## Wednesday 5 October 2022

### On This Day in Math - October 5

If it's just turning the crank it's algebra, but if it's got an idea in it, it's topology.
~Solomon Lefschetz

The 278th day of the year; 278 = 2x2x2x2x2x2x2x2+22

1789 - 278= 1511 is prime (278th prime minus 278).Derek's Daily Math  for more

278 is the fifth smallest number n such that nn starts with the digits of n, $278^278 = 2.78... × 10^679$

278 can be written as a sum of consecutive naturals, namely, 68 + ... + 71. Are there other strings of consecutive numbers that sum to 278?

For more fun with daily calendar math see Dereks Daily Math
and Ben Vitale

EVENTS
3761 BC The epoch (origin) of the modern Hebrew calendar *Wik (Interesting that the Mayan Calendar and the Hewbrew calendar both begin in the same century)

1582 The dates 5–14 October did not exist in Catholic countries due to the adoption of the Gregorian calendar. 15 October 1983 began the second year of the second 400 year cycle of that calendar. *VFR

1750 Maria Gaetana Agnesi receives a response from Pope Benedict XIV on the publication of her book, Instituzioni Analitiche , a two volume presentation covering algebra, calculus and differential equations. The pope sends her a gold medal, a wreath laid with precious stones and named her honorary professor at the University of Bologna.

1793 The French revolutionaries, in their anticlerical zeal, adopted the “calendar of reason.” The year had twelve months, each with three weeks of ten days, plus ﬁve or six epagomenal days. The day was divided into 10 hours of 100 minutes each. The calendar lasted until January 1, 1806. *Sky and Telescope, vol. 64, December 1982, p. 533 VFR

1853 Antioch College opened. It was the ﬁrst nonsectarian college to grant equal scholastic oppor¬tunities to men and women. Horace Mann was the ﬁrst president. *VFR Antioch College was a private, independent liberal arts college in Yellow Springs, Ohio, United States. It was the founder and the flagship institution of the six-campus Antioch University system. Founded in 1852 by the Christian Connection, the college began operating in 1853 with politician and education reformer Horace Mann as its first president. Between 1921 and 2008, the college's educational approach blended practical work experience with classroom learning, and participatory community governance. Students received narrative evaluations instead of academic letter grades. In June 2007, the University’s Board of Trustees announced that Antioch College would be suspending operations as of July 2008.[2] Antioch University transferred the assets, including the college campus, a $20$ million endowment, Glen Helen and the Antioch Review, to the Antioch College Continuing Corporation in 2009 for $5$ million. Since then, the Antioch College Continuing Corporation has raised nearly \$17 million from alumni in its quest to reopen in fall 2011. On May 5, 2011, the chancellor of the Ohio Board of Regents approved the request by Antioch College to offer Bachelor of Arts and Bachelor of Science degrees when it reopens this fall. It plans to reopen as an independent four-year college, with classes starting Oct. 4 *Wik

1854 Bernhard Reimann gives his first lecture at Gottinger to eight students. Dedekind, his friend and fellow Privatdozent, relates that Reimann was a very poor lecturer whose intellect took such large leaps that students often found it impossible to follow. *John Derbyshire, Prime Obsession, pg 132

1923 On the night of October 5-6, 1923, Carnegie astronomer Edwin P. Hubble took a plate of the Andromeda Galaxy (Messier 31) with the Hooker 100-inch telescope of the Mount Wilson Observatory. This plate, with identification number H335H ("Hooker plate 335 by Hubble"), is famous for having led to his discovery of the first Cepheid variable star in M31, which established beyond any doubt that M31 was a separate galaxy from our own. *obs.carnegiescience.edu

In 1931, Clyde Pangborn and Hugh Herndon completed the first nonstop flight across the Pacific Ocean, arriving in Washington state about 41 hours after leaving Japan.*TIS (For those, like many of my students, who have known the joy of living near MisawaShi in Aomori Prefecture Japan, this is the Miss Veedol Flight that took off from Sabishiro Beach. )
 Miss Veedol monument *Wik

BIRTHS

1644 Olaus Roemer, Danish astronomer, born. He was the ﬁrst to measure the speed of light. *VFR (,5 Oct 1644 {25 Sep OS};23 Sep 1710) Astronomer who demonstrated conclusively that light travels at a finite speed. He measured the speed by precisely measuring the length of time between eclipses of Jupiter by one of its moons. This observation produces different results depending on the position of the earth in its orbit around the sun. He reasoned that meant light took longer to travel the greater distance when earth was traveling in its orbit away from Jupiter.*TIS "Ole Rømer took part in several other achievements considering measurement. He developed a temperature scale that is now famous as the Fahrenheit scale. Fahrenheit improved and distributed his ideas after visiting Rømer. In his last years, he was even given the position as second Chief of the Copenhagen Police and invented the first street oil lamps in the city of Copenhagen.
Further achievements and inventions may be added to Rømer's biography, like his innovative water supply system and his urban planning concept. " *Yovista.blogspot

1713 Birthdate of Denis Diderot whose great Encyclopedie was published in 17 volumes of articles and 10 of splendid plates from 1751 to 1766. D’Alembert was editor for mathematical subjects. *VFR

1732 Nevil Maskelyne (5 Oct 1732, 9 Feb 1811) In 1761 the Royal Society sent Maskelyne to the island of St Helena to observe a transit of Venus. This was important since accurate measurements would allow the distance from the Earth to the Sun to be accurately measured and the scale of the solar system determined. During the voyage he experimented with the lunar position method of determining longitude. Maskelyne returned to Chipping Barnet in 1761, where he was a curate, and worked on publishing a book. He published the lunar distance method for determining longitude in The British Mariner's Guide (1763).
In 1764 he went on a voyage to Barbados to carry out trials of Harrison's timepiece. Soon after his return, in 1765, he was appointed (the fifth)Astronomer Royal. He published the first volume of the Nautical Almanac in 1766 and continued to work on this project up to the time of his death.
Maskelyne proposed to the Royal Society in 1772, an experiment for determining the Earth's density with the use of a plumb line. He was not the first to suggest such an experiment. Bouguer and La Condamine had tried such an experiment over 30 years before.
Maskelyne carried out the experiment in 1774 on Schiehallion, a mountain in Perthshire, Scotland. Schiehallion was chosen because it was surprisingly regular and conical in shape so its volume could be determined accurately. From his observations Maskelyne computed that the Earth's density is approximately 4.5 times that of water. He was awarded the Copley medal of the Royal Society in 1775 for this work. *SAU (Several other sources list his birth as Oct 6)

1781 Bernard Placidus Johann Nepomuk Bolzano (5 Oct 1781, 18 Dec 1848) His “Rein analytischer Beweiss” of 1817 ﬁrst formulated and proved the intermediate value theorem of the calculus. *VFR Bolzano successfully freed calculus from the concept of the infinitesimal. He also gave examples of 1-1 correspondences between the elements of an infinite set and the elements of a proper subset.*SAU

1861  Thomas Little Heath, (5 October 1861 – 16 March 1940) whose main interest was Greek mathematics. The Thirteen Books of Euclid’s Elements, which he published in 1908, is still in print by Dover. *VFR(A nice online version of the Elements can be found online here)

1882 Robert Hutchings Goddard (5 Oct 1882; 10 Aug 1945) American professor, physicist and inventor, "father of modern rocketry". From age 17 Goddard was interested in rockets (1899) and by 1908 he conducted static tests with small solid-fuel rockets. He developed mathematical theory of rocket propulsion (1912) and proved that rockets would functioned in a vacuum for space flight (1915). During WW I, Goddard developed rocket weapons. He wrote A Method of Reaching Extreme Altitudes, in 1919. Over the following two decades he produced a number of large liquid-fuel rockets at his shop and rocket range at Roswell, N.M. During WW II he developed rocket-assisted takeoff of Navy carrier planes and variable-thrust liquid-fuel rocket motors. At the time of his death Goddard held 214 patents in rocketry.*TIS

1882 Giorgio Abetti (5 Oct 1882; 24 Aug 1982) Italian astronomer known for his studies of the sun at the University of Padua where was director at the Arcetri Observatory (1921-52), taking over from his father who also held the post (1894-1921). In 1913, Giorgio Abetti took part, as a geodetic and geophysical astronomer, in the De Filippi expedition in Karakorum, Himalaya and Turkestan. He went on expeditions to observe eclipses of the sun, including one to Siberia to observe the total eclipse on 19 Jun 1936 and in 1952 to Sudan. With the advice of George Hale, he built a solar tower at the observatory (opened 1925). He wrote a popular text on the sun, a handbook of astrophysics (1936) and a popular history of astronomy (1963).*TIS

1898 Philip Franklin (October 5, 1898 in New York — January 27, 1965 in Belmont, Massachusetts) was an American mathematician and professor whose work was primarily focused in analysis.
His dissertation, The Four Color Problem, was supervised by Oswald Veblen. After teaching for one year at Princeton and two years at Harvard (as the Benjamin Peirce Instructor), Franklin joined the MIT Department of Mathematics, where he stayed until his 1964 retirement.
In 1922, Franklin gave the first proof that all planar graphs with at most 25 vertices can be four-colored.
In 1928, Franklin gave the first description of an orthonormal basis for L²([0,1]) consisting of continuous functions (now known as "Franklin's system").
In 1934, Franklin published a counterexample to the Heawood conjecture, this 12-vertex cubic graph is now known as the Franklin graph.
He was married to Norbert Wiener's sister Constance. *Wik

1930 (Another Beautiful Mind is born?) Reinhard Selten (5 Oct 1930, ) German mathematician who shared the 1994 Nobel Prize for Economics with John F. Nash and John C. Harsanyi for their development of game theory, a branch of mathematics that examines rivalries among competitors with mixed interests. Selten achieved a decisive breakthrough in game theory: The introduction of the concepts of sub-game perfect and perfect equillibria reduced the set of Nash equillibria drastically by excluding threats that are not credible. Thus, more precise and sensible predictions can be made for many games, e.g. markets. Additionally, game theory has found applications in all of social sciences and even in biology. *TIS

1932 Hyman Bass (October 5, 1932 - ) is an American mathematician, known for work in algebra and in mathematics education. From 1959-1998 he was Professor in the Mathematics Department at Columbia University, where he is now professor emeritus. He is currently the Roger Lyndon Collegiate Professor of Mathematics and Professor of Mathematics Education at the University of Michigan. *Wik

1973 Cédric Villani (5 October 1973, ) is a French mathematician working primarily on partial differential equations and mathematical physics. He was awarded the Fields Medal in 2010. Villani has worked on the theory of partial differential equations involved in statistical mechanics, specifically the Boltzmann equation, where, with Laurent Desvillettes, he was the first to prove how fast convergence occurred for initial values not near equilibrium. He has also written with Giuseppe Toscani on this subject. With Clément Mouhot, he has also worked on nonlinear Landau damping. He has worked on the theory of optimal transport and its applications to differential geometry, and with John Lott has defined a notion of bounded Ricci curvature for general measured length spaces. He received the Fields Medal for his work on Landau damping and the Boltzmann equation. *Wik

DEATHS

1565 Lodovico Ferrari (2 Feb 1522 in Bologna, Italy - 5 Oct 1565) Italian mathematician who was the first to find an algebraic solution to the biquadratic, or quartic, equation (an algebraic equation that contains the fourth power of the unknown quantity but no higher power).*TIS born in Bologna, Italy. In 1536 he was sent to live with Girolamo Cardano, who taught him Latin, Greek, and mathematics. He collaborated with Cardano in research on third and fourth degree equations. *VFR He began as the servant of Cardano but was extremely bright, so Cardano started teaching him mathematics. Ferrari aided Cardano on his solutions for quadratic equations and cubic equations, and was mainly responsible for the solution of quartic equations that Cardano published. While still in his teens, Ferrari was able to obtain a prestigious teaching post after Cardano resigned from it and recommended him. Ferrari eventually retired young (only 42) and quite rich. He then moved back to his home town of Bologna where he lived with his widowed sister Maddalena to take up a professorship of mathematics at the University of Bologna in 1565. Shortly thereafter, he died of white arsenic poisoning, allegedly murdered by his greedy sister.*Wik

1777 Jan Segner was a Hungarian mathematician who was the first professor of mathematics at Göttingen. He made substantial contributions to the theoery of Dynamics.*SAU

1880 William Lassell (18 Jun 1799, 5 Oct 1880) William Lassell was a wealthy amateur English astronomer. He set up an observatory at Starfield, near Liverpool. England, He built his own 24" diameter telescope, and devised steam-driven equipment for grinding an polishing the speculum metal mirror. This telescope was the first of its size to be mounted "equitorially" to allow easy tracking of the stars. He discovered Triton, a moon of Neptune, and Ariel and Umbriel, satellites of Uranus. Later, Lassell built a 48" diameter telescope with the same design and took it to Malta for observations with clearer skies.*TIS

1972 Solomon Lefschetz (3 Sept 1884, 5 Oct 1972) Solomon Lefschetz was a Russian born, Jewish mathematician who was the main source of the algebraic aspects of topology. *SAU (Lefschetz set out to be an engineer until he lost both hands in a laboratory accident.  He had prosthetic claws on each hand which were always covered with black gloves.  One student assistant had the responsibility of putting a piece of chalk in one claw at the beginning of the day, and removing the stub at the end.)

1985 Karl Menger (January 13, 1902 – October 5, 1985) was a mathematician.
He was the son of the famous economist Carl Menger. He is credited with Menger's theorem. He worked on mathematics of algebras, algebra of geometries, curve and dimension theory, etc. Moreover, he contributed to game theory and social sciences.
His most famous popular contribution was the Menger sponge (mistakenly known as Sierpinski's sponge), a three-dimensional version of Sierpinski's carpet. It is also related to the Cantor set. With Arthur Cayley, Menger is considered one of the founders of distance geometry; especially by having formalized definitions to the notions of angle and of curvature in terms of directly measurable physical quantities, namely ratios of distance values. The characteristic mathematical expressions appearing in those definitions are Cayley–Menger determinants.
He was an active participant of the Vienna Circle which had discussions in the 1920s on social science and philosophy. During that time, he proved an important result on the St. Petersburg paradox with interesting applications to the utility theory in economics. Later he contributed to the development of game theory with Oskar Morgenstern.*Wik (Recently there have been computer illustrations of the image when a Menger sponge is sliced on a diagonal, very interesting.).
(From George W. Hart's Web page... "As far as I know, Sebastien Perez Duarte was the first to pose this puzzle. His computer-rendered image is here.  And as far as I know, my nylon model shown above (top of this blog) is the first physical model of this.)

1985 Harald Cramér (September 25, 1893 – October 5, 1985) was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory. He was once described by John Kingman as "one of the giants of statistical theory". *Wik

1996 Seymour Cray (28 Sep 1925, 5 Oct 1996) The father of the supercomputer, Seymour Cray​ died due to injuries sustained in a car accident two weeks earlier. Cray was born Sept. 28, 1925, in Chippewa Falls, Wis. Cray worked among computer pioneers after graduating from the University of Minnesota in 1951 with bachelor’s and master’s degrees. With several others, he founded Control Data Corp., where he built the CDC 1604 and CDC 6600; the latter was the most powerful computer of its time -- three times more powerful than IBM’s Stretch. Cray founded his own company, Cray Research​, in 1972 and built supercomputers in a cylindrical design that aimed to cut down on the length of internal wiring. Crays are used primarily for scientific research and computer graphics. *CHM

2011 Steven Paul "SteveJobs (February 24, 1955 – October 5, 2011) was an American computer entrepreneur and inventor. He was co-founder, chairman, and chief executive officer of Apple Inc. Jobs also previously served as chief executive of Pixar Animation Studios; he became a member of the board of directors of The Walt Disney Company in 2006, following the acquisition of Pixar by Disney. He was credited in Toy Story (1995) as an executive producer.
In the late 1970s, Jobs, with Apple co-founder Steve Wozniak, Mike Markkula and others designed, developed, and marketed one of the first commercially successful lines of personal computers, the Apple II series. In the early 1980s, Jobs was among the first to see the commercial potential of Xerox PARC's mouse-driven graphical user interface, which led to the creation of the Macintosh. After losing a power struggle with the board of directors in 1985, Jobs resigned from Apple and founded NeXT, a computer platform development company specializing in the higher-education and business markets. Apple's subsequent 1996 buyout of NeXT brought Jobs back to the company he co-founded, and he served as its CEO from 1997 until 2011.*Wired.co.UK

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