1847; 20 Jan 1921) American astronomer who trained with Maria Mitchell and succeeded her as professor and director of the Vassar College Observatory. As Mitchell had before her, Whitney championed science education the advancement of professional opportunities for women. She developed the astronomy department. Four years before her 1910 retirement, there were 160 students and eight different astronomy courses, including some of the first courses anywhere on astrophysics and on variable stars. During her tenure as director, the Observatory staff published 102 papers in major astronomical journals reporting their work on comets, asteroids, and variable stars. From 1896, photographic plates were used to study and measure star clusters.*TIS

1877 Sir James Hopwood Jeans (11 Sep 1877; 16 Sep 1946) was an English physicist, astronomer, and mathematician who was the first to propose that matter is continuously created throughout the universe. He made other innovations in astronomical theory but is perhaps best known as a writer of popular books about astronomy. Died in Dorking, Surrey.*TIS

1884 Harvey Fletcher (11 Sep 1884; 23 Jul 1981) American acoustical engineer who was the first to demonstrate stereophonic sound (1934). He was a trail blazing investigator of the nature of speech and hearing, noted for his contributions in acoustics, electrical engineering, speech, medicine, music, atomic physics, sound pictures, and education. He guided the development of the Western Electric Hearing Aid, the first such device to use vacuum tubes. He developed a group survey method using recorded sound of decreasing volume which has wide acceptance in schools throughout the nation.*TIS

1890 Euphemia Lofton Haynes (September 11, 1890 - July 25, 1980) After graduating from Washington D.C. Miner Normal School with distinction, she went on to earn an undergraduate mathematics major (and psychology minor) from Smith College in 1914. In 1917 she married Harold Appo Haynes.
Haynes pursued graduate studies in mathematics and education at the University of Chicago, earning a masters degree in education in 1930. She continued her graduate work in mathematics at the Catholic University of America where in 1943 she became the first African-American woman to earn a Ph.D. in mathematics. Her dissertation on "The Determination of Sets of Independent Conditions Characterizing Certain Special Cases of Symmetric Correspondences" was written under the supervision of Professor Aubrey Landrey.
Euphemia Haynes devoted her life to education in the Washington, D.C. area for forty-seven years, including teaching mathematics at Armstrong High School and Dunbar High School. She became a professor of mathematics at Miner Teachers College in 1930 where she established the mathematics department and served as chair of the Division of Mathematics and Business Education (in 1955 Minor Teachers College and Wilson Teachers College united to form the District of Columbia Teachers College.) From July 1966 to July 1967, Haynes served as the first woman to chair the District of Columbia School Board. She played a central role in the integration of the DC public schools. Upon her death, she left $700,000 to the Catholic University of America which was used to establish the Euphemia Lofton Haynes Chair in the Department of Education and to support a student loan fund in the School of Education. *ASC
1917 Kenkichi Iwasawa (September 11, 1917 – October 26, 1998) was a Japanese mathematician who is known for his influence on algebraic number theory.*Wik

1768 Joseph-Nicolas Delisle (4 Apr 1688, 11 Sep 1768) French astronomer who proposed that the series of coloured rings sometimes observed around the Sun is caused by diffraction of sunlight through water droplets in a cloud. He also worked to find the distance of the Sun from the Earth by observing transits of Venus and Mercury across the face of the Sun.*TIS

1843 Joseph Nicolas Nicollet (24 Jul 1786, 11 Sep 1843) Joseph Nicolas Nicollet was a French mathematician, explorer, and cartographer with an interest in astronomy. He was born in France, but financially ruined by the 1830 Revolution, he left for the U.S. in 1831. He made a private survey of the Mississippi region (1836-7), the results of which he presented in Washington. In 1838, he led a surveying expedition for the U.S. government party mapping out the lakes and waterways of northcentral Minnesota. He stressed to map publishers the importance of elevation marks on published maps. His maps were considered among the most accurate and useful until the surveyors for the great logging companies arrived in Minnesota's vast pine forests.*TIS

1861 Johann Martin Zacharias Dase​ (June 23, 1824, September 11, 1861) was a German mental calculator. He attended schools in Hamburg from a very early age, but later admitted that his instruction had little influence on him. He used to spend a lot of time playing dominoes, and suggested that this played a significant role in developing his calculating skills. Dase suffered from epilepsy from early childhood throughout his life.
At age 15 he began to travel extensively, giving exhibitions in Germany, Austria and England. Among his most impressive feats, he multiplied 79532853 × 93758479 in 54 seconds. He multiplied two 20-digit numbers in 6 minutes; two 40-digit numbers in 40 minutes; and two 100-digit numbers in 8 hours 45 minutes. The famous mathematician Carl Friedrich Gauss commented that someone skilled in calculation could have done the 100-digit calculation in about half that time with pencil and paper. In 1844, Dase calculated π to 200 decimal places in his head, a record for the time, from the Machin-like formula:
\frac{\pi}{4} = \arctan \frac{1}{2} + \arctan \frac{1}{5} + \arctan \frac{1}{8}.
He also calculated a 7-digit logarithm table and extended a table of integer factorizations from 7,000,000 to 10,000,000.
Dase had very little knowledge of mathematical theory. The mathematician Julius Petersen tried to teach him some of Euclid's theorems, but gave up the task once he realized that their comprehension was beyond Dase's capabilities. Gauss however was very impressed with his calculating skill, and he recommended that the Hamburg Academy of Sciences should allow Dase to do mathematical work on a full-time basis, but Dase died shortly thereafter.
The book "Gödel, Escher, Bach" by Douglas Hofstadter mentions his calculating abilities. "... he also had an uncanny sense of quantity. That is, he could just 'tell', without counting, how many sheep were in a field, or words in a sentence, and so forth, up to about 30."*Wik

1890 Felice Casorati (17 Dec 1835, 11 Sept 1890). He is best remembered for the Casorati-Weierstrass theorem characterising the behaviour of a function near an essential singularity.*SAU

1943 Oswald Teichmüller (18 June 1913, 11 Sept 1943) His main contribution is in the area of geometric function theory.*SAU

1972 Johannes de Groot (7 May 1914 , 11 Sept 1972) De Groot worked in topology and group theory. In group theory one of the topics he studied was that of groups with only trivial automorphisms. Later de Groot worked on set-theoretic topology. He introduced the concept of co-compactness and other topological concepts. *SAU

1989 Colossus' Team Member Chandler died. W.W. Chandler was born in Bridport, England. He obtained his B.Sc. from London University in 1938 by private study while working as a telephone engineer at the British Post Office Research Department. During the war he was responsible for the installation and maintenance of the Colossus at Bletchley Park. The Colossus represented the first electronic computer, however it was programmed by a mechanical switchboard. Its was used to crack the German Fish codes which guarded the highest levels of German communication. Winston Churchill characterized the Bletchley Park team as the geese who laid the golden eggs but never cackled.
After the war Chandler participated in development and installation of the MOSAIC computer and worked on optical character recognition. He died on September 11, 1989. *CHM
The maximum number p of pieces that can be created with a given number of cuts n, where n ≥ 0, is given by the formula
 p = \frac{n^2+n+2}{2}.
Using binomial coefficients, the formula can be expressed as
p = {\tbinom {n + 1} 2} + 1 = {\tbinom n 2}+{\tbinom n 1}+{\tbinom n 0}.

*ASC = Agnes Scott College, Biographies of Women Mathematicians
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum

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