Sunday, 10 January 2021

On This Day in Math - January 10

The sun comes up just about as often as it goes down, in the long run, but this doesn't make its motion random.
~Donald Knuth

The 10th day of the year; The ten decimal digits 0,1,2,3,4,5,6,7,8,9 can form 3265920 ten digit pandigital numbers. (How many of them are prime?)

And 10! seconds is exactly six weeks.

10 balls can be arranged in the plane as a triangle, and in space as a tetrahedron.

Ramanujan said this exotic formula came to him in a dream:
Cliff Pickover @pickover 

Logarithms uses ten different letters. Algorithms also uses ten different letters, but both use exactly the same ten letters. Are there other math terms that are anagrams with all distinct letters? Can you find the math anagram for the nine letters in triangle So?
There is also only one number that is spelled with ten distinct letters, eighty-four.

At Haggard Hawks I learned about a Finnish unit of measurement for the distance at which a dog bark could be heard.  It was called a peninkulma  . " As a unit of measurement, that being said, the peninkulma was originally defined not using the fairly imprecise yardstick of a dog’s long-distance bark, but as a unit of length equal to 5 virsta—a measurement (based on the even older Russian verst) equal to around two-thirds of a mile. That made the original peninkulma equivalent to roughly 3.3 miles, but in the early seventeenth century it was redefined as 10 virsta—or 6.6 miles. Then, when Finland adopted the metric system in 1880, the peninkulma was redefined to 10 kilometres—or 6.2 miles. " 

More Math Facts for every Year Day

In 1696 Thomas Savery was issued British Letters Patent No.347 for his invention for "Navigation improved; or the art of rowing ships of all rates in calms with a more easy, swift, and steady motion than oars can." ( which involved paddle-wheels driven by a capstan and which was dismissed by the Admiralty following a negative report by the Surveyor of the Navy,Edmund Dummer.) He went on to invent the first use of steam power and on 2 Jul 1698, he received Letters Patent No. 356 for what he called "The Miner's Friend; or an engine to raise water by fire" which was the first application of steam power for pumping water. *TIS

1765 When Frederick the Great saw Lambert for the first time he exclaimed that the greatest blockhead had been suggested for his Academy. He based this opinion on Lambert’s strange dress and behavior, but later he saw the “immesurableness of insight" that Lambert possessed and so appointed him to the Academy on this date. *VFR  Lambert, a self-taught polymath had met Tobias Mayer in 1756 and for a dozen years sought a position for himself.  Finally, on this date, he obtained a place in the Academie Royaled des Sciences et Belles-letters in Berlin. He would stay for the dozen remaining years of his life.  He seems to be remember by specialists in different area for a singular act, and the sum of his talents seems to escape attention. To the mathematician, he proved the irrationality of Pi and e, and did some work on non-Euclidean Geometry, to the Opticians, he is remembered for his cosine law of optics, to the astronomer for his work on comets, and the the meteorologist for his hygrometer.  A true polymath who followed his curiosity. 

1844 George Boole submitted his first paper to the Philosophical Transactions of the Royal Society. The council of the Royal Society almost rejected it without looking at it because the author was unknown. After considerable argument it was sent to two referees—thereby setting a precedent of refereeing papers. One referee rejected it, the other recommended a special prize. In 1844 this paper was the first mathematics paper to receive a gold medal from the Royal Society. *MacHale, George Boole, His Life and Work, p 61. (This seems to only be partly true. I find the following in the Stanford Encyclopedia of Philosophy: "In 1841 Boole also published his first paper on invariants, a paper that would strongly influence Eisenstein, Cayley, and Sylvester to develop the subject. Arthur Cayley​ (1821–1895), the future Sadlerian Professor in Cambridge and one of the most prolific mathematicians in history, wrote his first letter to Boole in 1844, complimenting him on his excellent work on invariants. He became a close personal friend, one who would go to Lincoln to visit and stay with Boole in the years before Boole moved to Cork, Ireland. In 1842 Boole started a correspondence with Augustus De Morgan​ (1806–1871) that initiated another lifetime friendship. In 1843 the schoolmaster Boole finished a lengthy paper on differential equations, combining an exponential substitution and variation of parameters with the separation of symbols method. The paper was too long for the CMJ—Gregory, and later De Morgan, encouraged him to submit it to the Royal Society. The first referee rejected Boole's paper, but the second recommended it for the Gold Medal for the best mathematical paper written in the years 1841–1844, and this recommendation was accepted." )

1854 Riemann presents a paper to the philosophical faculty at G¨ottingen in which he challenged the mathematical world to redefine the concept of infinity to be either endless or unbounded. [George Martin, Foundation of Geometry and the Non-Euclidean Plane, Intext, 1975, p. 311] *VFR

In 1863 London's Metropolitan, the world's first underground passenger railway, opened to fare-paying passengers. The four mile, 33-min route had seven stations between Farringdon St. and Paddington. At 6 am, six steam locomotives each with four carriages, left 15-min apart, and made a total of 120 journeys in both directions, carrying over 30,000 passengers. Charles Pearson first proposed the underground railway to relieve congestion in London. The Metropolitan Railway Co. was founded in Aug 1854. After financial delays, the first shaft was sunk at Euston Square, in 1860. The tunnel was built by "cut-and-cover" whereby a trench following the route was dug to the rail level, then covered with beams and a new surface. *TIS

1891 John William Strutt, aka Lord Rayleigh, who discovered argon, received an unsolicited letter from a German hausfrau Miss Agnes Pockels. Such events are not uncommon for well-known scientists, but what happened next was perhaps more unusual.
Miss Pockels wrote:
My lord,
Will you kindly excuse my venturing to trouble you with a German letter on a scientific subject? Having heard of the fruitful researches carried on by you last year on the hitherto little understood properties of water surfaces, I thought it might interest you to know of my own observations on the subject For various reasons I am not in a position to publish them in scientific periodicals, and I therefore adopt this means of communicating to you the most important of them. First, I will describe a simple method, which I have employed for several years, for increasing or diminishing the surface of a liquid in any proportion, by which its purity may be altered at pleasure. … …
The letter went on to describe many of the results of Strutt's own experiments, and described results and conjectures even beyond his, all done in her own kitchen.

Lord Rayleigh demonstrated the integrity he was known for, by translating the letter into English, and sending it to the journal Nature, requesting it be printed without correction.

The story, with some additional detail about curiosity with his urine stream and its relation to the discovery of ink-jet printing can be found in Len Fisher's blog here. *Len Fisher
Her article was published in Nature on 12 March, 1891.
Despite her lack of formal training, Pockels was able to measure the surface tension of water by devising an apparatus known as the Pockels trough, a key instrument in the new discipline of surface science. Using an improved version of this slide trough, American chemist Irving Langmuir made additional discoveries on the properties of surface molecules, which earned him a Nobel Prize in chemistry in 1932. She published a number of papers and eventually received recognition as a pioneer in the new field of surface science. In 1931, together with Henri Devaux, Pockels received the Laura Leonard award from the Colloid Society. In the following year, the Braunschweig University of Technology granted her an honorary PhD. Pockels died in 1935 in Brunswick, Germany. She never married.*Wik

1911 First photograph to be taken in the U.S. from an airplane was made. The photographer was Major H.A. "Jimmie" Erickson while flying in a Curtiss biplane piloted by Charles Hamilton over San Diego, California. *TIS The first photographs taken from a heavier-than-air craft were from a rocket, not an airplane:

FLIGHT, CAMERA, ACTION! By Douglas E. Campbell

1942 Peter Hilton arrived at Bletchley Park where he was greeted by the question “Do you play chess?” The “somewhat strange individual” who asked the question was the logician Alan Turing. Thus much of Hilton’s first day of war service was spent solving a chess problem. The group of pure mathematicians at Bletchley Park was involved in breaking German codes during WW II. (Peter Hilton, “Reminiscences of Bletchley Park, 1942–1945,” pp. 291–301 in A Century of Mathematics in America, Part I, especially p. 292.) *VFR

In 1946, the U.S. Army Project Diana team detected radar signals reflected off the moon's surface. A 180 cycle wave pulse with a 1/4 sec duration was beamed by the Army Signal Corps from the Evans Signal Laboratories, Belmar, N.J. The echo was received 2.4 sec. later, proving that radio waves could penetrate Earth's atmosphere. The experiment was supervised by Lt. Col. John H. De Witt, the broadcasting pioneer and amateur astronomer who first came up with the idea in 1940. His early amateur attempts were unsuccessful, but his chance came a few years later, after WW II, courtesy of the U.S. Army, at the Signal Corps Laboratories. During the war, he had developed radar for locating mortars and directing counterfire.*TIS

1962 The International Business Machines (IBM) Data Processing Division (DPD) releases an operational version of COBOL (Common Business Oriented Language). *the great geek manual

1991 Here is one for those of you who have always distrusted statistics: “... according to a study conducted by Caroline Nielsen of the University of Connecticut. She followed 10 women who joined an expensive health club and another 10 who joined a ‘simple’ club; after three months, 63 percent of those who joined the no-frills club improved in fitness, compared with 25 percent for those at the luxury club.” “It must be a joke, but I just don’t get it.” writes (on the computer net) Richard Griffith of Carleton University in Ottawa, Canada, who found it in the Globe and Mail, page A18, Social Studies, Gyms: Less is More. *VFR

1985 Sir Clive Sinclair, a pioneer of handheld computer technology, demonstrates his latest invention, the Sinclair C5 electric car. Despite it’s marketable price, it will fail so badly that it will soon become the object of industry ridicule, selling only about seventeen thousand units. *the great geek manual
The Sinclair C5 was a small one-person battery electric vehicle, technically an "electrically assisted pedal cycle". (Although widely described as an "electric car", Sinclair characterized it as a "vehicle, not a car" *Wik


1573 Simon Marius (10 Jan 1573; 26 Dec 1624 (OS)) (Also known as Simon Mayr) German astronomer, pupil of Tycho Brahe, one of the earliest users of the telescope and the first in print to make mention the Andromeda nebula (1612). He studied and named the four largest moons of Jupiter as then known: Io, Europa, Ganymede and Callisto (1609) after mythological figures closely involved in love with Jupiter. Although he may have made his discovery independently of Galileo, when Marius claimed to have discovered these satellites of Jupiter (1609), in a dispute over priority, it was Galileo who was credited by other astronomers. However, Marius was the first to prepare tables of the mean periodic motions of these moons. He also observed sunspots in 1611. *TIS

1747 Abraham-Louis Bréguet (10 Jan 1747; 17 Sep 1823) Swiss-French horologist and inventor who became the leading French watchmaker of his time because of his artistic as well as technical skill. His innovations included a self-winding or "perpétuelle" watch (1780), the gong spring which decreased the size of repeater watches, and the first anti-shock device or "pare-chute", which improved the reliability of his watches while making them less fragile. In 1775 he founded the Breguet watchmaking firm. After a two year interruption during the French Revolution, he continued business with more inventions. He sold the first modern carriage clock to Bonaparte, and created the tact watch by which time could be read by touch. *TIS

1875 Issai Schur (10 Jan 1875 in Mogilev, Russian Empire (now Belarus) - 10 Jan 1941 in Tel Aviv, Palestine (now Israel)) is mainly known for his fundamental work on the representation theory of groups but he also worked in number theory and analysis.*SAU

1905 Ruth Moufang (10 Jan 1905 in Darmstadt, Germany - 26 Nov 1977 in Frankfurt, Germany) Moufang studied projective planes, introducing Moufang planes and non-associative systems called Moufang loops. *SAU

1906 Grigore Constantin Moisil (10 January 1906 in Tulcea, Romania – 21 May 1973 in Ottawa, Canada) was a Romanian mathematician, computer pioneer, and member of the Romanian Academy. His research was mainly in the fields of mathematical logic, (Łukasiewicz-Moisil algebra), Algebraic logic, MV-algebra, algebra and differential equations. He is viewed as the father of computer science in Romania.*wik

1936 Robert Woodrow Wilson (10 Jan 1936, ) American radio astronomer who shared, with his coworker Arno Penzias, the 1978 Nobel Prize for Physics for their discovery of cosmic microwave background radiation using a microwave horn antenna at Bell Laboratories, Holmdel, New Jersey. Their discovery in 1964 is now widely interpreted as being the remnant radiation from the "big bang" model for the creation of the universe several billion years ago. Wilson is continuing his astrophysics work with Penzias, looking for interstellar molecules and determining the relative abundances of interstellar isotopes. (Soviet physicist Pyotr Leonidovich Kapitsa also shared the Nobel award, for unrelated research.)*TIS

1938 Donald Ervin Knuth, born, best known for his ongoing multi-volume book series The Art of Computer Programming. Knuth's books provide surveys of the software field, comparing algorithms for performing some of the most fundamental computer science procedures. The book project, which is expected to last his entire lifetime, was born out of a desire to eliminate duplication of effort by programmers. Knuth also took a decade-long diversion from the book series to create the language TeX, when he received galley-proofs of one of his books and noticed how poor the state of technical typesetting was. Knuth has based much of his writing on his theory that programming a computer is an art form, like the creation of poetry or music. He received the 1980 Computer Society Pioneer Award.*CHM

1949 Ann Watkins born in Los Angeles. Today she is professor at  California State University Northridge and editor of The College Mathematics Journal. Of her first love, teaching, she says: “It’s often said that the best way to learn something is to teach it. That’s certainly true about mathematics. If you can get the math clear enough in your head to explain it to someone else, either orally or in writing, then you’ve really ‘got it’.” [Quoted from Karl J. Smith, The Nature of Mathematics, sixth edition, 1991, p. 646.] *VFR


1833 Adrien-Marie Legendre (18 Sep 1752, 10 Jan 1833) French mathematician who contributed to number theory, celestial mechanics and elliptic functions. In 1794, he was put in charge of the French government's department that was standardizing French weights and measures. In 1813, he took over as head of the Bureau des Longitudes upon the death of Lagrange, its former chief. It was in a paper on celestial mechanics concerning the motion of planets (1784) that he first introduced the Legendre Polynomials. His provided outstanding work on elliptic functions (1786), and his classic treatise on the theory of numbers (1798) and also worked on the method of least squares.*TIS

1850 William Reid Clanny (1776, 10 Jan 1850) Irish physician who invented one of the first safety lamps (1813) for use in coal mines. In the late 18th century, the flammable gas methane (firedamp), remained a common hazard of English coal mines. Clanny's first invention - his "bellows lamp" was a tin lantern with glass window, candle and bellows. The flame was separated from the atmosphere by water seals. It required continual pumping for operation, was unwieldy and found no practical application. However, some of its features were incorporated in Sir Humphry Davy's safety lamp (1815), which was the precursor of modern safety lamps. On 16 Oct 1815, Clanny's second lamp, the "blast"-lamp, was tested in a mine, and on 20 Nov 1815, his third lamp, the "steam"-lamp was also tested. *TIS

1864 Nicholas Joseph Callan (22 Dec 1799, 10 Jan 1864) Irish pioneering scientist in electrical science, who invented the induction coil (1836) before that of better-known Heinrich Ruhmkorff. Callan's coil was built using a horseshoe shaped iron bar wound with a secondary coil of thin insulated wire under a separate winding of thick insulated wire as the "primary" coil. Each time a battery's current through the "primary" coil was interrupted, a high voltage current was produced in the electrically separate "secondary" coil. By 1837, Callan used a clock mechanism to rock a wire in and out of a small cup of mercury to interrupt the circuit 20 times/sec on a giant induction machine, producing 15-inch sparks (estimated at 600,000 volts).*TIS

1919 Wallace Clement Ware Sabine (13 Jun 1868, 10 Jan 1919) was a U.S. physicist who founded the science of architectural acoustics. After experimenting in the Fogg lecture room at Harvard, to investigate the effect of absorption on the reverberation time, on 29 of October 1898 he discovered the type of relation between these quantities. The duration T of the residual sound to decay below the audible intensity, starting from a 1,000,000 times higher initial intensity is given by: T = 0.161 V/A (V=room volume in m3, A=total absorption in m2). The first auditorium Sabine designed applying his new insight in acoustics, was the new Boston Music Hall, formally opened on 15 Oct 1900. Now known as the Symphony Hall, and still considered one of the world's three finest concert halls.*TIS

1929 Karl Heun (3 April 1859 in Wiesbaden, Germany - 10 Jan 1929 in Karlsruhe, Germany) was a German mathematician best known for the Heun differential equation which generalises the hypergeometric differential equation. *SAU

1941 Issai Schur (10 Jan 1875 in Mogilev, Russian Empire (now Belarus) - 10 Jan 1941 in Tel Aviv, Palestine (now Israel))is mainly known for his fundamental work on the representation theory of groups but he also worked in number theory and analysis.*SAU

1944 Thomas Scott Fiske​ (12 May 1865 in New York - 10 Jan 1944 in Poughkeepsie, New York) was an American mathematician. He was born in New York City and graduated in 1885 (Ph.D., 1888) from Columbia University, where he was a fellow, assistant, tutor, instructor, and adjunct professor until 1897, when he became professor of mathematics. In 1899 he was acting dean of Barnard College. He was president in 1902–04 of the American Mathematical Society, and he also edited the Bulletin (1891–99) and Transactions (1899-1905) of this society. In 1902 he became secretary of the College Entrance Examination Board. In 1905–06 he also served as president of the Association of Teachers of Mathematics of the Middle States and Maryland. Besides his mathematical papers, he was author of Theory of Functions of a Complex Variable (1906; fourth edition, 1907)*Wik

1984 Lancelot Stephen Bosanquet (26 Dec 1903 in St. Stephen's-by-Saltash, Cornwall, England - 10 Jan 1984 in Cambridge, Cambridgeshire, England) Bosanquet wrote many papers on the convergence and summability of Fourier series. He also wrote on the convergence and summability of Dirichlet series and studied specific kinds of summability such as summability factors for Cesàro means. His later work on integrals include two major papers on the Laplace-Stieltjes integral published in 1953 and 1961. Other topics he studied included inequalities, mean-value theorems, Tauberian theorems, and convexity theorems. *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 

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