## Saturday 31 August 2024

### On This Day in Math - August 31

The pursuit of the good and evil are now linked in astronomy as in almost all science. ... The fate of human civilization will depend on whether the rockets of the future carry the astronomer's telescope or a hydrogen bomb.
~Sir Bernard Lovell

The 243rd day of the year; 243 is the largest three digit number that can be expressed as a fifth power (35).

243 is also the sum of five consecutive prime numbers (41 + 43 + 47 + 53 + 59).

Venus' day is 243 Earth days. *Derek Orr

243 is a Harshad number, divisible by the sum of it's digits, and every permutation of its digits is also. Students should try to figure out why.

I have heard it was Feynman who first noted that 1/243 = .00 4 11 5 22 6 33 7 44 8 55 9 67 0 78 1 89 3..  If you think of the zero in 67 0 78 as the zero of a ten, you can understand the 67, 78, etc

243, like all odd numbers, is the difference in consecutive squares, 122^2-121^2 = 243, because it is 3 mod6 it is also the difference of two squares of integers that differ by 3, 42^2 - 39^2. And with multiple 3's you get more differences, 18^2 - 9^2

243 is a palindrome in base 8 (363)

3^3 + 6^3 = 243

On April 14, 2014,  Almost exactly a year after Yitang Zhang announced a proof (see April 17) that there are infinitely many pairs of prime numbers which differ by 70 million or less Terrance Tao's online group attack on the problem reduced the number to 243. Zhang's proof is the first to establish the existence of a finite bound for prime gaps, resolving a weak form of the twin prime conjecture.

EVENTS

1682 Michael Rolle published an elegant solution to a difficult problem publicly posed by Ozanam: Find four integers the difference of any two of which is a perfect square as well as the sum of the first three will be a perfect square. This brought him public recognition. *VFR Ozanam believed that the smallest of the four numbers that would satisfy these properties would have at least 50 digits. Rolle found four numbers, all satisfying the conditions Ozanam posed, containing only seven digits in each of the four numbers. *Michel Rolle and His Method of Cascades, Christopher Washington

He published his most important work Traité d'algèbre  in 1690 on the theory of equations. In this treatise, he invented the notation $\sqrt[�]{�}$ for the $�$th root of  and, as a consequence, it became the standard notation.  He is best known for Rolle's theorem (1691), and  is also the co-inventor in Europe of Gaussian elimination (1690).

$�$

1831, New London Bridge opened to traffic in London. In 1821, a committee was formed by Parliament to consider the poor condition of the existing centuries-old bridge. The arches had been badly damaged by the Great Freeze, so it was decided to build a new bridge. Building commenced under John Rennie in 1825, and completed in 1831, at the expense of the city. The bridge is composed of five arches, and built of Dartmoor granite. It was opened with great splendor by King William the fourth, accompanied by Queen Adelaide, and many of the members of the royal family, August 1st, 1831. In the 1960's it was auctioned and sold for \$2,460,000 to Robert McCulloch who moved it to Havasu City, Arizona. The rebuilt London Bridge was completed and dedicated on 10 Oct 1971. *TIS

In 1842, the U.S. Naval Observatory was authorized by an act of Congress, one of the oldest scientific agencies in the U.S. James Melville Gilliss (1811-1865) is considered its founder, who in 1842 he secured the Congressional appropriation for the Depot of Charts and Instruments (est. 1830) to become the Naval Observatory. Its primary task was to care for the Navy's charts, navigational instruments and chronometers, which were calibrated by timing the transit of stars across the meridian. Initially located at Foggy Bottom, the observatory moved in 1893 to its present facility in Washington, DC. Gillis visited Europe to procure instruments, and the books that formed the core of the Naval Observatory Library. Matthew Fontaine Maury was the first director, followed by Gillis (1861-65)*TIS

The time ball was one of the first systems to enable the Observatory to disseminate time to support remote users. The ball was dropped daily (except Sundays) at the astronomically determined instant of Mean Solar Noon in Washington, which enabled the navigators of ships anchored in the Potomac River to check the rates of their chronometers.

Depicted is the time ball atop the dome of the 9.6-inch refractor telescope at the USNO's Foggy Bottom site, its home from 1844 until 1893.

 *Navy.mil

1846 Le Verrier's announces his prediction of the location of the yet to be discovered planet Neptune. Using only mathematics and astronomical observations of the known planet Uranus and encouraged by physicist Arago, Director of the Paris Observatory, Le Verrier was intensely engaged for months in complex calculations to explain small but systematic discrepancies between Uranus's observed orbit and the one predicted from the laws of gravity of Newton. At the same time, but unknown to Le Verrier, similar calculations were made by John Couch Adams in England. Le Verrier announced his final predicted position for Uranus's unseen perturbing planet publicly to the French Academy on 31 August 1846, two days before Adams's final solution, which turned out to be 12° off the mark, was privately mailed to the Royal Greenwich Observatory. Le Verrier transmitted his own prediction by 18 September letter to Johann Galle of the Berlin Observatory. The letter arrived five days later, and the planet was found with the Berlin Fraunhofer refractor that same evening, 23 September 1846, by Galle and Heinrich d'Arrest within 1° of the predicted location near the boundary between Capricorn and Aquarius.

Some of the earliest recorded observations ever made through a telescope, Galileo Galilei's drawings on 28 December 1612 and 27 January 1613 contain plotted points that match up with what is now known to have been the positions of Neptune on those dates. On both occasions, Galileo seems to have mistaken Neptune for a fixed star when it appeared close—in conjunction—to Jupiter in the night sky. *Wik

 statue of Le Verrier

1869 Mary Ward was an Anglo Irish amateur scientist who was killed when she fell under the wheels of an experimental steam car built by her cousins. As the event occurred in 1869, she is the world's first known fatal motor vehicle accident victim."

Ward was a keen amateur astronomer, sharing this interest with her cousin William Parsons, 3rd Earl of Rosse. Parsons built the Leviathan of Parsonstown, a reflecting telescope with a six-foot mirror which remained the world's largest until 1917. *Wik

In 1886, the first U.S. earthquake on record with significant human consequence - the loss of some 100 lives - hit Charleston, S.C. and its massive effect spread through many eastern States. The epicenter was 15 miles northwest of Charleston, where 41 people died, 90 percent of the city's 6,956 brick buildings were damaged, and nearly all of its 14,000 chimneys were broken off at the roof. However, geologically the most severe earthquakes in U.S. history had occurred earlier in the century near the present town of New Madrid, Missouri (16 Dec 1811). The epicenter then was in a sparsely populated region and caused no known casualties, so the human consequences were relatively not significant, although the violent movement of the ground changed the course of the Mississippi River and created many new lakes.*TIS

Figure 7. Damage on Hayne Street, Charleston. (From Dutton, 1889.)  from U.S. GEOLOGICAL SURVEY CIRCULAR 985

1895, Count Ferdinand von Zeppelin patented in Germany his invention of the rigid airship, known as the Zeppelin. The overall cylindrical shape with rounded ends was covered with a cotton shell, framed with aluminium struts, wire-braced and contained a number of independent hydrogen balloons used for lift. Two or more seperate engines were suspended below for propulsion. The patent title, “Lenkbarer Luftfahrzug” (steerable air-cruising train), referred to a feature whereby additional cylindrical mid-segments could be connected together for a longer airship with greater carrying capacity, though none were ever made in this form. A similar U.S. patent was issued on 14 Mar 1899 for his “Navigable Balloon.” He made his first flight with the LZ-1 on 2 Jul 1900 over Lake Constance, Germany.

Image: First LZ 1 Ascent

1899 Cantor, in a letter to Dedekind, remarked that his “diagonal process” can be used to show that the power set of a set has more elements than the set itself. *VFR

1946 The New Yorker Magazine devoted its cover, and the entire issue to a ground breaking article by war correspondent John Hersey, Describing the actual after-effects of the Hiroshima bomb, exposing the suffering, and long-lasting effects of the bomb. The US military, US government, and General Groves had pushed the white-wash that there were no significant after-effects, and one spokesman described the bomb as a "nice way to die."

1950 G¨odel addressed the International Congress of Mathematicians, in Cambridge, Massachusetts, on his work in relativity theory. *VFR

At the International Congress at Toronto in 1924 it had been decided that at each international mathematical congress two gold medals should be awarded. Professor J C Fields, the Secretary of the 1924 Congress, presented a fund to subsidise these medals. They were first awarded in Oslo in 1936. The Committee to select the winners of the 1950 medals was: Professor Harald Bohr (Chairman), Professors L V Ahlfors, Karol Borsuk, Maurice Fréchet, W V D Hodge, A N Kolmogorov, D Kosambi, and Marston Morse.

The medals in 1950 were awarded to Professor Laurent Schwartz of the University of Nancy and to Professor Atle Selberg of the Institute for Advanced Study. Professor Bohr gave an excellent résumé of the work of Schwartz on distributions and of the work of Selberg on the Riemann zeta function and his elementary proof of the celebrated prime number theorem.

Professor Bohr gave an excellent résumé of the work of Schwartz on distributions and of the work of Selberg on the Riemann zeta function and his elementary proof of the celebrated prime number theorem.

 Prof. Harald Bohr

1994 Aldus Corp. and Adobe Systems Inc. finalized their merger. The two companies hoped to combine forces in creating powerful desktop publishing software, building on the field Aldus founder Paul Brainerd had created in 1985 with his PageMaker software. Pagemaker was one of three components to the desktop publishing revolution. The other two were the invention of Postscript by Adobe and the LaserWriter laser printer from Apple. All three were necessary to create a desktop publishing environment.

1994 David Charles Hahn, later called the "Radioactive Boy Scout" or the "Nuclear Boy Scout", attracted the attention of local police when he was stopped on another matter and they found material in his vehicle that troubled them and he warned that it was radioactive. The gift of a Chemistry set at age twelve sparked his interest, first to make nitroglycerin and then, at age seventeen, to build a homemade breeder nuclear reactor. A Scout in the Boy Scouts of America, Hahn conducted his experiments in secret in a backyard shed at his mother's house in Commerce Township, Michigan. His mother's property was cleaned up by the Environmental Protection Agency ten months later as a Superfund cleanup site. Hahn attained Eagle Scout rank shortly after his lab was dismantled. *R. R. Johnson, Romancing the Atom

2012 A Blue Moon, or the second of two full moons in a single month. August 2012 will have a blue moon on August 31 The last month with two full moons was March of 2010 March 1 and March 30. The next month with a blue moon will be in January of 2018. Once in a Blue moon really isn’t all that often.
Their are alternate definitions for blue moon,f or instance the fourth moon in a quarter.  For that you have to wait until June of 2019. Tonight in 2023 will be the first Blue Moon since 2018.  The nexr blue moon will be on May 31, 2026.

2012 "Japanese mathematician Shinichi Mochizuki posted four papers on the Internet.
The titles were inscrutable. The volume was daunting: 512 pages in total. The claim was audacious: he said he had proved the ABC Conjecture, a famed, beguilingly simple number theory problem that had stumped mathematicians for decades." From The Paradox of the Proof
by Caroline Chen
.

BIRTHS

1663 Guillaume Amontons (31 Aug 1663; 11 Oct 1705)French physicist, who developed the air thermometer - which relies on increase in volume of a gas (rather than a liquid) with temperature - and used it (1702) to measure change in temperature in terms of a proportional change in pressure. This observation led to the concept of absolute zero in the19th century. Deaf since childhood, Amontons worked on inventions for the deaf, such as the first telegraph, which relied on a telescope, light, and several stations to transmit information over large distances. Amontons' laws of friction, relied upon by engineers for 300 years, state that the frictional force on a body sliding over a surface is proportional to the load that presses them together and is also independent of the areas of the surfaces. *TIS

1821 Hermann Ludwig Ferdinand von Helmholtz (31 Aug 1821; 8 Sep 1894) was a German scientist who contributed much to physiology, optics, electrodynamics, mathematics, and meteorology, including the law of the conservation of energy (1847). He also developed thermodynamics, in particular introducing concept of free energy. In 1850, he measured the speed of a nerve impulse and, in 1851, invented the ophthalmoscope. He discovered the function of the cochlea in the inner ear and developed Thomas Young's theory of color vision (published 1856). His study of muscle action led him to formulate a much more accurate theory concerning the conservation of energy than earlier proposed by Julius Mayer and James Joule. *TIS

1837 Édouard Jean-Marie Stephan (31 August 1837 – 31 December 1923) was a French astronomer. His surname is sometimes spelled Stéphan in some literature, but this is apparently erroneous.  He was born in Sainte Pezenne (today one of the districts of the town of Niort) and attended the Ecole Normale Superieure, and graduated at the top of his class in 1862.

He was the director of the Marseille Observatory from 1864 to 1907 (until 1872 he was subordinate to Urbain le Verrier). In the early part of his career there, he had limited opportunities to do observations because he was preoccupied with improving the observatory. He discovered the asteroid 89 Julia in 1866. In 1867 he used the new telescope to observe a transit of Mercury. *Wik

The Marseilles Observatory had a new reflecting telescope built by Leon Foucault, the first to have a mirror ground from glass. *LH

1848 Emil Weyr
(1 July 1848 in Prague, Bohemia (now Czech Republic) - 25 Jan 1894 in Vienna, Austria) His father Frantisek Weyr, was a professor of mathematics at a realschule (secondary school) in Prague from 1855. Emil was four years older than his brother Eduard Weyr who also became a famous mathematician. Emil attended the realschule in Prague where his father taught, then studied at the Prague Polytechnic from 1865 to 1868 where he was taught geometry by Vilém Fiedler.
He studied in Italy with Cremona and Casorati during the academic year 1870-71 returning to Prague where he continued to teach. In 1872 he was elected to be Head of the Union of Czech Mathematicians and Physicists. In 1875 he was appointed as professor of mathematics at the University of Vienna. He, together with his brother Eduard Weyr, were the main members of the Austrian geometric school. They were interested in descriptive geometry, then in projective geometry and their interests turned towards algebraic and synthetic methods in geometry. Among many works Emil Weyr published were Die Elemente der projectivischen Geometrie and Über die Geometrie der alten Aegypter.
Emil Weyr led the geometry school in Vienna throughout the 1880's up until his death. Together with Gustav von Escherich, Emil Weyr founded the important mathematical journal Monatshefte fuer Mathematik und Physik in 1890. The first volumes of the journal contain papers written by his brother Eduard. In 1891 Emil Weyr became one of the first 19 founder members of the Royal Czech Academy of Sciences. *SAU

1864 Robert Hardie (31 Aug 1864 in George Street, Edinburgh, Scotland - 9 March 1942 in Edinburgh, Scotland) graduated from Oxford and occupied various posts in the Philosophy department of Edinburgh University. He was a founder member of the EMS. *SAU

1880 Heinrich Franz Friedrich Tietze (August 31, 1880 – February 17, 1964) contributed to the foundations of general topology and developed important work on subdivisions of cell complexes. The bulk of this work was carried out after he took up the chair at Munich in 1925.*SAU He is remimbered for the Tietze extension theorem. He also developed the Tietze transformations for group presentations, and was the first to pose the group isomorphism problem.
He was born in Schleinz, Austria and died in Munich, Germany. *Wik

1884  George Alfred L´eon Sarton, (August 31, 1884; Ghent, Belgium - March 22, 1956, Cambridge, Massachusetts) ,historian of science and founder of the journal Isis. *VFR Sarton intended to complete an exhaustive nine volume history of science — which, during the preparation of the second volume, induced him to learn Arabic and travel around the Middle East inspecting original manuscripts of Islamic scientists — but at the time of his death only the first three volumes had been completed. (I. From Homer to Omar Khayyam. — II. From Rabbi Ben Ezra to Roger Bacon, pt. 1-2. — III. Science and learning in the fourteenth -century, pt. 1-2. 1927-48.) The project was inspired by his study of Leonardo da Vinci but the period of Leonardo's life was not reached before the death of Sarton.

He is considered the founder of the discipline of the history of science as an independent field of study.

He established the journal Isis, a quarterly peer-reviewed academic journal published by the University of Chicago Press. It covers the history of science, history of medicine, and the history of technology, as well as their cultural influences.*Wik

1885 Herbert Westren Turnbull (31 Aug 1885; 4 May 1961)English mathematician who made extensive and notable contributions to the study of algebraic invariants and concomitants of quadratics. Turnbull was also interested in the history of mathematics, writing The Mathematical Discoveries of Newton (1945), and began work on the Correspondence of Isaac Newton.*TIS

1913 Sir Alfred Charles Bernard Lovell (31 Aug 1913, ) is an English radio astronomer who established and directed (1951-81) Jodrell Bank Experimental Station, Cheshire, England, with (then) the world's largest steerable radiotelescope, now named after him Prior to WW II, he worked at Manchester University on cosmic ray research. During the war, he helped develop aircraft onboard radar systems. After the war, to escape interference to radar equipment from city trams, he moved his research to the University's more remote Jodrell Bank property. In 1946, he showed that radar echoes could detect optically invisible daytime meteor showers. He gained funding to build the 250-ft-diam. telescope. When completed in 1957, it was able to track the first artificial satellite, Sputnik I. *TIS

 The Lovell Telescope at Jodrell Bank, *wik

1916 Robert Hanbury Brown (31 Aug 1916; 16 Jan 2002) British astronomer who was a pioneer in radar and observational astronomy. During and after WW II he worked with R.A. Watson-Watt and then E.G. Bowen to develop radar for uses in aerial combat. In the 1950s he applied this experience to radio astronomy, developing radio-telescope technology at Jodrell Bank Observatory and mapping stellar radio sources. He designed a radio interferometer capable of resolving radio stars while eliminating atmospheric distortion from the image (1952). With R.Q. Twiss, Brown applied this method to measuring the angular size of bright visible stars, thus developing the technique of intensity interferometry. They set up an intensity interferometer at Narrabri in New South Wales, Australia, for measurements of hot stars.*TIS

DEATHS

1721 John Keill (1 Dec 1671, 31 Aug 1721) Scottish mathematician and natural philosopher, who was a major proponent of Newton’s theories. He began his university education at Edinburgh under David Gregory, whom he followed to Oxford, where Keill lectured on Newton's work, and eventually became professor of astronomy. In his book, An Examination of Dr. Burnett's Theory of the Earth (1698), Keill applied Newtonian principles challenging Burnett's unsupportable speculations on Earth's formation. In 1701, Keill published Introductio ad Veram Physicam, which was the first series of experimental lectures and provided a clear and influential introduction to Isaac Newton’s Principia. He supported Newton against priority claims by Leibnitz for the invention of calculus.*TIS

1811 Louis-Antoine de Bougainville (12 November 1729 – 31 August 1811) was a French soldier and explorer who wrote a calculus book, but is better known for his other exploits.*SAU A contemporary of James Cook, he took part in the French and Indian War and the unsuccessful French attempt to defend Canada from Britain. He later gained fame for his expeditions to settle the Falkland Islands and his voyages into the Pacific Ocean.*Wik

1918 André-Louis Cholesky (October 15, 1875, August 31, 1918, ) was a French military officer and mathematician. He worked in geodesy and map-making, was involved in surveying in Crete and North Africa before World War I. But he is primarily remembered for the development of a matrix decomposition known as the Cholesky decomposition which he used in his surveying work. He served the French military as engineer officer and was killed in battle a few months before the end of World War I; his discovery was published posthumously by his fellow officer in the "Bulletin Géodésique". *Wik

1945 Stefan Banach died. (30 Mar 1892, 31 Aug 1945) Polish mathematician who founded modern functional analysis and helped develop the theory of topological vector spaces. In addition, he contributed to measure theory, integration, the theory of sets, and orthogonal series. In his dissertation, written in 1920, he defined axiomatically what today is called a Banach space. The idea was introduced by others at about the same time (for example Wiener introduced the notion but did not develop the theory). The name 'Banach space' was coined by Fréchet. Banach algebras were also named after him. The importance of Banach's contribution is that he developed a systematic theory of functional analysis, where before there had only been isolated results which were later seen to fit into the new theory. *TIS

1950 Subbayya Sivasankaranarayana Pillai (April 5, 1901 Nagercoil, Tamil Nadu - 31 August 1950, Cairo, Egypt) was an Nagercoil native Indian mathematician specializing in number theory. His contribution to Waring's problem was described in 1950 by K. S. Chandrasekharan as "almost certainly his best piece of work and one of the very best achievements in Indian Mathematics since Ramanujan". In number theory, a Pillai prime, named for him, is a prime number p for which there is an integer n > 0 such that the factorial of n is one less than a multiple of the prime, but the prime is not one more than a multiple of n. To put it algebraically, $n! \equiv -1 \mod p$ but $p \not\equiv 1 \mod n$. The first few Pillai primes are 23, 29, 59, 61, 67, 71, 79, 83, 109, 137, 139, 149, 193, ... (sequence A063980 in OEIS). *Wik

2005 Sir Joseph Rotblat (4 Nov 1908, 31 Aug 2005)Polish-born British physicist who is a leading critic of nuclear weaponry. Rotblat and the Pugwash Conferences, "for their efforts to diminish the part played by nuclear arms in international politics and in the longer run to eliminate such arms," received the Nobel Peace Prize in 1995. Forty years earlier, he and other scientists, with philosopher Bertrand Russell and Albert Einstein, published a manifesto calling on researchers to take responsibility for their work, particularly those working on the atomic bomb. This led to the Pugwash Conferences on Science and World Affairs, first convened in 1957 in Pugwash, Nova Scotia, Canada. He was secretary-general (1957-73), and president (from 1988) of this London-based worldwide organization. *TIS

1946 Nigel John Kalton (June 20, 1946 – August 31, 2010) was a British-American mathematician, known for his contributions to functional analysis.

After studying mathematics at Trinity College, Cambridge, he received his PhD, which was awarded the Rayleigh Prize for research excellence, from Cambridge University in 1970. He then held positions at Lehigh University in Pennsylvania, Warwick, Swansea, University of Illinois, and Michigan State University, before becoming full professor at the University of Missouri, Columbia, in 1979.

He received the Stefan Banach Medal from the Polish Academy of Sciences in 2005] A conference in honour of his 60th birthday was held in Miami University of Ohio in 2006. He died in Columbia, Missouri, aged 64.

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