Saturday, 19 December 2020

On This Day in Math - December 19


Nine Point Circle

If equations are trains threading the landscape of numbers,
then no train stops at pi.
~Richard Preston

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

On 19th December 1705 the demonstrator of experiments at the Royal Society turned the crank on the apparatus, that he had constructed especially for this demonstration, setting an evacuated glass globe in rotation against which he pressed a woollen cloth. There was “quickly produced a beautiful Phaenomenon, viz, a fine purple light and vivid to that degree, that all the included Apparatus was easily and distinctly discernable by the help of it.” *Renaissance Mathematicus

1765 Joseph Priestley, visiting in London, is introduced to Benjamin Franklin, and other members of the "Honest Whigs" by John Canton in a popular coffee house in the shadow of St Pauls cathedral. Priestly had presented himself to Canton with a letter of introduction from Priestley's friend and rector at Warrington Academy that read, "You will find a benevolent, sensible man, with a considerable sense of learning. If Dr. Franklin be in Town,I believe Dr. Priestley would be glad to be made known of him." Before the night was over, Priestly had acquired their support for a book about their mutual efforts in the discovery of electricity. In 1767, the 700-page The History and Present State of Electricity was published to positive reviews. The first half of the text is a history of the study of electricity to 1766; the second and more influential half is a description of contemporary theories about electricity and suggestions for future research. Priestley reported some of his own discoveries in the second section. *Stephen Johnson, The Invention of Air

1894 Karl Pearson introduced the Pearson family of densities. [Springer’s 1985 Statistics Calendar] *VFR

1894 Karl Pearson first uses the term "Binomial Distribution" in Contributions to the Mathematical Theory of Evolution---II. Skew Variation in Homogeneous Material, Received by the Royal Society of London December 19, 1894, It would be read on January 24, 1895,” Philosophical Transactions of the Royal Society of London for the year MDCCCXCV. A footnote has: “This result seems of considerable importance, and I do not believe it has yet been noticed. It gives the mean square error for any binomial distribution, and we see that for most practical purposes it is identical with the value npq , hitherto deduced as an approximate result, by assuming the binomial to be approximately a normal curve.” Jeff Miller, Earliest Known Uses of Some of the Words of Mathematics

1908 Scientific American offered a $500 prize for a simple explanation of the fourth dimension. They were surprised to receive a huge number of serious responses from around the globe. Many mentioned Charles Hinton, who was popularizing the idea of four-space (he invented the term tesseract, and the baseball pitching machine) but not one associated the fourth dimension with time, and none mentioned Einstein or his work.
* By Michio Kaku , Hyperspace: a scientific odyssey through parallel universes, time warps, and ... pg 75

In 1958, the first known radio broadcast from outer space was transmitted. President Eisenhower's voice issued a Christmas greeting from a pre-recorded tape on a recorder aboard an orbiting space satellite. His full message was, "This is the President of the United States speaking. Through the marvels of scientific advance, my voice is coming to you from a satellite circling in outer space. My message is a simple one. Through this unique means I convey to you and all mankind America's wish for peace on earth and good will to men everywhere." The broadcast came from the first experimental satellite, Project SCORE, which had been launched two days earlier. The battery-operated 132 MHz all vacuum tubes transmitter had an 8-W output.*TIS

In 1974, the pioneering Altair 8800 microcomputer was first put on sale in the U.S. as a do-it-yourself computer kit, for $397. It used switches for input and flashing lights as a display. Ed Roberts founded Micro Instrumentation and Telemetry Systems (MITS) to market his product that used the 8800 microprocessor. The demand for the $395.00 machine exceeded the manufacturer's wildest expectations. The Altair 8800 was featured on the cover of the Jan 1975 issue of Popular Electronics. The first commercially successful personal computer, the Commodore PET, which integrated a keyboard and monitor in its case, came out in early 1977. The Apple II followed later that year. *TIS


1615 Sir Charles Scarborough MP FRS FRCP (19 December 1615 – 26 February 1693) was an English physician and mathematician.
He was born in St. Martin's-in-the-Fields, London in 1615, the son of Edmund Scarburgh, and was sent to St. Paul's School, whence he proceeded to Caius College, Cambridge, and educated at St Paul's School, Gonville and Caius College, Cambridge (BA, 1637, MA, 1640) and Merton College, Oxford (MD, 1646). While at Oxford he was a student of William Harvey, and the two would become close friends. Scarborough was also tutor to Christopher Wren, who was for a time his assistant.
Following the Restoration in 1660, Scarborough was appointed physician to Charles II, who knighted him in 1669; Scarborough attended the king on his deathbed, and was later physician to James II and William and Mary. During the reign of James II, Scarborough served (from 1685 to 1687) as Member of Parliament for Camelford in Cornwall.
Scarborough was an original fellow of the Royal Society and a fellow of the Royal College of Physicians, author of a treatise on anatomy, Syllabus Musculorum, which was used for many years as a textbook, and a translator and commentator of the first six books of Euclid's Elements (published in 1705). He also was the subject of a poem by Abraham Cowley, An Ode to Dr Scarborough.
Scarborough died in London in 1693. He was buried at Cranford, Middlesex, where there is a monument to him in the parish church erected by his widow. *Wik

1714 John Winthrop (December 19, 1714 – May 3, 1779) was the 2nd Hollis Professor of Mathematics and Natural Philosophy in Harvard College. He was a distinguished mathematician, physicist and astronomer, born in Boston, Mass. His great-great-grandfather, also named John Winthrop, was founder of the Massachusetts Bay Colony. He graduated in 1732 from Harvard, where, from 1738 until his death he served as professor of mathematics and natural philosophy. Professor Winthrop was one of the foremost men of science in America during the 18th century, and his impact on its early advance in New England was particularly significant. Both Benjamin Franklin and Benjamin Thompson (Count Rumford) probably owed much of their early interest in scientific research to his influence. He also had a decisive influence in the early philosophical education of John Adams, during the latter's time at Harvard. He corresponded regularly with the Royal Society in London—as such, one of the first American intellectuals of his time to be taken seriously in Europe. He was noted for attempting to explain the great Lisbon earthquake of 1755 as a scientific—rather than religious—phenomenon, and his application of mathematical computations to earthquake activity following the great quake has formed the basis of the claim made on his behalf as the founder of the science of seismology. Additionally, he observed the transits of Mercury in 1740 and 1761 and journeyed to Newfoundland to observe a transit of Venus. He traveled in a ship provided by the Province of Massachusetts - probably the first scientific expedition ever sent out by any incipient American state. *Wik

1783 Birthdate of Charles-Julien Brianchon who, in 1820 published the nine-point circle theorem. Although this theorem has been independently discovered many times he gave the first complete proof and coined the phrase “nine-point circle”. *VFR He also published a geometrical theorem (named as Brianchon's theorem) while a student (1806). He showed that in any hexagon formed of six tangents to a conic, the three diagonals meet at a point. In fact, this theorem is simply the dual of Pascal's theorem which was proved in 1639. After graduation, Brianchon became a lieutenant in artillery fighting in Napoleon's army until he left active service in 1813 due to ill health.*TIS

1813 Thomas Andrews (19 Dec 1813; 26 Nov 1885) Irish chemist and physicist, who demonstrated the continuity of the gaseous and liquid states whereby during changes between the two states, physical properties display no abrupt changes. He discovered the critical temperature for carbon dioxide (1861), above which the gas cannot be liquefied by pressure alone. He wrote: We may yet live to see...such bodies as oxygen and hydrogen in the liquid, perhaps even in the solid state. He accurately measured heats of neutralisation, formation and reaction; and latent heats of evaporation. Andrews was the first to use a "bomb calorimeter" - a strong, sealed, metal vessel for measuring heat of combustion. He studied ozone, and proved that is an allotrope - or altered form - of oxygen.*TIS

1852 Albert Abraham Michelson (19 Dec 1852; 9 May 1931) was a German-born American physicist who accurately measured the speed of light and received the 1907 Nobel Prize for Physics "for his optical precision instruments and the spectroscopic and metrological investigations" he carried out with them. He designed the highly accurate Michelson interferometer and used it to establish the speed of light 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). The experiment yielded 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

1854 Marcel Brillouin worked on topics ranging from history of science to the physics of the earth and the atom.*SAU

1908 Anne Anastasi (19 Dec 1908; 4 May 2001) American psychologist, known as the "test guru," for her pioneering development of psychometrics, the measurement and understanding of psychological traits. Her seminal work, Psychological Testing (1954), remains a classic text in the subject. In it, she drew attention to the ways in which trait development is influenced by education and heredity. She explored how variables in the measurement of those traits include differences in training, culture, and language. In 1972, she became the first woman to be elected president of the American Psychological Association in half a century. For her accomplishments, she was awarded the National Medal of Science in 1987*TIS

1887 Charles G Darwin was the grandson of the famous biologist and graduated from Cambridge. He lectured on Physics at Manchester and after service in World War I and a period back at Cambridge he became Professor of Physics at Edinburgh. He left eventually to become head of a Cambridge college. He worked in Quantum Mechanics and had controversial views on Eugenics. *SAU

1910 Helmut Wielandt worked on finite groups and on finite and infinite permutation groups.*SAU

1918 Leon Mirsky worked in Number Theory, Linear Algebra and Combinatorics.*SAU

1921 APL Co-Inventor Adin D. Falkoff is born in New Jersey. He received a BChE in chemical engineering from the City College of New York in 1941 and MA in mathematics from Yale in 1963. He has worked for IBM since 1955. With Kenneth E. Iverson, Falkoff developed A Programming Language​ (APL). Iverson credited him for choosing the name APL and the introduction of the IBM golf-ball typewriter with the replacement typehead, which provided the famous character set to represent programs. Falkoff received IBM’s Outstanding Contribution Award for development APL and APL/360, and ACM’s Award for outstanding contribution to the development and application of APL. *CHM

1932 Crispin St. John Alvah Nash-Williams (December 19, 1932 – January 20, 2001) was a British and Canadian mathematician. His research interest was in the field of discrete mathematics, especially graph theory.
Hilton writes that "Themes running through his papers are Hamiltonian cycles, Eulerian graphs, spanning trees, the marriage problem, detachments, reconstruction, and infinite graphs." In his first papers Nash-William considered the knight's tour and random walk problems on infinite graphs; the latter paper included an important recurrence criterion for general Markov chains, and was also the first to apply electrical network techniques of Rayleigh to random walks. His graduate thesis, which he finished in 1958, concerned generalizations of Euler tours to infinite graphs. Welsh writes that his subsequent work defining and characterizing the arboricity of graphs (discovered in parallel and independently by W. T. Tutte) has "had a huge impact," in part because of its implications in matroid theory. Nash-Williams also studied k-edge-connected graphs, Hamiltonian cycles in dense graphs, versions of the reconstruction conjecture for infinite graphs, and the theory of quasi-orders. He also gave a short elegant proof on Kruskal's tree theorem.*Wik

1937 Barry Charles Mazur (born December 19, 1937) is a professor of mathematics at Harvard.
Born in New York City, Mazur attended the Bronx High School of Science and MIT, although he did not graduate from the latter on account of failing a then-present ROTC requirement. Regardless, he was accepted for graduate school and received his Ph.D. from Princeton University in 1959, becoming a Junior Fellow at Harvard from 1961 to 1964. He is currently the Gerhard Gade University Professor and a Senior Fellow at Harvard. In 1982 he was elected a member of the National Academy of Sciences. Mazur has received the Veblen Prize in geometry, the Cole Prize in number theory, the Chauvenet Prize for exposition, and the Steele Prize for seminal contribution to research from the American Mathematical Society.*Wik He is the author of the popular math book, Imaginary Numbers

1943 Victor G. Kac (born 19 December 1943 in Buguruslan, Russia, USSR) is a Soviet and American mathematician at MIT, known for his work in representation theory. He discovered Kac–Moody algebras, and used the Weyl–Kac character formula for them to reprove the Macdonald identities. He classified the finite-dimensional simple Lie superalgebras, and found the Kac determinant formula for the Virasoro algebra. Kac studied mathematics at Moscow State University, receiving his M.S. in 1965 and his Ph.D. in 1968. From 1968 to 1976, he held a teaching position at the Moscow Institute of Electronic Engineering. He left the Soviet Union in 1977, becoming an associate professor of mathematics at MIT. In 1981, he was promoted to full professor. Kac received a Sloan Fellowship in 1981 and a Guggenheim Fellowship in 1986 and the medal of the College de France (1981). He received the Wigner Medal(1994)"in recognition of work on affine Lie algebras that has had wide influence in theoretical physics". In 1978 he was an Invited Speaker (Highest weight representations of infinite dimensional Lie algebras) at the ICM in Helsinki, In 1988 a plenary speaker at the AMS centennial conference. In 2002 he gave a plenary lecture (Classification of Supersymmetries) at the ICM in Beijing. He is a Fellow of the American Mathematical Society., a Honorary member of the Moscow Mathematical Society, Fellow of the American Academy of Arts and Sciences and a Member of the National Academy of Sciences. The research of Victor Kac primarily concerns representation theory and mathematical physics. His work has been very influential in mathematics and physics and instrumental in the development of quantum field theory, string theory and the theory of integrable systems. Kac published 5 books and over 200 articles in mathematics and physics journals.
His brother Boris Katz is a principal research scientist at MIT. *Wik

1944 Mitchell Jay Feigenbaum (born December 19, 1944) is a mathematical physicist whose pioneering studies in chaos theory led to the discovery of the Feigenbaum constants.*Wik


1887 Balfour Stewart (1 Nov 1828, 19 Dec 1887) Scottish meteorologist and geophysicist who studied terrestrial magnetism and radiant heat. His researches on radiant heat contributed to foundation of spectrum analysis. He was the first to discover that bodies radiate and absorb energy of the same wavelength. In meteorology, he pioneered in ionospheric science, making a special study of terrestrial magnetism. He proposed (1882) that the daily variation in the Earth's magnetic field could be due to air currents in the upper atmosphere, which act as conductors and generate electrical currents as they pass through the Earth's magnetic field. He also investigated sunspots. In 1887, he suffered a stroke while crossing to spend Christmas at his estate in Ireland and died soon after at the age of 59.*TIS

1939 Dmitry Aleksandrovich Grave (September 6, 1863 – December 19, 1939) was a Russian and Soviet mathematician. Naum Akhiezer, Nikolai Chebotaryov, Mikhail Kravchuk, and Boris Delaunay were among his students.
Dmitry Grave was educated at the University of St Petersburg where he studied under Chebyshev and his pupils Korkin, Zolotarev and Markov. Grave began research while a student, graduating with his doctorate in 1896. He had obtained his masters degree in 1889 and, in that year, began teaching at the University of St Petersburg.
For his Master's Degree Grave studied Jacobi's methods for the three body problem, a topic suggested by Korkin. His doctorate was on map projections, again a topic proposed by Korkin, the degree being awarded in 1896. The work, on equal area plane projections of the sphere, built on ideas of Euler, Joseph Louis Lagrange and Chebyshev.
Grave became professor at Kharkov in 1897 and, from 1902, he was appointed professor at the University of Kiev, where he remained for the rest of his life. Grave is considered as the founder of the Kiev school of algebra which was to become the centre for algebra in the USSR.
At Kiev Grave studied algebra and number theory. In particular he worked on Galois theory, ideals and equations of the fifth degree. Among his pupils were O J Schmidt, N G Chebotaryov, B N Delone and A M Ostrowski. *WIK

1946 Paul Langevin (23 Jan 1872, 19 Dec 1946) French physicist who was the first scientist to explain the effects of paramagnetism and diamagnetism (the weak attraction or repulsion of substances in a magnetic field), in 1905, using statistical mechanics. He further theorized how the effects could be explained by how electron charges behaved within the atom. He popularized Einstein's theories for the French public. During WW I, he began developing a source for high intensity ultrasonic waves, which made sonar detection of submarines possible. He created the ultrasound from piezoelectric crystals vibrated by high-frequency radio circuits. In WW II, he spoke out against the Nazis, for which he was arrested and imprisoned, though he managed to escaped and fled to Switzerland.*TIS

1952 Otto Szász (11 December 1884, Hungary – 19 December 1952, Cincinnati, Ohio) was a Hungarian mathematician who worked on real analysis, in particular on Fourier series. He proved the Müntz–Szász theorem and introduced the Szász–Mirakyan operator. The Hungarian Mathematical and Physical Society awarded him the Julius König prize in 1939.*Wik

1953 Robert Andrews Millikan (22 Mar 1868, 19 Dec 1953) American physicist who was awarded the 1923 Nobel Prize for Physics for "his work on the elementary charge of electricity and on the photoelectric effect." Millikan's famous oil-drop experiment (1911) was far superior to previous determinations of the charge of an electron, and further showed that the electron was a fundamental, discrete particle. When its value was substituted in Niels Bohr's theoretical formula for the hydrogen spectrum, that theory was validated by the experimental results. Thus Millikan's work also convincingly provided the first proof of Bohr's quantum theory of the atom. In later work, Millikan coined the term "cosmic rays" in 1925 during his study of the radiation from outer space.*TIS

1983 Kate Sperling Fenchel (December 21, 1905 - December 19, 1983) Born in Berlin, Germany. Studied mathematics, philosophy, and physics at the University of Berlin from 1924 to 1928. She was encouraged to write a thesis, but she could not afford to continue her studies and research jobs for women appeared to be difficult to obtain. Thus she never received a Ph.D. in mathematics. From 1931 to 1933 she taught mathematics at the high school level, but was fired when the Nazis came to power in Germany because she was Jewish. She emigrated to Denmark with Werner Fenchel, a former fellow student, and the two married in December, 1933. Fenchel worked from 1933 to 1943 for a Danish mathematics professor. In 1943 she had to escape to Sweden with her husband and 3-year old son while Germany occupied Denmark. They returned to Denmark after the end of the war. Fenchel held a part-time lecturer's job at Aarhus University, Denmark, from 1965-1970.
Fenchel did research in finite nonabelian groups and published several papers, the last at the age of 73. *ASC

1997 David N. Schramm (25 Oct 1945, 19 Dec 1997) American theoretical astrophysicist who was an authority on the particle-physics aspects of the Big Bang theory of the origin of the universe. He considered the nuclear physics involved in the synthesis of the light elements created during the Big Bang comprising mainly hydrogen, with lesser quantities of deuterium, helium, lithium, beryllium and boron. He predicted, from cosmological considerations, that a third family of neutrinos existed - which was later proven in particle accelerator experiments (1989). Schramm worked to evaluate undetected dark matter that contributed to the mass of the universe, and which would determine whether the universe would ultimately continue to expand. He died in the crash of a small airplane he was piloting.*TIS

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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