Friday 7 October 2022

On This Day in Math - October 7


Contraria sunt complementa.
Opposites are complementary.
Motif on Niels Bohr's coat of arms

The 280th day of the year; There are 280 plane trees with ten nodes. As a consequence of this, 18 people around a round table can shake hands without crossing arms in 280 different ways (up to rotations)

The sum of the first 280 consecutive primes mod 280 is prime. *Prime Curios (Stijn Dierckx ‏@Stanny1990 told me there are 108 such days in a year [almost 30% of the days satisfy this property]. Next one in 5 days!)  (for example, 2 + 3 + 5 + 7 + 11 =28, and 28 mod 5 = 3, a prime.)

280 = 71^2 - 69^2 = 37^2 - 33^2 = 19^2 - 9^2 = 17^2 - 3^2 = 4^3 + 6^3
On July 10, 1796 The entry in Gauss's Diary  "EγPHKA! num=Δ+Δ+Δ" , recording his discovery that every positive integer is the sum of (at most) three triangular numbers. Can you find the three or less for 280? 280 is also sum of five consecutive triangular numbers; 36 + 45 + 55 + 66 + 78 =280.

\(280 = 10!_3\) = 10 x 7 x 4 x 1  (my notation, I will not be moved)


1601 Baptismal date of Florimond DeBeaune whose fame rests on two brief notes published in Schooten’s Latin edition of Descartes (1649 and 1659–60). In the second of these he raised the first inverse tangent problem: determine a curve from a property of its tangent. *VFR (This is the first example of a first order differential equation problem.) This is often listed as his birth date (SAU and others) but appears not to have been.

1854 In an addendum to his paper An Introductory Memoir upon Quantics, Arthur Cayley would add a second differential equation and state that "a covariant is a expression which, if it satisfies one of these equations, it satisfies the other. This would be the backbone of his new formulation of covariants in his next paper, A second Memoire upon Quantics. *James Joseph Sylvester: Life and Work in Letters, edited by Karen Hunger Parshall

1864 The mathematical seminar at Berlin began. It was the oldest such seminar in Germany and the model for many others. Kummer, Weierstrass, and Kronecker ran it. One of its goals was to improve teaching. *ISIS 66(1975), p 584

1893 When the poet/mathematician Omar Khayyam died in 1123 he was buried in a spot where the North wind would scatter rose petals over his grave. On this date a rose tree started from those on Khayyam’s grave was transplanted to the grave of Edward FitzGerald (1809-1883), the Irish translator who made Khayyam’s poetry so famous in modern times. For Khayyam’s geometric solution to the cubic see Eves, Great Moments in Mathematics (before 1650), p. 155. *VFR (FitzGerald is buried in the churchyard of the small, isolated Church of St Michael and All Angels, Boulge, Suffolk, England (Near Ipswitch). Six more rose trees were planted around the grave in 1972.If anyone has an image of the roses in bloom around his grave, I would appreciate a note.

1913 Danish physicist Niels Bohr proposed a new model for the atom on this date. He described the atom as a miniature solar system with electrons revolving around a heavy nucleus. He received the 1922 Nobel Prize in Physics for “his services in the investigation of the structure of atoms and of the radiation emanating from them.” *
1943  When German troops entered Niels Bohr's home to arrest him late in 1943, Danish resistance laid down cover fire as he grabbed a beer bottle with heavy water and escaped out the back door.  A fishing boat took him to Sweden and he made his way to Stockholm. The British sent a De Haviland Mosquito to carry him to England.  Laying on his back in the converted bomb bay,  Bohr did not put on his oxygen as directed. One story suggests his head was too big for the mask.  At altitude he passed out and his life was saved when the pilot realized he could not get a response from Bohr, and descended to a lower altitude.  When the plane landed Bohr went to the hospital clutching the precious beer bottle full of heavy water.  Alas, he shortly discovered that in his rush to leave, he had grabbed a regular bottle of beer.  One wonders what the reaction was if someone later tried to open the bottle of heavy water and drink it.  *various sources

1988 The Computer Bowl Begins. The first round of The Computer Bowl, an annual televised game show of computer trivia pitting the gurus of the East versus the wizards of the West, was held. Mitch Kapor and Bill Joy were the MVPs, winning a place on the all star team. *CHM

2014 Sky watchers heading to bed early tonight: Early tomorrow a total lunar eclipse, a "blood moon", will be visible, weather permitting, from much of North America, as well as to observers in Australia, western Asia and across the Pacific Ocean. Observers east of the Mississippi in the US may see the total eclipse of the moon and the rising sun simultaneously. The little-used name for this effect is called a "selenelion," a phenomenon that celestial geometry says cannot happen. But thanks to Earth's atmosphere, the images of both the sun and moon are apparently lifted above the horizon by atmospheric refraction. This allows people on Earth to see the sun for several extra minutes before it actually has risen and the moon for several extra minutes after it has actually set.
The phrase “blood moon” comes from an interpretation of a Biblical prophecy concerning the upcoming tetrad of total lunar eclipses. That is to say, the April 15, 2014 total lunar eclipse is one of four total lunar eclipses that will take place, with no partial lunar eclipses between them. As you might imagine, this is a relatively rare astronomical event. There are only 8 tetrads in the 21st century. In some centuries, a tetrad does not occur at all. The word “blood” comes into play presumably because at totality, the eclipsed moon appears reddish brown. You could even call it blood red.*
(if you miss it, there is another chance to catch one on September 27/ 28, 2015. After that a Supermoon eclipse will not happen again until October 7/8, 2033.


1858 Charles Marvin (October 7, 1858 – June 5, 1943) U.S. meteorologist who invented the clinometer that figures height of clouds over airports. He was Chief of the U.S. Weather Bureau (1913-34). He worked on, and wrote about, the Robinson cup anemometer, from early in his career with the Weather Bureau until years after his retirement. For early systematic investigations of the upper air, he designed and constructed kites and kite instruments. He also devised the Marvin pyrheliometer and inaugurated the regular measurement of solar radiation intensity by the Weather Bureau. Marvin designed a seismograph operated by the Weather Bureau. He was also particularly interested in the application of mathematical statistics to meteorological problems.*TIS (Teachers who have student's create clinometers with a straw, protractor and plumbline might include this historical artifact as a preliminary to the lesson.)

1875 Raymond Clare Archibald (7 Oct 1875, 26 July 1955) studied in Canada, at Harvard and at Strasbourg. He spent most of his career at Brown University in Rhode Island. His main interests were in the History of Mathematics. *SAU

1885 Niels Henrik David Bohr (7 Oct 1885, 18 Nov 1962) was a Danish physicist, born in Copenhagen, who was the first to apply the quantum theory, which restricts the energy of a system to certain discrete values, to the problem of atomic and molecular structure. For this work he received the Nobel Prize for Physics in 1922. He developed the so-called Bohr theory of the atom and liquid model of the nucleus. Bohr was of Jewish origin and when the Nazis occupied Denmark he escaped in 1943 to Sweden on a fishing boat. From there he was flown to England where he began to work on the project to make a nuclear fission bomb. After a few months he went with the British research team to Los Alamos in the USA where they continued work on the project. *TIS (Bohr and his brother, the mathematician Harald Bohr, were both outstanding athletes. An amusing anecdote about their sporting lives here.)

1899 Oystein Ore (7 October 1899 in Oslo, Norway – 13 August 1968 in Oslo) was a Norwegian mathematician. Ore is known for his work in ring theory, Galois connections, and most of all, graph theory. His early work was on algebraic number fields, how to decompose the ideal generated by a prime number into prime ideals. He then worked on noncommutative rings, proving his celebrated theorem on embedding a domain into a division ring. He then examined polynomial rings over skew fields, and attempted to extend his work on factorisation to non-commutative rings.
In 1930 the Collected Works of Richard Dedekind were published in three volumes, jointly edited by Ore and Emmy Noether. He then turned his attention to lattice theory becoming, together with Garrett Birkhoff, one of the two founders of American expertise in the subject. Ore's early work on lattice theory led him to the study of equivalence and closure relations, Galois connections, and finally to graph theory, which occupied him to the end of his life.
Ore had a lively interest in the history of mathematics, and was an unusually able author of books for laypeople, such as his biographies of Cardano and Niels Henrik Abel. *Wik

1939 Sir Harold W. Kroto (7 Oct 1939, )English chemist who, with Richard E. Smalley and Robert F. Curl, Jr., was awarded the 1996 Nobel Prize for Chemistry for their joint discovery of the carbon compounds called fullerenes. These new forms of the element carbon contain 60 or more atoms arranged in closed shells. The number of carbon atoms in the shell can vary, and for this reason numerous new carbon structures have become known. Formerly, six crystalline forms of the element carbon were known, namely two kinds of graphite, two kinds of diamond, chaoit (1968) and carbon(VI) (1972). Fullerenes are formed when vaporized carbon condenses in an atmosphere of inert gas. The carbon clusters can then be analyzed with mass spectrometry.*TIS


1719 Pierre Rémond de Montmort (27 Oct 1678, 7 Oct 1719) was a French mathematician who wrote an important work on probability. Montmort's reputation was made by his book on probability Essay d'analyse sur les jeux de hazard which appeared in 1708. The book, which is a collection of combinatorial problems, is a systematic study of games of chance and shows that there is important mathematics in this area. Montmort collaborated with Nicolaus(I) Bernoulli and he was also a friend of Taylor. At a time of high feelings in the Newton-Leibniz controversy it says a lot for Montmort that he could be friends with followers of both camps. In addition, Montmort corresponded with Craig, Halley, Hermann and Poleni. Montmort was elected to be a Fellow of the Royal Society in 1715, when he was on a trip to England. The following year he was elected to the Académie Royal des Sciences. *SAU

1903 Rudolf Otto Sigismund Lipschitz (14 May 1832, 7 Oct 1903) is remembered for the "Lipschitz condition", an inequality that guarantees a unique solution to the differential equation y' = f (x, y).*SAU

1965 Jesse Douglas (3 Jul 1897, 7 Oct 1965) American mathematician who was awarded one of the first two Fields Medals in 1936 for solving the Plateau problem. which had first been posed by the Italian-French mathematician Joseph-Louis Lagrange in 1760. The Plateau problem is one of finding the surface with minimal area determined by a fixed boundary. Experiments (1849) by the Belgian physicist Joseph Plateau demonstrated that the minimal surface can be obtained by immersing a wire frame, representing the boundaries, into soapy water. Douglas developed what is now called the Douglas functional, so that by minimizing this functional he could prove the existence of the solution to the Plateau problem. Douglas later developed an interest in group theory.*TIS

1992 Martin Eichler (29 March 1912 – 7 October 1992) was a German number theorist. He received his Ph.D. from the Martin Luther University of Halle-Wittenberg in 1936.
Eichler once stated that there were five fundamental operations of mathematics: addition, subtraction, multiplication, division, and modular forms. He is linked with Goro Shimura in the development of a method to construct elliptic curves from certain modular forms. The converse notion that every elliptic curve has a corresponding modular form would later be the key to the proof of Fermat's last theorem.*Wik

1995 Gerard Henri de Vaucouleurs (25 Apr 1918, 7 Oct 1995) French-born U.S. astronomer whose pioneering studies of distant galaxies contributed to knowledge of the age and large-scale structure of the universe. He produced three Reference Catalogues of bright galaxies (1964, 1976, 1991). Each was a homogenization of data from widely different sources, so that the catalogues would not be merely finding lists or data collection lists, but astrophysically useful databases. Using data in the Reference Catalogues, he was able to develop new distance indicators and refine others. His unique philosophy on distance matters was "spreading the risks," that is, applying as many different and independent techniques as possible to check for scale and zero-point errors.*TIS

1995 Olga Taussky-Todd (August 30, 1906– October 7, 1995) was a Czech-American mathematician who worked first in algebraic number theory, with a doctorate at the University of Vienna supervised by Philipp Furtwängler. During that time in Vienna she also attended the meetings of the Vienna Circle. Later, she started to use matrices to analyze vibrations of airplanes during World War II, at the National Physical Laboratory in the United Kingdom. She became the torchbearer for matrix theory.
In 1938 she married another mathematician, John Todd and in 1945 the Todds immigrated to the United States and worked for the National Bureau of Standards. In 1957 they joined the faculty of California Institute of Technology in Pasadena, California.
She was a Fellow of the AAAS, a Noether Lecturer and a recipient of the Austrian Cross of Honour for Science and Art. She also supervised Caltech's first female Ph.D. in Math, Lorraine Foster. *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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