not too difficult, amusing, and without peril to the state.
~Plato
On non-leap years, this is the 217th day of the year; 217 is both the sum of two positive cubes and the difference of two positive consecutive cubes in exactly one way: 217 = 63 + 13 = 93 − 83. (How frequently would the difference of two consecutive cubes also be expressible as the sum of two cubes?)
on leap years this is the 218th day of the year; 218 = 72 + 132
218 is the number of nonequivalent ways to color the 12 edges of a cube using at most 2 colors, where two colorings are equivalent if they differ only by a rotation of the cube.
218 is the smallest number with a Merten funtion =3. (an acceptable definition for students is that the Merten number for n, M(n), is the count of square-free integers up to n that have an even number of prime factors, minus the count of those that have an odd number.) The function is named in honor of Franz Merten, who was a teacher of Schrodinger.
More Math Facts for every Year Day here
1638 One of the early reports on hurricanes came from John Taylor, domestic adventurer, poet, propagandist, Royalist, and sometime overseer of the Company of Watermen in London. In 1638 he seems to have published New and Strange News from St. Christophers, of a tempestuous Spirit, which is called by the Indians a Hurry Cano, which happeneth in many of those Islands of America, or the West-Indies, as it did in August last the 5. 1638. Blowing downe houses, tearing up trees by the rootes, and it did puffe men up from the earth, as they had beene Feathers, killing divers men. *PACHS blog
For those, like me, who are not sure of the meaning of Watermen, "A waterman is a river worker who transfers passengers across and along city centre rivers and estuaries in the United Kingdom and its colonies. Most notable are those on the River Thames and River Medway in England, but other rivers such as the River Tyne and River Dee, Wales, also had their watermen who formed guilds in medieval times. Waterman can also be a person who navigates a boat carrying passengers. These boats were often rowing boat or boats with sails. Over the years watermen acquired additional skills such as local pilotage, mooring vessels at berths, jetties, buoys, and docks, and acting as helmsman aboard large vessel." *Wik
The Doggett's Coat and Badge, the oldest rowing race in the world, sees apprentice watermen competing on the River Thames. painting by Thomas Rowlandson (1756–1827).
1775 Montucla, who was the anonymous editor, served as Royal Censer for a new edition of Jacques Ozanam’s book on mathematical recreations (the first edition was written in Ozanam’s spare time during war time and published in 1694). *VFR The book was later published in English by Charles Hutton in 1803.
Hutton rose from digging coal in the Newcastle area to start his own mathematical school and became an English mathematician and surveyor. He was professor of mathematics at the Royal Military Academy, Woolwich from 1773 to 1807. He is remembered for his calculation of the density of the earth from Nevil Maskelyne's measurements collected during the Schiehallion experiment.
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1766 Eclipse observed southeast of Newfoundland: Eclipse Island (part of Burgeo Islands). Mentioned in the Chronology of Captains James Cooks (1728-1779) travels by Paul Capper. *NSEC
In 1816, Francis Ronalds built a working telegraph in the garden of the family house in Hammersmith in west London. Part of it was underground, but above ground he strung out 8 miles of insulated wire in ribbon-candy fashion, with clocks at each end whose faces contained letters instead of numbers; the electrical signals in some way synchronized the clocks and spelled out a message. Apparently, the device worked; he gave a demonstration on 5 August, 1816 for the Admiralty, offering it to them gratis, but the Secretary of the Admiralty, John Barrow, rejected it as an unnecessary invention, preferring the semaphore telegraph then in use. Two years later, Barrow distinguished himself by sending out the first ships in search of a Northwest Passage, but he has never quite lived down the ignominy of rejecting the electrical telegraph as useless. It would be 20 more years before England re-entered the telegraph business, and by that time, they were well behind the Americans. Many today regard Ronalds as the true inventor of the telegraph, and there was considerable scholarly commotion in his behalf in 2016, the bicentennial of his invention. *Linda Hall Org
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In 1864, Giovanni Batista Donati (1827-73) made the first spectroscopic observations of a comet tail (from the small comet, Tempel, 1864 II). At a distance from the Sun the spectrum of a comet is identical to that of the Sun, and its visibility is due only to reflected sunlight. Donati showed that comet tail formed close to the Sun contains luminous gas. In the spectrum of light from the comet tail, Donati saw three absorption lines bands superimposed on a continuous spectrum, which he named alpha, beta and gamma, and are now known as the Swan bands. These bands were also seen in a comet tail viewed by Pietro Secchi in 1866. Sir William Huggins (1868) identified that these were due to the presence of carbon (molecular carbon, C2).*TIS
Swan bands are a characteristic of the spectra of carbon stars, comets and of burning hydrocarbon fuels.They are named for the Scottish physicist William Swan, who first studied the spectral analysis of radical diatomic carbon (C2) in 1856. *Wik
1900 On this day in 1900, the engineer Frank Baldwin was awarded a U.S. Patent for his mechanical calculator. This machine was capable of doing a calculation such as 54679285×3298=180332281930 in about 20 seconds with eight turns of the handle. The "Baldwin Computing Engine", a machine by which multiplication or division was performed by one stroke for each digit.
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1912 “At the final session of the Spectral Classification Committee, on August 5, the Solar Union dissolved its old committees and regrouped into new ones for the work to be done over the next three years, before they would all meet again in Rome. “When the names of committees were read,” wrote Miss Cannon(Annie Jump Cannon, 49 at this time.), “I was very much surprised to find that I was put on the Committee on Classification of Stellar Spectra—and one of the novel experiences of the summer was to meet with this Committee. They sat at a long table, these men of many nations, and I was the only woman. Since I have done almost all the world’s work in this one branch, it was necessary for me to do most of the talking.””
1935 Institute of Mathematical Statistics founded.*VFR The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. The Institute currently has about 4,000 members in all parts of the world. Beginning in 2005, the institute started offering joint membership with the Bernoulli Society for Mathematical Statistics and Probability as well as with the International Statistical Institute.
1962 a lunar occultation on August 5 enabled Australian radio astronomers to more precisely fix the location of the previously known radio source 3C 273, in Virgo. In 1963 this became the first member of a new class of object eventually to be called quasars or "quasi-stellar radio sources." Maarten Schmidt, using the Hale optical telescope, saw it as a faint star-like object with a visible jet. Its spectrum featured unusual emission lines, which he identified as ordinary hydrogen lines shifted toward longer wavelengths (redshifted) by 16%. If the shift is due to velocity, it is moving away at one-sixth the speed of light and one of the most distant objects visible. Quasars radiate as much energy per second as a hundred or more galaxies. 3C273 is the brightest quasar known.*TIS
image:3C 273 as imaged by the Hubble Space Telescope's Advanced Camera for Surveys. Light from the bright quasar nucleus is blocked by a coronagraph so that the surrounding host galaxy can be more easily seen. Credit: NASA/ESA, *Wik
1977 Fermilab announces the discovery of what would come to be known as the Bottom Quark. In the summer of 1977, a team of physicists, led by Leon M. Lederman, working on experiment 288 in the proton center beam line of the Fermilab fixed target areas discovered the Upsilon. This discovery was eventually understood as being the bound state of the bottom quark and its antiquark. Their data was confirmed in experiments conducted in 1978 *Fermilab History and Archives Projec
The bottom quark or b quark, also known as the beauty quark, is a third-generation heavy quark with a charge of −1/3 e. All quarks are described in a similar way by electroweak and quantum chromodynamics, but the bottom quark has exceptionally low rates of transition to lower-mass quarks. The bottom quark is also notable because it is a product in almost all top quark decays, and is a frequent decay product of the Higgs boson.
The bottom quark was first described theoretically in 1973 by physicists Makoto Kobayashi and Toshihide Maskawa to explain CP violation. The name "bottom" was introduced in 1975 by Haim Harari.
Kobayashi and Maskawa won the 2008 Nobel Prize in Physics for their explanation of CP-violation. *Wik
Image Wilson Building at Fermilab, named for former director Robert R. Wilson, was reportedly inspired by the Gothic cathedral in Beauvais, France.
1982 Cook 3061 (1982 UB1): Minor planet discovered October 21, 1982 by E. Bowe II at Anderson Mesa. Named for James Cook (1728-1779), British circumnavigator and one of the first scientific navigators. He observed the Solar Eclipse of 1766 August 5 from Newfoundland and in 1769 measured the transit of Venus from Tahiti. Named proposed by the discoverer.*NSEC
1798 John Wrottesley, 2nd Baron Wrottesley, (5 August 1798 – 27 October 1867) was an English astronomer, who published Catalogue Of The RA Of 1318 Stars. He was a founder member of the Royal Astronomical Society. From his first Observatory in Blackheath, London, he recorded over 12,000 observations. After he inherited the title and the Staffordshire family estate at Wrottesley in 1841, he built an observatory there. In 1855, the city of Wolverhampton nearby decreed that if any ... furnace chimney ...was built ... within three miles of the observatory, it shall be constructed on the best and approved principles "for consuming the smoke arising ... therefrom". This of course was so that observations from the observatory would not be hampered by smoke pollution.*TIS
1802 Neils Henrik Abel (5 August 1802 – 6 April 1829) was born at Fomm¨oy, a small island near Stavanger in Norway. Before going to the university in 1821 he attacked, with the vigor and immodesty of youth, the problem of the solution of the quintic equation. He submitted a solution for publication but found an error before it was published. In 1823 he proved the impossibility of a solution involving radicals that solves fifth or higher degree equations. *VFR He developed the concept of elliptic functions independently of Carl Gustav Jacobi, and the theory of Abelian integrals and functions became a central theme of later 19th-century analysis. He had difficulty finding an academic position, was troubled by poverty, and died in poverty in his late twenties.*TIS I love Abel's comment on Gauss' writing style, "He is like the fox, who effaces his tracks in the sand with his tail."
1855 William Henry Dines (5 August 1855 – 24 December 1927) was an English meterologist and inventor of related measurement instruments such as the Dines pressure tube anemometer (the first instrument to measure both the velocity and direction of wind, 1901), a very lightweight meteorograph, and a radiometer (1920). He joined the Royal Meteorological Society study of the cause of the disastrous Tay Bridge collapse of 1879. His measurements of upper air conditions, first with kites and later by balloon ascents (1907), brought an understanding of cyclones from dynamic processes in the lower stratosphere rather than thermal effects nearer to the ground.*TIS
1855 Alfredo Capelli (5 Aug 1855, Milan, Italy – 28 Jan 1910, Naples, Italy) was an Italian mathematician who discovered Capelli's identity.
Capelli graduated from the University of Rome in 1877, and moved to the University of Pavia where he worked as an assistant for Felice Casorati. In 1881 he became a professor at the University of Palermo, replacing Cesare Arzelà who had recently moved to Bologna. In 1886, he moved again to the University of Naples, where he held the chair in algebra. He remained at Naples until his death in 1910. As well as being a professor there, he was editor of the Giornale di Matematiche di Battaglini from 1894 to 1910, and was elected to the Accademia dei Lincei.*Wik
In mathematics, Capelli's identity, named after Alfredo Capelli (1887), is an analogue of the formula det(AB) = det(A) det(B), for certain matrices with noncommuting entries, related to the representation theory of the Lie algebra . It can be used to relate an invariant ƒ to the invariant Ωƒ, where Ω is Cayley's Ω process.
1878 Louis Charles Karpinski (5 August 1878 – 25 January 1956) was an American mathematician.
He was born on August 5, 1878, in Rochester, New York. His parents were Henry Hermanagle Karpinski of Warsaw, Poland and Mary Louise Engesser of Guebwiller, France. He earned his Bachelor of Arts at Cornell University in 1901 and his Ph.D. at Universität Straßburg in 1903.
At Columbia University, Karpinski became a fellow and a university extension lecturer. He taught at Berea College and at the Normal School in Oswego, New York, now SUNY Oswego. He then accepted a position at the University of Michigan, where he became a full professor of mathematics by 1919. He devoted his attention chiefly to the history and pedagogy of mathematics.
Karpinski served as the president of the History of Science Society from 1943 to 1944
1930 Neil Alden Armstrong, (August 5, 1930, August 25, 2012) U.S. astronaut, was the first man to walk on the moon (20 Jul 1969, Apollo 11). He served as a Navy pilot during the Korean War, then joined the National Advisory Committee for Aeronautics (which became NASA), as a civilian test pilot. In 1962, he was the first civilian to enter the astronaut-training program. He gained experience as command pilot of the Gemini 8 mission, which accomplished the first physical joining of two orbiting spacecraft. Later he was commander of the Apollo 11 lunar mission. From 1971, he worked as professor of aerospace engineering at the University of Cincinnati. He was a member of the commission that investigated the 1986 Challenger space shuttle disaster.*TIS Armstrong died following complications resulting from cardiovascular procedures. *Mercury News
1936 Ki-Hang Kim (Korean: 김기항; 5 August 1936 – 15 January 2009), also known as Kim Ki-Hang Butler, Hang Kim, Keyhany Keem, or Kim Ki-Hang was a Korean-American Mathematician and Alabama State University professor known for his contributions in semigroups, Boolean matrices, and Social Sciences. He frequently co-wrote with Fred Roush.
1946 Shirley Ann Jackson (August 5, 1946; Washington D.C. - ) is an American physicist, and the 18th president of Rensselaer Polytechnic Institute. She received her Ph.D. in physics from the Massachusetts Institute of Technology in 1973, becoming the first African American woman to earn a doctorate from MIT in nuclear physics.
Jackson joined the Theoretical Physics Research Department at AT&T Bell Laboratories in 1976, examining the fundamental properties of various materials. She began her time at Bell Labs by studying materials to be used in the semiconductor industry. In 1978, Jackson became part of the Scattering and Low Energy Physics Research Department, and in 1988 she moved to the Solid State and Quantum Physics Research Department. At Bell Labs, Jackson researched the optical and electronic properties of two-dimensional and quasi-two dimensional systems. In her research, Jackson has made contributions to the knowledge of charged density waves in layered compounds, polaronic aspects of electrons in the surface of liquid helium films, and optical and electronic properties of semiconductor strained-layer superlattices. On these topics and others she has prepared or collaborated on over 100 scientific articles.
Jackson served on the faculty at Rutgers University in Piscataway and New Brunswick, New Jersey from 1991 to 1995, in addition to continuing to consult with Bell Labs on semiconductor theory. Her research during this time focused on the electronic and optical properties of two-dimensional systems.
In 1995, President Bill Clinton appointed Jackson to serve as Chairman of the U.S. Nuclear Regulatory Commission (NRC), becoming the first woman and first African American to hold that position.*Wik
1729 Thomas Newcomen (shortly before 24 February 1664 – 5 August 1729) inventor of the atmospheric steam engine, died in London. His invention of c.1711 came into use to pump water out of coal mines by 1725. It had a piston connected to one end of a large crossbeam; the other end was connected to a very heavy pump piston. On each stroke, water chilled and condensed the steam in the cylinder, dropping the piston thus moving the crossbeam and operating the pump. This was wasteful of fuel needed to reheat the cylinder for the next stroke. Although it was slow and inefficient, Newcomen's engine was relied on for the first 60 years of the new steam age it began. *TIS
1853 Théodore Olivier (21 Jan 1793 in France - 5 Aug 1853 in France) From the 1840's Olivier wrote textbooks. His greatest fame, however, is as a result of the mathematical models which he created to assist in his teaching of geometry. Some of the models were of ruled surfaces, with moving parts to illustrate to students how the ruled surfaces were generated. Others were designed to illustrate the curves of intersection of certain surfaces. In fact Olivier earned quite a good income from selling these models, particularly in the United States.
The United States Military Academy at West Point had 23 mathematical models made for them by Olivier to use as teaching aids.
These models are built on wooden boxes as bases, have metal supports, and consist of strings suspended from movable arms and arranged to form a variety of geometrical figures. The strings are held in place by lead weights that are concealed by the bases. The models illustrate such things as the intersection of two half cones, the intersection of a plane, hyperbolic paraboloid and a hyperboloid of one sheet, and the intersection of two half cylinders.
Other institutions in the United States such as the Columbia School of Mines also purchased models from Olivier while Princeton had copies of Olivier's models made for them. In 1849 Olivier presented a full set of the range of models he had created to the Conservatoire National des Arts et Métiers. The models had been manufactured by the firm of Pixii, Père et Fils, and later by the firm of Fabre de Lagrange which took over their manufacture. In 1857, four years after Olivier died, Harvard University purchased 24 of Olivier's models from Fabre de Lagrange and after the university received the order Benjamin Peirce gave a series of lectures on the mathematics which they illustrated. These models are still in Harvard's collection of scientific instruments.
Even after giving a complete set of his models to the Conservatoire National des Arts et Métiers, forty models were still in Olivier's possession at the time of his death. These were sold in 1869 to William Gillispie from Union College in Schenectady, east-central New York, United States. Gillispie exhibited the models at Union College which was appropriate since, twenty years earlier, Union College had became one of the first liberal arts colleges in the United States to give engineering courses. When Gillispie died Olivier's models were sold to the college. *SAU
1872 Charles-Eugène Delaunay (9 April 1816 – 5 August 1872) French mathematician and astronomer whose theory of lunar motion advanced the development of planetary-motion theories. After 20 years of work, he published two volumes on lunar theory, La Théorie du mouvement de la lune (1860,1867). This is an important case of the three body problem. Delaunay found the longitude, latitude and parallax of the Moon as infinite series. These gave results correct to 1 second of arc but were not too practical as the series converged slowly. However this work was important in the beginnings of functional analysis. Delaunay succeeded Le Verrier as director of the Paris Observatory in 1870 but two years later he and three companions drowned in a boating accident.*TIS
1910 Julius Petersen (16 June 1839, Sorø, West Zealand – 5 August 1910, Copenhagen) was a Danish mathematician who worked on geometry and graph theory. He is best remembered for the Petersen graph. *SAU In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph is named for Julius Petersen, who in 1898 constructed it to be the smallest bridgeless cubic graph with no three-edge-coloring. Although the graph is generally credited to Petersen, it had in fact first appeared 12 years earlier, in a paper by A. B. Kempe (1886). Donald Knuth states that the Petersen graph is "a remarkable configuration that serves as a counterexample to many optimistic predictions about what might be true for graphs in general." *Wik
One of the remarkable things about the Petersen graph is that is the smallest hypohamiltonian graph -- it has no Hamiltonian cycle, but deleting any vertex makes it Hamiltonian. In less formal terms, it's possible to start at any node and visit all 10 nodes while traveling on line segments alone, but there's no way to close the loop and return to the starting node at the end of the trip; but if you remove one vertex, any of them, then it is possible to connect every node in a complete circuit. This fact seems to have first been discovered by René Sousselier in 1963.
1957 Heinrich Otto Wieland (4 June 1877 – 5 August 1957) was a German chemist. He won the 1927 Nobel Prize in Chemistry for his research into the bile acids.
German chemist, winner of the 1927 Nobel Prize for Chemistry for his studies of steroid chemistry in which he determined the molecular structure of bile acids. He is also noted for studying the conversion of food into energy. In 1912, he began work on bile acids, secretions of the liver known for the best part of a century to consist of a large number of substances. He studied three of them: cholic acid, deoxycholic acid, and lithocholic acid, finding that they were all steroids, very similar to each other, and all convertible into cholanic acid. After 1921, he studied some curious alkaloids including toxiferin (curare's active ingredient), bufotalin (in venom from toads), and phalloidine and amatine (poisonous ingredients in the deadly amanita mushroom). *TiS
1981 Jerzy Neyman, (April 16, 1894 – August 5, 1981) in a paper with his long-time friend and colleague Elizabeth Scott, wrote:
Each morning before breakfast every single one of us approaches an urn filled with white and black balls. We draw a ball. If it is white, we survive the day. If it is black, we die. The proportion of black balls in the urn is not the same for each day, but grows as we become older ... Still there are always some white balls present, and some of us continue to draw them day after day for many years.
On this date, Neyman, age 87, drew a black ball. As he wished of many of his friends, “May the earth rest lightly on him.” [From a review, by Robert V. Hogg, of Neyman—From Life, by Constance Reid (Springer, 1983), in the The College Mathematics Journal, 15(1984), 82–84]*VFR
Neyman was a Russian-American mathematician who was one of the principal architects of modern theoretical statistics. His papers on hypothesis testing (1928-33) helped establish the subject. During 1934-38, he gave a theory of confidence intervals (important in the analysis of data); extended statistical theory to contagious distributions, (for interpretation of biological data); wrote on sampling stratified populations (which led to such applications as the Gallup Poll); and developed the model for randomised experiments (widely relevant across the fields of science, including agriculture, biology, medicine, and physical sciences). His later research applied statistics to meteorology and medicine. In 1968 he was awarded the prestigious National Medal of Science.*TIS
1985 Mary P. Dolciani Halloran, noted writer of several High School texts, of Hunter College died at the age of 62. The MAA book series Dolciani Mathematical Expositions is named in her honor. *VFR
Dolciani earned her Bachelor of Arts degree (B.A.) at Hunter College in New York City, and she completed her Doctor of Philosophy (Ph.D.) degree at Cornell University in 1947 with B. W. Jones as thesis advisor. She taught briefly at Vassar College before returning to Hunter, where she spent the next forty years. Dolciani taught mathematics there, and at times, she also served as a Dean or the Provost.
Although Dolciani is not well known by the general public, she was influential in developing the basic modern method used for teaching basic algebra in the United States (called "Dolciani algebra", which teaches it on the basis of drill like arithmetic, rather than on the basis of proofs as in Euclidean geometry). Dolciani also popularized the short-form names of the Properties that are familiar to many high school algebra students, e.g. the "Zero Property". *Wik
1986 Banesh Hoffmann,(September 6, 1906 - August 6, 1986) a physicist, mathematician and author who was a colleague and biographer of Albert Einstein.
In 1935, Mr. Hoffmann joined the Institute for Advanced Study in Princeton, N.J., where he worked with Einstein and a Polish physicist, Leopold Infeld, on a paper, "Gravitational Equations and the Problem of Motion."
While at Oxford, he was invited to go to Princeton and work as research associate to Dr. Oswald Veblen, a mathematics professor. In 1932, he received a doctorate in mathematics and physics from Princeton.
Mr. Hoffman worked as instructor at the University of Rochester from 1932 until 1935 and joined the faculty of Queens College in 1937. He rose to full professor and retired in the late 70s.
Hoffmann had been for the last quarter-century perhaps the best-known critic of multiple-choice testing. In his 1962 book The Tyranny of Testing and other writings, Mr. Hoffmann vehemently opposed standardized tests as superficial measures of a person`s knowledge. He died August 6, 1986 at his home in Flushing, N.Y. He was 79. *Sun Sentinal Obituary
Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell
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