Pat'sBlog

Thursday, 8 October 2015

On This Day in Math - October 8

It is the perennial youthfulness of mathematics itself which marks it off

with a disconcerting immortality from the other sciences.

~Eric Temple Bell

The 281st day of the year, 281 is a prime and is the sum of the first fourteen prime numbers. It is the sixth, and last, day of the year such that the sum of the first k primes is a prime. (I just noticed that all of them except 2, is the smaller of pair of twin primes. Unfortunately, the next one after that is not.)
281 appears in the sequence of primes generated by $f(x)= x^2 + x + 41 $ Which is often called the Euler Polynomial. (although Euler actually used $x^2 -x + 41$ which is prime for x values from 1 to 40. Legendre noticed that the positive x form produced the same primes for values from 0 to 39.)

EVENTS
In 1604, the supernova now called "Kepler's nova" was first sighted in the constellation Ophiuchus, the Serpent Bearer. Johannes Kepler observed it from the time of its appearance as an apparently new star. It encouraged him to write The New Star in 1606.*TIS

1834 Jakob Steiner appointed extraordinary professor at the University of Berlin, a post he held until his death in 1863. *VFR

1996 The U.S. Postal Service issued a special "Computer Technology" stamp to mark the 50th anniversary of the ENIAC. In a ceremony at the Army’s Aberdeen Proving Ground, speakers paid tribute to computer pioneers with the image of a brain partially covered by small blocs that contain parts of circuit boards and binary language. The stamp was designed entirely on a computer. A Postal Service news release from Oct. 8 introduced the
stamp with a discussion of the ENIAC’s origins: "Long before PCs became standard office equipment and surfing on the information superhighway became a national obsession, calculations were done the ‘old-fashioned way’ by hand. And, as is often the case, it took a war to bring the world into the computer age specifically, the need for the United States Army to rapidly compute ballistic firing tables." *CHM
There also seems to be a US 3 cent stamp of the Eniac. The date on the page I saw has 1943, but on the stamp it says eniac was "completed in 1946" . If someone knows the true date this stamp was released, please advise.

2008 The Mathematics Library at Notre Dame was rededicated and named for Prof. O. Timothy O’Meara. Prof. O’Meara is a noted Mathematician, who has been on the faculty of the Mathematics Department since 1962, and twice served as its chairman. In 1976 he was named to the Kenna Endowed Chair in Mathematics. He is noted for serving as the first lay Provost of the University, 1978-1996. He is now an emeritus faculty member, but still very active and interested in the library *ND Web Site

2014 A total lunar eclipse 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. http://www.space.com

BIRTHS
1561 Edward Wright (baptised 8 October 1561; November 1615) was an English mathematician and cartographer noted for his book Certaine Errors in Navigation (1599; 2nd ed., 1610), which for the first time explained the mathematical basis of the Mercator projection, and set out a reference table giving the linear scale multiplication factor as a function of latitude, calculated for each minute of arc up to a latitude of 75°. This was in fact a table of values of the integral of the secant function, and was the essential step needed to make practical both the making and the navigational use of Mercator charts.*Wik At his Renaissance Mathematicus blog, Thony Christie points out that "Mercator printed and published a world map constructed according to this method (cylindrical) of projection in 1569 but he did not explain the mathematical rules on which it was based. He was a professional cartographer and globe maker and he probably hoped that if he kept his method secret then the people who wished to take advantage of this new development would have to order their maps and charts from him.... John Dee and Thomas Harriott both independently solved the mathematical problem of the projection but like Mercator neither of them made the knowledge public. We can however assume that both of them made use of this knowledge when teaching navigation and cartography, Dee to the pilots of the Muscovy Company and Harriot to Walter Raleigh’s sea captains.
The first person to publish the mathematical method of constructing such a chart was another English mathematicus Edward Wright in his book Certaine Errors in Navigation, first published in 1599."

1850 Peter Scott Lang (8 Oct 1850, 5 July 1926) graduated from Edinburgh University and after a period as assistant in Edinburgh he became Regius Professor of Mathematics at St Andrews. He held this position for 42 years. *SAU

1873 Ejnar Hertzsprung (8 Oct 1873; 21 Oct 1967) Danish astronomer who classified types of stars by relating their surface temperature (or colour) to their absolute brightness. A few years later Russell illustrated this relationship graphically in what is now known as the Hertzsprung-Russell diagram, which has become fundamental to the study of stellar evolution. In 1913 he established the luminosity scale of Cepheid variable stars.*TIS

1908 Hans Arnold Heilbronn (8 October 1908 – 28 April 1975) was a mathematicianb orn into a German-Jewish family. He was a student at the universities of Berlin, Freiburg and Göttingen, where he met Edmund Landau, who supervised his doctorate. In his thesis, he improved a result of Hoheisel on the size of prime gaps. *Wik

1932 Kenneth Ira Appel (October 8, 1932 – April 19, 2013) was an American mathematician who in 1976, with colleague Wolfgang Haken at the University of Illinois at Urbana-Champaign, solved one of the most famous problems in mathematics, the four-color theorem. They proved that any two-dimensional map, with certain limitations, can be filled in with four colors without any adjacent "countries" sharing the same color. Their conclusion, that four colors would suffice for any map, depended on 1,200 hours of computer time — the equivalent of 50 days — and 10 billion logical decisions all made automatically and out of sight by the innards of an I.B.M. computer at the University of Illinois in Urbana.
He died of esophageal cancer on April 19, 2013. *Wik

1944 E. E. "Pat" Ballew , Whose greatest contribution to mathematics was in helping to educate many great young people who went on to be successful in numerous walks of life. Editor/author of this blog. So "Happy Birthday to me".

DEATHS
1647 Christian Longomontanus (4 Oct 1562, 8 Oct 1647) Byname of Christian Severin, a Danish astronomer and astrologer who is best known for his association with, and published support for, Tycho Brahe. He became the first professor of astronomy at the University of Copenhagen, and in 1610 he received funds for instruments and he probably constructed a small observatory at his home. Longomontanus used Tycho's data to compile the Astronomia danica (1622), an exposition of the Tychonic system, which holds that the Sun revolves around the Earth and the other planets revolve around the Sun. He began the construction of the Copenhagen Observatory in 1632, but died before its completion.*TIS

1652 John Greaves (1602, 8 Oct 1652) Greaves was appointed as Professor of Geometry at Gresham College, London, in February 1631. He was able to retain his fellowship at Merton College, Oxford. His main scientific aim was the "practical and sober project of standardizing and synchronizing the weights and measures of all ancient and modern nations."
His desire to find out about measurements in the ancient world led him to plan visits to Italy and Egypt, where he wanted to make measurements of the pyramids. As Shalev puts it "It is metrology which fuelled Greaves's fascination with ancient monuments, and with the Great Pyramid above all."
In 1649 he published A Discourse of the Roman Foot, and Denarius; from whence, as from two Principles, the Measures and Weights used by the Ancients may be deduced. In the same year he published Elementa Linguae Persicae.*SAU

1883 Professor Enoch Beery Seitz,(August 24, 1846 Rushcreek Township, Ohio – October 8, 1883 Kirksville, Mo.) of Missouri State Normal School(now Truman State University), was “stricken by that ‘demon of death.’ typhoid fever, and passed the mysterious shades, to be numbered with the silent majority.” “Prof. Seitz was in mathematics what Demosthenes was in oratory; Shakespeare in poetry; and Napoleon in war: the equal of the best, the peer of all the rest.” In case you have never heard him, see the biography in the ﬁrst volume (1894) of the Americal Mathematical Monthly, pp. 3–6. *VFR
A nice problem from Professor Seitz, Perhaps inspired by the Greenville (Ohio) hometown legend Annie Oakly and her rifleman ship, Seitz offered the problem:
"A cube is thrown into the air and a random shot fired through it; find the chance that the shot passes through the opposite side." From a nice biography of the professor *by John E. Zimmerman, Washington & Jefferson College

1940 Robert Emden (4 Mar 1862, 8 Oct 1940) Swiss astrophysicist and mathematician who wrote Gaskugeln (Gas Spheres, 1907), giving a mathematical model of stellar structure as the expansion and compression of gas spheres, wherein the forces of gravity and gas pressure are in equilibrium. He expanded on earlier work by J. H. Lane (1869) and A. Ritter (1878-83) who first derived equations describing stars as gaseous chemical, spherical bodies held together by their own gravity and obeying the known gas laws of thermodynamics. For four decades, the Lane-Emden equation was the foundation of theoretical work on the structure of stars: their central temperatures and pressures, masses, and equilibria. Emden also devised a hypothesis, no longer taken seriously, to explain sunspots. *TIS

1973 Evan Tom Davies (24 Sept 1904, 8 Oct 1973) graduated from the University of Wales at Aberystwyth and then studied in Rome and Paris. After lecturing at King's College London he was appointed to a professorship in Southampton. He worked in Differential Geometry and the Calculus of Variations. *SAU

2001 Caryl Parker Haskins (August 12, 1908 to October 8, 2001) was a scientist, author, inventor, philanthropist, governmental adviser and pioneering entomologist in the study of ant biology. In the 1930s he was inspired by Alfred Lee Loomis to establish his own research facility. Along with Franklin S. Cooper, he founded the Haskins Laboratories, a private, non-profit research laboratory, in 1935. Affiliated with Harvard University, MIT, and Union College in Schenectady, NY, Haskins conducted research in microbiology, radiation physics, and other fields in Cambridge, MA and Schenectady. In 1939 Haskins Laboratories moved its center to New York City. Seymour Hutner joined the staff to set up a research program in microbiology, genetics, and nutrition. The descendant of this program is now part of Pace University in New York. In the 1940s Luigi Provasoli joined the Laboratories to set up a research program in marine biology which disbanded with his retirement in 1978. Since the 1950s, the main focus of the research of Haskins Laboratories has been on speech and its biological basis. The main facility of Haskins Laboratories moved to New Haven, Connecticut in 1970 where it entered into affiliation agreements with Yale University and the University of Connecticut. Haskins Laboratories continues to be a leading, multidisciplinary laboratory with an international scope that does pioneering work on the science of the spoken and written word.
Haskins served as President, Research Director, and Chairman of the Board of Haskins Laboratories, 1935-'87; Director, E.I. du Pont de Nemours, 1971-'81 and Research Professor, Union College, 1937-'55. In 1956, he was appointed to the Presidency of the Carnegie Institution of Washington, a position he held until 1971. He was also President of the Sigma Xi society in 1967-'68. He remained a Trustee of Carnegie Institution and of Haskins Laboratories, as well as Trustee Emeritus of the National Geographic Society until his death. He also continued his research on entomology, working with his wife, Edna Haskins, and other colleagues. *Wik

2005 Alfred William Goldie (10 Dec 1920, 8 Oct 2005) was an English mathematician who proved an important result in Ring Theory. Goldie's first paper in this area Decompositions of semi-simple rings (1956) made an immediate impact since Jacobson included one of Goldie's theorems in his classic monograph Structure of Rings of 1956, acknowledging that it had been communicated by Goldie. Over the next few years Goldie's work on non-commutative Notherian rings would totally revolutionise the subject. He was able to prove totally unexpected structure theorems. Even his first steps towards these results were startling *SAU

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

Wednesday, 7 October 2015

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

EVENTS
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.

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. http://www.space.com
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.*http://sciencenotes.org

BIRTHS
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

DEATHS
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

Tuesday, 6 October 2015

On This Day in Math - October 6

[after proving Euler's formula e ^{π i} + 1 = 0 in a lecture]
Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it is the truth.
~Benjamin Peirce

The 279th day of the year; Every positive integer is the sum of at most 279 eighth powers. See Waring's problem

279 = 3^2 + 3^3 + 3^5 (powers are consecutive primes). *Derek Orr

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

EVENTS
1570 Cardano imprisoned for 87 days on charges of impiety (casting a horoscope of Christ). He spent the remaining ﬁve years of his life in Rome under the eye of a suspicious pope who nonetheless gave him a pension. See “Girolamo Cardano’s Horoscope of Christ,” pp. 53–90 in Renaissance Curiosa by Wayne Shumaker, especially p. 55 *VFR

1651 Sir Charles Cavendish writes to John Pell about Thomas Harriot’s Doctrine of Triangular Numbers; “Sr. Th Alesburie remembers him to you & desires to know if you would be pleased to shew the use of Mr. Harriots doctrine of triangulare numbers; which if you will doe, he will send you the original; I confess I was so farre in loue with it that I coppied it out; though I doute I vnderstand it not all; much less the many vses which I assure myself you will finde of it.” *Thomas Harriot’s Doctrine of Triangular Numbers, Beery &Stedall, pg 3

1668 (Oct 16 NS) Wallis writes to thank Oldenburg for gift of "Lalovera's book" (La Loubere), veterum geometria promota, in septem de cycloide libris. La Loubere is often cited as the first man to bring the "Siamese" method of solving nxn odd magic squares to the West. *Philip Beeley, Christoph J. Scriba; Correspondence of John Wallis

1729 The ﬁrst known letter which contains an interpolating function for the factorials was written by Daniel Bernoulli on October 6, 1729. Bernoulli suggests for an arbitrary (positive) x and an inﬁnite number A the inﬁnite product $$ (A + \frac{x}{2})^{x-1} *((\frac{2}{1+x}) *(\frac{3}{2+x})* ... *(\frac{A}{A-1+x})$$

In 1783, the self-winding clock was patented by Benjamin Hanks.*TIS

1807 Humphry Davy first isolated potassium by electrolysis of molten KCl in the basement of Royal Institute. *Anthony Hardwicke Tweet

1860 J. J. Sylvester, in a dinner invitation for Thomas Archer Hirst to join him with Arthur Cayley and Sylvester's "young French mathematical friend", (Camille Jordan); Sylvester entices him with a bit of mathematics, "I shall have something very striking to tell you about algebraic quantities of any order of irrationality and their representation by multiple definite integrals when we meet." *James Joseph Sylvester: Life and Work in Letters, edited by Karen Hunger Parshall

1983 Lotus Development Corp. went public after recording revenues of $12.8 million for the previous 12 months. The company, founded by Mitch Kapor and Jonathan Sachs in 1982, found its success with Kapor’s spreadsheet program, Lotus 1-2-3. Lotus 1-2-3 bypassed the operating system of the IBM PC, making it much faster than its competitors. In addition, its combination of spreadsheet capabilities with graphics and data retrieval made the program popular. IBM acquired Lotus in 1995.*CHM

1994 Fermat confirmed, FINALLY. Wiles sends corrected proof. Over the course of three lectures delivered at Isaac Newton Institute for Mathematical Sciences on June 21, 22, and 23 of 1993, Andres Wiles had announced his proof of the Taniyama–Shimura conjecture, and hence of Fermat's Last Theorem. There was a relatively large amount of press coverage afterwards.
(Nick) Katz was a referee on his manuscript and he asked Wiles a series of questions that led Wiles to recognize that the proof contained a gap. There was an error in a critical portion of the proof which gave a bound for the order of a particular group: the Euler system used to extend Flach's method was incomplete. Wiles and his former student Richard Taylor spent almost a year resolving it. Wiles indicates that on the morning of September 19, 1994 he realized that the specific reason why the Flach approach would not work directly suggested a new approach with the Iwasawa theory which resolved all of the previous issues with the latter and resulted in a CNF that was valid for all of the required cases. On 6 October Wiles sent the new proof to three colleagues including Faltings. The new proof was published and, despite its size, widely accepted as likely correct in its major components. *Wik

In 1995, the first discovery of a planet around a star similar to the sun was announced (about 160 times the mass of the Earth around the star 51 Pegasus).*TIS

2008 First Space object observed before it hit the earth. At 06:38 UTC on October 6, astronomers at the University of Arizona discovered an object provisionally called 8TA9D69 that appeared to be on a collision course with Earth. Three other observatories reported sightings within the next few hours -- Sabino Canyon in Arizona and Siding Spring Observatory and a Royal Astronomical Society site, both in Australia. Together these four observers provided enough data on the object so that a Minor Planet Electronic Circular was issued at 14:59 UTC the same day, giving 8TA9D69 the more formal name 2008 TC3, and advising the astronomical community that "The nominal orbit given above has 2008 TC3 coming to within one earth radius around Oct. 7.1. The absolute magnitude indicates that the object will not survive passage through the atmosphere. Steve Chesley (JPL) reports that atmospheric entry will occur on 2008 Oct 07 0246 UTC over northern Sudan."
The object wouldn't be more than a big meteor, but even so, it represented the first time ever that an object had been observed before it was to hit Earth, and, clearly, astronomers around the world scrambled to their telescopes to observe it before it was to pass into Earth's shadow (and, therefore, invisibility) just before 01:50 UTC. *The Planetary Society

BIRTHS
1552 Matteo Ricci (6 Oct 1552, 11 May 1610) Matteo Ricci was an Italian Jesuit who went to China as a missionary and introduced the Chinese to Western mathematics.*SAU More detail about this student of Clavius at the Renaissance Mathematicus

1732 Nevil Maskelyne (6 Oct 1732, 9 Feb 1811) (SAU gives 5 Oct for birhtdate)
British astronomer noted for his contribution to the science of navigation. In 1761 the Royal Society sent Maskelyne to the island of St Helena to make accurate measurements of a transit of Venus. This in turn gives the distance from the Earth to the Sun, and the scale of the solar system. During the voyage he also experimented with the lunar position method of determining longitude. In 1764 he went on a voyage to Barbados to carry out trials of Harrison's timepiece, followed by appointment as Astronomer Royal (1765). In 1774, he carried out an experiment on a Scottish mountain with the use of a plumb line to determine the Earth's density. He found it was approximately 4.5 times that of water. *TIS

1735 Jesse Ramsden (6 Oct 1735; 5 Nov 1800) British pioneer in the design of precision tools. At 23, Ramsden chose to apprentice to a maker of mathematical instruments. By age 27 he had his own business in London and was known as the most skilful designer of mathematical, astronomical, surveyingand navigationalinstruments in the 18th Century. He is best known for the design of a telescope and microscope eyepiece (ocular) still commonly used today and bearing his name. The French scientist N. Cassegrain proposed a design of a reflecting telescope in 1672, but Ramsden, however, 100 years later, who found that this design reduces blurring of the image caused by the sphericity of the lenses or mirrors. He also built lathes, barometers, manometers and assay balances.*TIS

1784 Pierre Charles François Dupin (6 Oct 1784, 18 Jan 1873) Dupin made contributions to differential geometry and in particular invented the 'Dupin indicatrix'.*SAU

1795 Benjamin Olinde Rodrigues (6 Oct 1795, 17 Dec 1851) was a French mathematician best known for his formula for the Legendre polynomials.*SAU

1831 (Julius Wilhelm) Richard Dedekind (6 Oct 1831, 12 Feb 1916 at age 84) German mathematician who developed a major redefinition of irrational numbers in terms of arithmetic concepts. Although not fully recognized in his lifetime, his treatment of the ideas of the infinite and of what constitutes a real number continues to influence modern mathematics. *TIS A 1904 academic calendar marked September fourth, 1899 as the day Dedekind died. He wrote the publisher saying that while 4 September might be correct, 1899 certainly was not, for on that day he had enjoyed a stimulating mathematical discussion with his dinner guest and honored friend, Georg Cantor. *VFR

1866 Reginald Aubrey Fessenden (6 Oct 1866, 22 Jul 1932) Canadian inventor and engineer with 300 patents. He broadcast the first program of voice and music. In 1893, Fessenden moved to Pittsburgh as the head of electrical engineering at the university, Fessenden read of Marconi's work and began experimenting himself. Marconi could only transmit Morse code. But Fessenden's goal was to transmit the human voice and music. He invented the "continuous wave": sound superimposed onto a radio wave for transmission. A radio receiver extracts the signal so the listener with the original sound. Fessenden made the first long-range transmissions of voice on Christmas Eve 1906 from a station at Brant Rock, Massachusetts, heard hundreds of miles out in the Atlantic.*TIS

1903 Ernest Thomas Sinton Walton(6 Oct 1903; 25 Jun 1995) Irish physicist, who was corecipient, with Sir John Douglas Cockcroft of England, of the 1951 Nobel Prize for Physics for the development of the first nuclear particle accelerator, known as the Cockcroft-Walton generator. The accelerator was built in a disused room in the Cavendish Laboratory, and supplied with several hundred kilovolts from a voltage multiplier circuit designed and built by Cockroft and Walton. On 14 Apr 1932 Walton turned the proton beam on to a lithium target. Despite all the odds against them, they succeeded in being the first to split the atom, and Walton was the first to see the reaction taking place. They identified the disintegration products as alpha particles (helium nuclei). *TIS

1908 Sergei Lvovich Sobolev (6 October 1908 – 3 January 1989) was a Soviet mathematician working in mathematical analysis and partial differential equations.*Wik

1918 Abraham Robinson (October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were incorporated into mathematics.*Wik

1936 Robert Phelan Langlands (October 6, 1936 - ) is a Canadian mathematician best known as the founder of the Langlands program, a vast web of conjectures and results connecting representation theory and automorphic forms to the study of Galois groups in number theory. He is an emeritus professor at the Institute for Advanced Study. Langlands has received the 1996 Wolf Prize (which he shared with Andrew Wiles), the 2005 AMS Steele Prize, the 1980 Jeffery-Williams Prize, the 1988 NAS Award in Mathematics from the National Academy of Sciences, the 2006 Nemmers Prize in Mathematics, and the 2007 Shaw Prize in Mathematical Sciences (with Richard Taylor) for his work on automorphic forms. *Wik Langlands occupies the office formerly held by Albert Einstein at Princeton. *Edward Frenkel, Love and Math

1950 Glen David Brin, (born October 6, 1950 - ) is an American scientist and award-winning author of science fiction. He has received the Hugo, Locus, Campbell and Nebula Awards.
Brin was born in Glendale, California in 1950. In 1973, he graduated from the California Institute of Technology with a Bachelor of Science in astrophysics. He followed this with a Master of Science in applied physics in 1978 and a Doctor of Philosophy in space science in 1981, both from the University of California, San Diego. He is a 2010 fellow of the Institute for Ethics and Emerging Technologies.*Wik

DEATHS
1809 Benjamin Peirce (4 Apr 1809, 6 Oct 1880) American astronomer, mathematician and educator who computed the general perturbations of the planets Uranus and Neptune. He was Harvard's Perkins Professor of Astronomy and Mathematics for nearly 40 years, and was largely responsible for introducing mathematics as a subject for research in American institutions. He is known especially for his contributions to analytic mechanics and linear associative algebra, but he is also remembered for his early work in astronomy and for playing a role in the discovery of Neptune. *TIS In number theory, he proved there is no odd perfect number with fewer than four prime factors. In algebra, he was notable for the study of associative algebras. He first introduced the terms idempotent and nilpotent in 1870 to describe elements of these algebras, and he also introduced the Peirce decomposition. *Wik

1840 François Budan de Boislaurent (28 Sept 1761, 6 Oct 1840) was a Haitian born amateur mathematician best remembered for his discovery of a rule which gives necessary conditions for a polynomial equation to have n real roots between two given numbers. Budan is considered an amateur mathematician and he is best remembered for his discovery of a rule which gives necessary conditions for a polynomial equation to have n real roots between two given numbers. Budan's rule was in a memoir sent to the Institute in 1803 but it was not made public until 1807 in Nouvelle méthode pour la résolution des équations numerique d'un degré quelconque. In it Budan wrote, "If an equation in x has n roots between zero and some positive number p, the transformed equation in (x - p) must have at least n fewer variations in sign than the original." *SAU (Sounds like a nice followup extension to Descartes Rule of signs in Pre-calculus classes. Mention the history, how many times do your students hear about a Haitian mathematician?)

Crelle Memorial in his hometown

1855 August Leopold Crelle (11 Mar 1780; 6 Oct 1855 at age 75). Although always interested in mathematics he lacked the money to enroll at a university and so became an engineer instead. In 1826, when he had the money, he founded the Journal f¨ur die rein und angewandte Mathematik and edited ﬁfty two volumes. Although not a great mathematician he had a gift for recognizing the abilities of such men as Abel, Jacobi, Steiner, Dirichlet, Pl¨ucker, M¨obius, Eisenstein, Kummer, and Weierstrass and oﬀered to publish their papers in his journal. *VFR As a civil engineer in the service of the Prussian Government and worked on the construction and planning of roads and the first railway in Germany (completed in 1838). He founded (1826) the world's oldest mathematical periodical still in existence, Journal für die reine und angewandte Mathematik ("Journal for Pure and Applied Mathematics"), now known as Crelle's Journal,and edited it for the rest of his life. In 1841, he was elected a foreign member of the Royal Swedish Academy of Sciences.*TIS

Monday, 5 October 2015

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 \)

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 Vedol Flight that took off from Sabishiro Beach. )

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 "Steve" Jobs (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 Markkulaand 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