Tuesday 20 December 2022

On This Day in Math - December 20


Our passion for learning is our tool for survival.
Somewhere, something incredible is waiting to be known.
~Carl Sagan

The 354th day of the year; 354 is the sum of the first four fourth powers 
and is also the sum of three distinct primes. (It is also the solution to one version of an unsolved recreational math problem called the Postage Stamp Problem, or sometimes Frobenius problem)

354 is the smallest number whose sum of its distinct prime factors is a cube, 2 + 3 + 59 = 64

 Of all the Primes less than 10^10, the largest difference between two consecutive primes is 354. *Derek Orr


1587 In Viviani's biography of Galileo he tells of how as a young student of 18 in 1581 Galileo made his first discovery about pendulums which would later lead to his design just before his death of a pendulum clock.
"one afternoon performing his devotions in the Cathedral of Pisa, and in full view of Maestro Possenti's beautiful bronze lamp which hung (and still hangs) from the roof of the nave. In order to light it more easily the attendant drew it towards him, and then let it swing back. Galileo at first observed this simple incident, as thousands of other worshipers had done before him and have done since, i.e. in a casual way, but quickly his attention became riveted to the swinging lamp. The oscillations, which were at first considerable became gradually less and less, but, notwithstanding, he could see that they were all performed in the same time, as he was able to prove by timing them with his pulse the only watch he possessed!"
It is a beautiful story of a brilliant young mind who would go on to greatness, but J. J. FAHIE in his biography of Galileo points out:
"Whether this be only a pretty fable, like that of Newton and the apple, cannot now be decided, but it is, at least, certain that Possenti's lamp was not the one which Galileo observed, since it was not made until 1587, and was only hung in its present place on the 2Oth December in that year."

1623 Wilhelm Schickard, in a letter to Kepler, described his calculating machine. *Dauben, A Selective Bibliography, p. 251
Only 3 documents about this machine have been found till now—two letters from Schickard to Kepler, and a sketch of the machine with instructions to the mechanician. I have also seen the date given as  February 25th, 1624, which may be more accurate.  *http://history-computer.com

1883 On the night before J J Sylvester's departure from Johns Hopkins his friends hosted a gala in his honor at Hopkins Hall.

In 1900, Michel Giacobini in France discovered a comet, which was rediscovered by a German, Ernst Zinner, on 23 Oct 1913, and since named the Giacobini-Zinner comet. It returns to the vicinity of the earth every six and two-thirds years. This comet became the first to be visited by a spacecraft. On 11 Sep 1985, the International Cometary Explorer (ICE) flew through its gas tail, 7,800-km downstream from the nucleus, at a speed of 21 km/sec. The nucleus was estimated to be 2.5-km across at its widest diameter. Instruments detected carbon monosulfide and hydroxyl molecules in the comet. The comet is the progenitor of the Draconid meteor shower, visible annually in early October, which produced intense meteor displays in 1933 and 1946.*TIS The most recent was on shower peaked on Oct 8, 2011.

1906 Nature publishes a letter from Francis Galton on "Cutting a round cake on scientific principles." A Numberphile video by Alex Bellos explaining the method is here.

In 1907, the first U.S. scientist to receive the Nobel Prize was Albert Michelson, a German-born ( actually born in Strzelno, Provinz Posen in the Kingdom of Prussia which is now part of Poland) American physicist who received the Nobel Prize for Physics "for his optical precision instruments and the spectroscopic and metrological investigations." He designed the highly accurate Michelson interferometer and used it to accurately measure the speed of light and establish it as a fundamental constant. With Edward Morley, he also used it in an attempt to measure the velocity of the earth through the ether (1887), yielding null results that eventually led Einstein to his theory of relativity. He measured the standard meter bar in Paris to be 1,553,163.5 wavelengths of the red cadmium line (1892-3) *TIS

1910 New Zealand born physicist Ernest Rutherford made his seminal gold foil experiment which led to first insight about the nature of the inner structure of the atom and to the postulation of Rutherford's concept of the "nucleus. He had already received the 1908 Nobel Prize in Chemistry for demonstrating that radioactivity was the spontaneous disintegration of atoms. *Yovista

1943 Norman Bel Geddes to Designs ASSC Machine Cover:
Thomas Watson Jr. informs Harvard University President James B. Conant that Norman Bel Geddes would be designing the cover of the Harvard Mark I computer. Bel Geddes was an American industrial designer who also worked on such things as Philco radio cabinets and a Graham Page car. He was deeply interested in the future, illustrating a book in 1932 that described, among other things, a huge passenger airplane with public lounges and an exercise center. Bel Geddes also desgined the GM pavilion at the 1939 World's Fair.*CHM

1949 N. J. Woodland and Bernard Silver filed a patent application for "Classifying Apparatus and Method", in which they described both the linear and bullseye printing patterns, as well as the mechanical and electronic systems needed to read the code. The patent was issued on 7 October 1952 as US Patent 2,612,994. In 1951, Woodland moved to IBM and continually tried to interest IBM in developing the system. The company eventually commissioned a report on the idea, which concluded that it was both feasible and interesting, but that processing the resulting information would require equipment that was some time off in the future.
In 1952 Philco purchased their patent, and then sold it to RCA the same year.*Wik

In 1951, at 1:50 p.m., the first electricity ever generated by atomic power began flowing from the EBR-1 turbine generator when Walter Zinn and his Argonne National Laboratory staff of scientists brought EBR-1 to criticality (a controlled, self-sustaining chain reaction) with a core about the size of a football. The reactor was started up and the power gradually increased over several hours. The next day, Experimental Breeder Reactor-1 generated enough electricity to supply all the power for its own building. Additional power and core experiments were then conducted until its decommissioning in Dec 1963. Construction began in 1949, between Idaho Falls and Arco, Idaho. Today, EBR-1 is a Registered National Historic Landmark.*TIS


1494 Oronce Fine (20 Dec 1494 in Briançon, France
- 8 Aug 1555 in Paris, France) was a French mathematician who published a major work on mathematics and astronomy. Before being awarded his medical degree, Fine had edited mathematics and astronomy books for a Paris printer. Among the texts which he edited were Peurbach's Theoricae Novae Planetarum, which presented Ptolemy's epicycle theory of the planets, and Sacrobosco's Tractatus de Sphaera, a book on astronomy in four chapters. The first book which Fine authored himself was published in 1526 and it was on the equatorium, an instrument which Fine was very interested in and which he worked on throughout his life, writing four further texts about it. The instrument can be used to determine the positions of the planets.*SAU

1648 Thommaso Ceva (20 Dec 1648; 3 Feb 1737) Italian mathematician, poet, and brother of the mathematician Giovanni Ceva. At the age of fifteen he entered the Society of Jesus. His education was entirely within the Jesuit Order and he obtained a degree in theology. His first scientific work, De natura gravium (1669), dealt with physical subjects, such as gravity and free fall, in a philosophical way. Tommaso Ceva's mathematical work is summed up in Opuscula Mathematica (1699) which examines geometry (geometric-harmonic means, the cycloid, and conic sections), gravity and arithmetic. He also designed an instrument to divide a right angle into a given number of equal parts. He gave the greater part of his time to writing Latin prose. His poem Jesus Puer was translated into many languages. *TIS

1838 Edwin Abbott Abbott (20 Dec 1838, 12 Oct 1926) His most famous work was Flatland: a romance of many dimensions (1884) which Abbott wrote under the pseudonym of A Square. The book has seen many editions, the sixth edition of 1953 being reprinted by Princeton University Press in 1991 with an introduction by Thomas Banchoff​. Flatland is an account of the adventures of A Square in Lineland and Spaceland. In it Abbott tries to popularise the notion of multidimensional geometry but the book is also a clever satire on the social, moral, and religious values of the period.
More recently, in 2002, an annotated version of Flatland has been produced with an introduction and notes by Ian Stewart who gives extensive discussion of mathematical topics related to passages in Abbott's text. *SAU
The Kindle edition of Flatland is available for less than $2.00 Flatland: A Romance of Many Dimensions [Illustrated] and the Stewart version is only a little more:

In a bold statement of personal opinion I add: This book should be read by every teacher and every student of mathematics.

1843 Paul Tannery (20 Dec 1843 in Mantes-la-Jolie, Yvelines, France - 27 Nov 1904 in Pantin, Seine-St Denis, France) His main contributions were to the history of Greek mathematics and to the philosophy of mathematics. He published a history of Greek science in 1887, a history of Greek geometry in the same year, and a history of ancient astronomy in 1893.
Tannery did work of great importance as an editor of famous mathematics texts. He edited the work of Fermat in three volumes (jointly with C Henry) between 1891 and 1896. In addition he edited the work of Diophantus in two volumes (1893-95). He was an editor of the twelve volume complete works of Descartes Oeuvres de Descartes (1897-1913).
Tannery became so skilled in using Greek numerals in his historical work that he believed that they had certain advantages over our present system. *SAU

1875 Francesco Cantelli (20 Dec 1875 in Palermo, Sicily, Italy
- 21 July 1966 in Rome, Italy)Cantelli's work in astronomy involved statistical analysis of data and his interests turned more towards the statistical style of mathematics and to applications of probability to astronomy and other areas. In particular he became interested in actuarial and social applications of probability theory. In 1903 took a job as an actuary at the Istituti di Previdenza where he undertook research into probability theory publishing some important papers, some which we mention below. He founded the Istituto Italiano degli Attuari for the applications of mathematics and probability to economics. He edited the journal of the Institute Giornale dell'Istituto Italiano degli Attuari from 1930 to 1958 during which time it became one of the leading journals in its field. *SAU

1876 Walter (Sydney) Adams (20 Dec 1876; 11 May 1956) was an American astronomer who is best known for his spectroscopic studies of sunspots, the rotation of the Sun, the velocities and distances of thousands of stars, and planetary atmospheres. He found (with Arnold Kohlschütter) that the relative intensities of stallar spectral lines depend on the absolute luminosities of the star, which in turn provides a spectroscopic method of determining stellar distances.By this method, he measured distances to hundreds of giant and main sequence stars. Adams identified Sirius B as the first white dwarf star known, and his measurement of its gravitational redshift was confirming evidence for the general theory of relativity. He was director of Mount Wilson (1923-46).*TIS

1901 Robert Jemison Van de Graaff (20 Dec 1901; 16 Jan 1967) American physicist and inventor of the Van de Graaff generator, a type of high-voltage electrostatic generator that can be used as a particle accelerator in atomic research. The potential differences achieved in modern Van de Graaff generators can be up to 5 MV. It is a principle of electric fields that charges on a surface can leap off at points where the curvature is great, that is, where the radius is small. Thus, a dome of great radius will inhibit the electric discharge and added charge can reach a high voltage. This generator has been used in medical (such as high-energy X-ray production) and industrial applications (sterilization of food). In the 1950s, Van de Graaff invented the insulating core transformer able to produce high voltage direct current.*TIS

1911 Grote Reber was born in Chicago on (b.12/22, 1911 .... d.12/20/2002). He was a ham radio operator, studied radio engineering, and worked for various radio manufacturers in Chicago from 1933 to 1947.
He learned about Karl Jansky’s discovery (1932) of radio waves from the Galaxy (i.e., the Milky Way), and wanted to follow up this discovery and learn more about cosmic radio waves. Were the waves coming only from the Milky Way, or from other celestial objects? What process produces the radio waves?
In the 1930s Reber applied for jobs with Karl Jansky at Bell Labs and with astronomical observatories to study cosmic radio waves, but none of them were hiring at the time, since it was in the middle of the great depression. Reber decided to study radio astronomy on his own.

A telescope was constructed by Grote Reber in 1937 in his back yard in Wheaton, Illinois (a suburb of Chicago). He built the telescope at his own expense while working full time for a radio company in Chicago.
The mirror, made of sheet metal 31.4 feet in diameter, focuses radio waves to a point 20 feet above the dish. The cylinder contains the radio receiver which amplifies the faint cosmic signals by a factor of many million, making them strong enough to be recorded on a chart. The wooden tower at the left is used for access to the receiver.
Reber built a parabolic dish reflector because this shape focuses waves to the same focus for all wavelengths. This principle had been used for a long time by astronomers for design of optical telescopes, to avoid chromatic aberration. Reber knew that it would be important to observe a wide range of wavelengths of radiation from the sky in order to understand how the radiation was being produced. A parabolic reflector is usable over a wide wavelength range.
Reber surveyed the radio radiation from the sky and presented the data as contour maps showing that the brightest areas correspond to the Milky Way. The brightest part is toward the center of the Milky Way galaxy in the south. Other bright radio sources, such as the ones in Cygnus and Cassiopeia, were recognized for the first time.
Grote Reber donated his telescope to NRAO at Green Bank, WV, and supervised its assembly there in the early 1960s. It remains there as a historical monument. It was put on a turntable allowing it to point in any direction. This picture was taken in the late 1970’s after the telescope was painted red, white, and blue for the US bicentennial.
Reber visited NRAO in Green Bank on many occasions.  While he was supervising the assembly of his telescope, he also supervised the construction of a full scale reproduction of the Jansky antenna.
In the 1950s, Reber sought a field that seemed neglected by most other researchers and turned his attention to cosmic radio waves at very low frequencies (1-2 MHz, or wavelength 150-300 meters). Waves of these frequencies cannot penetrate the Earth’s ionosphere except in certain parts of the Earth at times of low solar activity. One such place is Tasmania, where Reber lived for many years. He died in Tasmania on December 20, 2002.
*Greenbank Observatory
The Grote Reber telescope as originally constructed in Wheaton, Illinois. (NSF/AUI)


1836 Johann Christian Martin Bartels​ (12 August 1769 – 7/20 December 1836) was a German mathematician. He was the tutor of Carl Friedrich Gauss in Brunswick and the educator of Lobachevsky at the University of Kazan.*Wik

1891 George Bassett Clark (14 Feb 1827, 20 Dec 1891) Elder son in the American family of telescope makers and astronomers, Alvan Clark & Sons of Cambridge, Mass., who figured importantly in the great expansion of astronomical facilities which occurred during the second half of the 19th century. Before the family business began, George made a telescope in 1844 out of the melted-down brass of his school's broken dinner bell. His father, Alvan Clark, was at the time an established portrait painter, but his son's interest also spurred his father to begin making refractor telescopes. (Refractor telescopes use paired lenses to focus light.) The father taught himself to be a master optician, and eventually in business with his sons made the finest refractor telescopes of their time including five of the world's largest.*TIS

1962 Emil Artin (3 Mar 1898; 20 Dec 1962 at age 64) Austro-German mathematician who worked in algebraic number theory, made a major contribution to field theory, and stated a law of reciprocity which included all previously known laws of reciprocity (1927). He also worked on the theory of braids (1925), and on rings with the minimum condition on right ideals, now called Artinian rings (1944). Artin has the distinction of solving (1927) one of the famous 23 problems previously posed by Hilbert in 1900. With his Jewish wife, he left Nazi Germany in 1937, and worked at universities in the U.S. until 1956, when he returned to his home country. *TIS He solved Hilbert’s seventeenth problem in 1927. *VFR (Can a multivariate polynomial that only has non-negative values over the reals be represented as a sum of squares of rational functions? Artin proved it could, An algorithm to do so was found by Charles Delzell.)

1984 Max Deuring (9 December 1907, Göttingen, Germany – 20 December 1984, Göttingen, Germany) was a mathematician. He is known for his work in arithmetic geometry, in particular on elliptic curves in characteristic p. He worked also in analytic number theory.
Deuring graduated from the University of Göttingen in 1930, then began working with Emmy Noether, who noted his mathematical acumen even as an undergraduate. When she was forced to leave Germany in 1933, she urged that the university offer her position to Deuring. In 1935 he published a report entitled Algebren ("Algebras"), which established his notability in the world of mathematics. He went on to serve as Ordinarius at Marburg and Hamburg, then took a position as ordentlicher Lehrstuhl at Göttingen, where he remained until his retirement.*Wik

1988 Elizabeth Scott (November 23, 1917 – December 20, 1988) was an American mathematician specializing in statistics.
Scott was born in Fort Sill, Oklahoma. Her family moved to Berkeley, California when she was 4 years old. She attended the University of California, Berkeley where she studied mathematics and astronomy. There were few options for further study in astronomy, as the field was largely closed to women at the time, so she completed her graduate studies in mathematics. She received her Ph.D. in 1949, and received a permanent position in the Department of Mathematics at Berkeley in 1951.
She wrote over 30 papers on astronomy and 30 on weather modification research analysis, incorporating and expanding the use of statistical analyses in these fields. She also used statistics to promote equal opportunities and equal pay for female academics.
In 1957 Elizabeth Scott noted a bias in the observation of galaxy clusters. She noticed that for an observer to find a very distant cluster, it must contain brighter than normal galaxies and must also contain a large number of galaxies. She proposed a correction formula to adjust for (what came to be known as) the "Scott effect".
The Committee of Presidents of Statistical Societies awards a prize in her honour to female statisticians.*Wik

1993 W(illiam) Edwards Deming (14 Oct 1900, 20 Dec 1993) was an American statistician, the father of "Total Quality Management." After WW II, he contributed to Japan's economic recovery by recommending statistical methods of quality control in industrial production. His method embraced carefully tallying product defects, examining their causes, correcting the problems, and then tracking the results of these changes on subsequent product quality. In his career before the war, he had developed statistical sampling techniques that were first used in the 1940 U.S. census. From the 1980's in the U.S. Deming continued to teach quality control through the statistical control of manufacturing processes for companies such as Ford, Xerox, and GM.*TIS

1996 Carl Edward Sagan 9 Nov 1934, 20 Dec 1996) U.S. astronomer and exobiologist and writer of popular science books. His studies were far-ranging. He coauthored a scientific paper about the dangers of nuclear winter. He researched the atmosphere of Venus, seasonal changes on Mars, surface conditions on planets, and created popular interest in the universe with his television series Cosmos. Sagan was a leading figure in the search for extraterrestrial intelligence. He urged the scientific community to listen with large radio telescopes for signals from intelligent extraterrestrial lifeforms. Sagan also played a prominent role in the U.S. space program, with his involvement in the Mariner, Viking, and Voyager spacecraft expeditions. *TIS  (and may I remind you all, in Carl's honor, that "we are all star-stuff."

2002 Grote Reber (22 Dec 1911, 20 Dec 2002) U.S. amateur astronomer and radio engineer who self-financed and built the first radio telescope. He pioneered the new field of radio astronomy, and was the first to systematically study the sky by observing non-visible radiation. After reading about Jansky's discovery (1932) of natural radio emissions from space, Reber constructed a 9-meter dish antenna in his back yard and built three different detectors before finding 160 MHz signals (1939). In 1940 and 1944 he published articles titled Cosmic Static in the Astrophysical Journal. He was the first to express received radio signals in terms of flux density and brightness, first to find evidence that galactic radiation is non-thermal, and first to produce radio maps of the sky (1941).*TIS

2005  Raoul Bott,(September 24, 1923 – December 20, 2005) was a Hungarian mathematician known for numerous basic contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem. *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

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