The mathematical (and other) thoughts of a (now retired) math teacher,
Saturday, 15 June 2024
On This Day in Math - June 15
A statistician is someone who is good with numbers
but lacks the personality to be an accountant.
~unknown (my apologies to all the statisticians out there)
The 166th day of the year; the reverse (661) of 166 is a prime. If you rotate it 180o (991) it is also prime. The same is true if you put zeros between each digit (60601). *Prime Curios 90901, 9091, and 9901 are all prime,
166, like 164, uses all the Roman digits from 100 down, once each. A difference is that 166 uses them in order of their size, CLXVI
166!-1 is a factorial minus one prime. It has 298 digits. (For which n is N! -1 or n! + 1 a prime? hint: there are thirteen year days (\ n<366 \) for which n! +1 is prime
166 is the sum of three consecutive triangular numbers, 166 = T9 + T10 + T11
166 in binary has the same number of 1's and 0's. There are 35 8-digit numbers with this property
166 is a Smith number, since the sum of its digits (13) coincides with the sum of the digits of its prime factors.
762 BC An eclipse more than 27 centuries old is regarded as one of the earliest events that can be pinpointed by scholars of the Near East. The June 15, 762 B.C. total solar eclipse is mentioned in Assyrian texts as well as the Book of Amos in the Hebrew Bible. While hotly debated (at least among archeo-astronomical types, who love to debate such things) the mention of this eclipse serves as a valuable reference point between ancient Assyrian and Hebrew chronology.*listosaur.com
1641 In a letter to Bernard Frenicle de Bessy, Fermat called the theorem that every prime of the form 4n+1 is the sum of two squares, the fundamental theorem of right triangles. He stated that he had a proof that was "irrefutable". Later he suggested he had a proof by infinite descent. Euler is credited with the first correct proof of the theorem, still called Fermat's theorem. Euler, after much effort, found a solution based on infinite descent. He announced it in two letters to Goldbach, on May 6, 1747 and on April 12, 1749; he published the detailed proof in two articles (between 1752 and 1755). Lagrange gave a proof in 1775 that was based on his study of quadratic forms. This proof was simplified by Gauss in his Disquisitiones Arithmeticae.
Fermat Statue, Beaumont-de-Lomagne *Wik
In 1752, Ben Franklin's kite-flying experiment proved lightning and electricity were related while flying a kite with a key attached. In Sep 1752, he equipped his house with a lightning rod, connecting it to bells that ring when rod is electrified. He explained how to perform a kite experiment in the 19 Oct 1752 issue of the Pennsylvania Gazette. He had earlier proposed use of lightning rods to protect houses in a 2 Mar 1750 letter to Collinson and in the same year, on 29 Jul 1750, he devised an experiment involving a sentry-box with a pointed rod on its roof, to be erected on hilltop or in church steeple, with rod attached to a Leyden jar which would collect the electrical charge, and thus prove lightning to be a form of electricity. *TIS
*HULTON ARCHIVE/GETTY IMAGES
1785 Pilâtre de Rozier became aviation’s first casualty when he died attempting the second aerial crossing of the English Channel. Rozier had piloted the first manned flight in a balloon from Paris in 1783. He and other supporters of Hydrogen balloons had competed with the Montgolfier brothers and supporters of the hot air ballons. Pilatre had reasoned that since both hydrogen and hot-air balloons had their separate advantages a combination of the two would be even better. Rozier was accustomed to living dangerously—one of his favorite chemical lecture-demonstrations consisted of flushing his lungs with hydrogen and then speaking in the resulting high-pitched voice (today we tend to use helium). The final flourish (today we would tend to omit this!) was to light the hydrogen as it issued from his mouth. Such a man was obviously the “Right Stuff” to fly a hybrid hot-air-hydrogen balloon. Alas, his luck ran out, and he and a companion crashed shortly after takeoff from Boulogne. *Derek A. Davenport, How the Right Professor Charles Went Up in the Wrong Kind of Balloon; ChemMatters December 1983 Page 14, American Chemical Society (See Deaths below)
A 1786 illustration of the Montgolfier brothers’ hot air balloon, flown by de Rozier and M. le Marquis d’Arlandes, 21 November 1783.
*ThisDayInAviation
1857 The Great Comet that didn't come, but still created panic. Astronomers became convinced of the periodic nature of many comets, and loose speculation began about their possible times of return.
an obscure prediction, apparently originally made by the German (or Belgian) Laensberg in his Liege Almanac, In his entry for the week commencing 15 Jun 1857, Laensberg had warned, “about this time, expect a comet”. Through the vagaries of reporting, this eventually came to be understood to be a specific prediction that not only would the comet appear on that date, but that it would also collide with the Earth, and that this would result in the end of the World. While this prediction was treated with scorn by many, it was also taken very seriously by large parts of the population. All this was a fertile field for satirists such as the French caricaturist Honoré Daumier. He gently mocked the Parisians’ comet obsession in a series of cartoons published in Le Charivari, and represented the offending German prognosticator as a magician playing a magic trick by releasing a comet-like duck. The joke, of course, was that the French for duck, “canard”, also means “hoax”
1915 The U.S. minted the only octagon-shaped coin in U.S. history. The coin was one of two $50 coins (the other one was round) issued as part of a set of five commemorative gold coins designed for the Panama-Pacific International Exposition held in San Francisco between February and December 1915. One hundred years later the coins trade for over a quarter-million dollars each. *Felicity Nie, Ready for Zero Blog
1949 Jay Forrester recorded a proposal for core memory in his notebook. A professor at MIT at the time, Forrester eventually installed magnetic core memory on the Whirlwind computer. Core memory made computers more reliable, faster, and easier to make. Such a system of storage remained popular until the development of semiconductors in the 1970s. *CHM
2015 Astronomers discovered the most powerful supernova ever seen, a star in a galaxy billions of light-years away that exploded with such force it briefly shone nearly 600 billion times brighter than our Sun and 20 times brighter than all the stars in the Milky Way combined. The explosion released 10 times more energy than the Sun will radiate in 10 billion years.
Discovered by ASAS-SN’s twin 14-centimeter telescopes operating in Cerro Tololo, Chile, the supernova just appeared as a transient dot of light in an image, and wasn’t immediately recognized as particularly special. *scientificamerican
Beijing Planetarium / Jin Ma / Wayne Rosing (artist rendering)
BIRTHS
1640 Bernard Lamy(15 June 1640, in Le Mans, France – 29 January 1715, in Rouen) was a French mathematician who wrote on geometry and mechanics. He developed the idea of a parallelogram of forces at about the same time as Newton and Verignon. The Law of Sines as applied to three static forces in mechanics is sometimes called Lamy's Rule.
1765 Henry T. Colebrook (June 15, 1765 – March 10, 1837) Sanscrit Scholar and British civil servant in India who translated "algebra with arithmetic and mensuration, from the sanscrit of Brahmagupta and Bhascara." *Wik 1765 Johann Gottlieb Friedrich von Bohnenberger (15 June 1765 – 19 April 1831) was born at Simmozheim, Württemberg. He studied at the University of Tübingen. In 1798, he was appointed professor of mathematics and astronomy at the University. He published: Anleitung zur geographischen Ortsbestimmung, (1795); Astronomie, (1811); and Anfangsgründe der höhern Analysis, (1812). In 1817, he systematically explained the design and use of a gyroscope apparatus which he called simply a “Machine.” Several examples of the 'Machine' were constructed by Johann Wilhelm Gottlob Buzengeiger of Tübingen. Johann Friedrich Benzenberg had already mentioned Bohnenberger's invention (describing it at length) in several letters beginning in 1810. *Wik
1884 William Watson (15 June 1884 in Musselburgh, East Lothian, Scotland -28 June 1952 in Edinburgh, Scotland) William Watson graduated in Mathematics and Physics from Edinburgh University. He became head of the Physics department at Heriot Watt College in Edinburgh. *SAU 1894 Nikolai Tschebotarjow (15 June[O.S. 3 June]1894 – 2 July 1947) or Chebotaryov proved his density theorem generalizing Dirichlet's theorem on primes in an arithmetical progression. *SAU (both spellings are used)
He was a student of Dmitry Grave, a Russian mathematician. Chebotaryov worked on the algebra of polynomials, in particular examining the distribution of the zeros. He also studied Galois theory and wrote a textbook on the subject titled Basic Galois Theory. His ideas were used by Emil Artin to prove the Artin reciprocity law. He worked with his student Anatoly Dorodnov on a generalization of the quadrature of the lune, and proved the conjecture now known as the Chebotaryov theorem on roots of unity.*Wik
1906 (William) Gordon Welchman (June 15, 1906, Bristol, England – October 8, 1985, Newburyport, Massachusetts, USA) was a British mathematician, university professor, World War II codebreaker at Bletchley Park, and author. Just before World War II, Welchman was invited by Commander Alastair Denniston to join the Government Code & Cypher School at Bletchley Park, in case war broke out. He was one of four early recruits to Bletchley (the others being Alan Turing, Hugh Alexander, and Stuart Milner-Barry), who all made significant contributions at Bletchley, and who became known as 'The Wicked Uncles'. They were also the four signatories to an influential letter, delivered personally to Winston Churchill in October 1941, asking for more resources for the code-breaking work at Bletchley Park. Churchill responded with one of his 'Action This Day' written comments. Welchman moved to the United States in 1948, and taught the first computer course at MIT in the United States. He followed this by employment with Remington Rand and Ferranti. He became a naturalised American citizen in 1962. In that year, he joined the MITRE Corporation, working on secure communications systems for the US military. He retired in 1971, but was still retained as a consultant. In 1982 his book The Hut Six Story was published by McGraw-Hill in the USA, and by Allen Lane in Britain. The National Security Agency disapproved. The book was not banned, but Welchman lost his security clearance (and therefore his consultancy with MITRE), and was forbidden to discuss with the media either the book or his wartime work. Welchman died in 1985. His final conclusions and corrections to the story of wartime codebreaking were published posthumously in 1986 in the paper 'From Polish Bomba to British Bombe: the birth of Ultra' in Intelligence & National Security, Vol 1, No l. The entire paper was included in the revised edition of The Hut Six Story published in 1997 by M & M Baldwin. *Wik
1916 Herbert Alexander Simon (June 15, 1916 – February 9, 2001) was an American social scientist who was a pioneer of the development of computer artificial intelligence. In 1956, with his long-time colleague Allen Newell, Simon produced the computer program, The Logic Theorist, a computer program that could discover proofs of geometric theorems. It was the first computer program capable of thinking, and marked the beginning of what would become known as artificial intelligence. It proved many of the theorems of symbolic logic in Whitehead and Russell's Principia Mathematica. He is further known for his contributions in fields including psychology, mathematics, statistics, and operations research, all of which he synthesized in a key theory for which he won the 1978 Nobel Prize for economics. *TIS
1933 Moshe Carmeli (June 15, 1933 - Sept 27, 2007) was the Albert Einstein Professor of Theoretical Physics, Ben Gurion University (BGU), Beer Sheva, Israel and President of the Israel Physical Society. He received his D.Sc. from the Technion-Israel Institute of Technology in 1964. He became the first full professor at BGU's new Department of Physics. He did significant theoretical work in the fields of cosmology, astrophysics, general and special relativity, gauge theory, and mathematical physics, authoring 4 books, co-authoring 4 others, and publishing 128 refereed research papers in various journals and forums, plus assorted other publications (146 in all). He is most notable for his work on gauge theory and his development of the theory of cosmological general relativity, which extends Albert Einstein's theory of general relativity from a four-dimensional spacetime to a five-dimensional space-velocity framework.
DEATHS
1734 Giovanni Ceva (December 7, 1647 – June 15, 1734) was an Italian mathematician widely known for proving Ceva's theorem in elementary geometry. His brother, Tommaso Ceva was also a well known poet and mathematician. *Wik
Ceva's theorem is a theorem in elementary geometry. Given a triangle ABC, and points D, E, and F that lie on lines BC, CA, and AB respectively, the theorem states that lines AD, BE and CF are concurrent, if and only if,
where AF indicates the directed distance between A and F (i.e. distance in one direction along a line is counted as positive, and in the other direction is counted as negative). There is also an equivalent trigonometric form of Ceva's Theorem, that is, AD,BE,CF concur if and only if
The theorem was proved by Giovanni Ceva in his 1678 work De lineis rectis, but it was also proven much earlier by Yusuf Al-Mu'taman ibn Hűd, an eleventh-century king of Zaragoza.
Associated with the figures are several terms derived from Ceva's name: cevian (the lines AD, BE, CF are the cevians of O), cevian triangle (the triangle DEF is the cevian triangle of O); cevian nest, anticevian triangle, Ceva conjugate. (Ceva is pronounced Chay'va; cevian is pronounced chev'ian.)*Wik
1785 Jean-François Pilatre de Rozier (30 March 1754 – 15 June 1785)French physicist and aeronaut who, with Marquis Francois Laurant d'Arlandes, became the first men to fly. Their hot-air balloon, built by the Montgolfier brothers, lifted off from La Muettte, a royal palace in the Bois de Boulogne, Paris. They flew nearly 6 miles in 25 mins, reaching an altitude of around 300-ft. King Louis XVI, who offered to send two prisoners for the test flight, but Rozier wanted to deny criminals the glory of being the first men to go into the atmosphere. Rozier died in attempt to cross English Channel in an apparatus composed of two balloons, one filled with hydrogen and the other with warm air. Thus, he was also the first man to die in an air crash. *TIS
1917 Kristian Olaf Bernhard Birkeland (born 13 December 1867 in Christiania (today's Oslo) – 15 June 1917 in Tokyo, Japan) was a Norwegian scientist, professor of physics at the Royal Fredriks University in Oslo. He is best remembered for his theories of atmospheric electric currents that elucidated the nature of the aurora borealis. In order to fund his research on the aurorae, he invented the electromagnetic cannon and the Birkeland–Eyde process of fixing nitrogen from the air. Birkeland was nominated for the Nobel Prize seven times.
Birkeland organized several expeditions to Norway's high-latitude regions where he established a network of observatories under the auroral regions to collect magnetic field data. The results of the Norwegian Polar Expedition conducted from 1899 to 1900 contained the first determination of the global pattern of electric currents in the polar region from ground magnetic field measurements.
Birkeland proposed in 1908 in his book The Norwegian Aurora Polaris Expedition 1902–1903 that polar electric currents, today referred to as auroral electrojets, were connected to a system of currents that flowed along geomagnetic field lines into and away from the polar region. Such field-aligned currents are known today as Birkeland currents in his honour. He provided a diagram of field-aligned currents in the book. The book on the 1902–1903 expedition contains chapters on magnetic storms on the Earth and their relationship to the Sun, the origin of the Sun itself, Halley's comet, and the rings of Saturn.
Birkeland's vision of what are now known as Birkeland currents became the source of a controversy that continued for over half a century, because their existence could not be confirmed from ground-based measurements alone. His theory was disputed and ridiculed at the time as a fringe theory by mainstream scientists, most notoriously by the eminent British geophysicist and mathematician Sydney Chapman who argued the mainstream view that currents could not cross the vacuum of space and therefore the currents had to be generated by the Earth. Birkeland's theory of the aurora continued to be dismissed by mainstream astrophysicists after his death in 1917.
Proof of Birkeland's theory of the aurora only came in 1967 after a probe was sent into space. The crucial results were obtained from U.S. Navy satellite 1963-38C, launched in 1963 and carrying a magnetometer above the ionosphere. Magnetic disturbances were observed on nearly every pass over the high-latitude regions of the Earth. These were originally interpreted as hydromagnetic waves, but on later analysis it was realized that they were due to field-aligned or Birkeland currents.
Norwegian 200-kroner banknote,
*APS Org
1922 Frederick William Sanderson (13 May 1857 – 15 June 1922) was headmaster of Oundle School from 1892 until his death. He was an education reformer, and both at Oundle, and previously at Dulwich College where he had started as assistant master, he introduced innovative programs of education in engineering. Under his headmastership, Oundle saw a reversal of a decline from which it had been suffering in the middle of the 19th century, with school enrollment rising from 92 at the time of his appointment to 500 when he died.
Sanderson was the inspiration for the progressive headmaster character in H. G. Wells' novel Joan and Peter. Wells had sent his own sons to Oundle, and was friendly with Sanderson. After Sanderson's death, which occurred shortly after delivering an address to Wells and others, Wells initially worked on his official biography, entitled Sanderson of Oundle, but later abandoned it in favor of an unofficial biography, The Story of a Great Schoolmaster. *Wik
1938 Hans Fitting (13 November, 1906 – 15 June, 1938) was a mathematician who worked in group theory. Hans Fitting's father, Prof Dr Friedrich Fitting (1862-1945), was a graduate secondary school teacher and a research mathematician who published over twenty papers. Friedrich Fitting is best known today for giving a proof, in 1931, that there are exactly 880 magic squares of order 4. These 880 magic squares had been given by Frenicle de Bessy in 1693 but no proof was found until Friedrich Fitting's 1931 paper appeared. He taught his son Hans in school and was thus able to quickly recognize his son's extraordinary mathematical talent. With his father's challenge to his understanding of the subject, Hans soon progressed far beyond what was customary for his age.
From 1925 to 1932 Fitting studied mathematics, physics and philosophy at the Universities of Tübingen and Göttingen, where he was awarded his Ph.D. in 1932 for his work on group theory. His thesis advisor at Göttingen was Emmy Noether.
Among the many mathematical achievements of Fitting we note that he gave a proof of the Remak-Krull-Schmidt theorem on the uniqueness of the direct product decomposition of groups into indecomposable subgroups, even for groups of operators. He devoted himself to an investigation of the ideal theory of noncommutative rings and also studied the theory of determinant ideals of finitely generated modules over a commutative ring R
Today,he is known as well as for Fitting's Lemma, he is remembered for the 'Fitting subgroup' which is used in the structure theory of finite groups.
1971 Wendell Meredith Stanley (16 August 1904 – 15 June 1971) was an American biochemist, virologist and Nobel laureate. Stanley was born in Ridgeville, Indiana, and earned a BS in Chemistry at Earlham College in Richmond, Indiana. He then studied at the University of Illinois, gaining an MS in science in 1927 followed by a Ph.D. in chemistry two years later. His later accomplishments include writing the book "Chemistry: A Beautiful Thing" and achieving his high stature as a Pulitzer Prize nominee. Stanley was awarded the Nobel Prize in Chemistry for 1946. His other notable awards included the Rosenburger Medal, Alder Prize, Scott Award, and the AMA Scientific Achievement Award. He was also awarded honorary degrees by many universities both American and foreign, including Harvard, Yale, Princeton and the University of Paris. Most of the conclusions Stanley had presented in his Nobel-winning research were soon shown to be incorrect (in particular, that the crystals of mosaic virus he had isolated were pure protein, and assembled by autocatalysis) Stanley married Marian Staples (1905-1984) in 1929 and had three daughters (Marjorie, Dorothy and Janet), and a son, (Wendell M. Junior). Stanley Hall at UC Berkeley (now Stanley Biosciences and Bioengineering Facility) and Stanley Hall at Earlham College are named in his honor. *Win
1995 John Vincent Atanasoff, OCM, (October 4, 1903 – June 15, 1995) was an American physicist and inventor credited with inventing the first electronic digital computer. Built in 1937-42 at Iowa State University by Atanasoff and a graduate student, Clifford Berry, it introduced the ideas of binary arithmetic, regenerative memory, and logic circuits. These ideas were communicated from Atanasoff to John Mauchly, who used them in the design of the better-known ENIAC built and patented several years later. On 19 Oct 1973, a US Federal Judge signed his decision following a lengthy court trial which declared the ENIAC patent invalid and named Atanasoff the original inventor of the electronic digital computer, the Atanasoff- Berry Computer or the ABC.*TiS
2013 Kenneth Geddes "Ken" Wilson (June 8, 1936 – June 15, 2013) was an American physicist who was awarded the 1982 Nobel Prize for Physics for his development of a general procedure for constructing improved theories concerning the transformations of matter called continuous, or second-order, phase transitions. These take place at characteristic temperatures (or pressures), but unlike first-order transitions they occur throughout the entire volume of a material as soon as that temperature (called the critical point) is reached. One example of such a transition is the complete loss of ferromagnetic properties of certain metals when they are heated to their Curie points (about ºC for iron). Wilson's work provided a mathematical strategy for constructing theories that could apply to physical systems near the critical point. *TiS
Credits : *CHM=Computer History Museum *FFF=Kane, Famous First Facts *NSEC= NASA Solar Eclipse Calendar *RMAT= The Renaissance Mathematicus, Thony Christie *SAU=St Andrews Univ. Math History *TIA = Today in Astronomy *TIS= Today in Science History *VFR = V Frederick Rickey, USMA *Wik = Wikipedia *WM = Women of Mathematics, Grinstein & Campbell
762 BC An eclipse more than 27 centuries old is regarded as one of the earliest events that can be pinpointed by scholars of the Near East. The June 15, 762 B.C. total solar eclipse is mentioned in Assyrian texts as well as the Book of Amos in the Hebrew Bible. While hotly debated (at least among archeo-astronomical types, who love to debate such things) the mention of this eclipse serves as a valuable reference point between ancient Assyrian and Hebrew chronology.*listosaur.com
Ceva's theorem is a theorem in elementary geometry. Given a triangle ABC, and points D, E, and F that lie on lines BC, CA, and AB respectively, the theorem states that lines AD, BE and CF are concurrent, if and only if,
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