Friday 14 October 2022

On This Day in Math - October 14


An expert problem solver must be endowed with two incompatible qualities, a restless imagination and a patient pertinacity.

Howard W. Eves, Mathematical Circles, Boston

The 287th day of the year; 287 is not prime, but it is the sum of three consecutive primes (89 + 97 + 101), and also the sum of five consecutive primes (47 + 53 + 59 + 61 + 67), and wait, it is also the sum of nine consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47).

287 is the smallest non-prime Kynea number, an integer of the form 4n + 2n − 1, studied by Cletus Emmanuel who named them after a baby girl. The binary expression of these numbers is interesting, 287[2] is 100011111. Each Kynea number has a one, followed by n-1 zeros, followed by n+1 ones. The Keyna primes are all two less than a square number. There are four year days that are Kynea numbers, but 287 is the only one that is composite. (Of course you are supposed to go find the three prime ones!)

287 is another number that require four positive squares for its sum. 287 = 15^2 +7^2 + 3^2 + 2^2.


Two weeks after Hans Lippershey applied for a patent for his "distance seeing instrument" a note was made in the meeting of the board of the province of Zeeland, on stating that an unnamed person [the clerck has not filled in his name] also claimed to have ‘the art of making an instrument to see far away objects near by’. Within days a third person,Jacob Adriaensz [Metius] of Alkmaar, the son of one of the most prominent engineers of the Dutch Republic, would claim to posses the knowledge.
Lippershey, on request of the council to develop his instrument to be used with both eyes, delivered the first binocular instrument in mid-December, 1608, and the other two in February
1609. All three instruments were considered to be working satisfactorily by the deputies
of the States General who had tested the instruments. The amount of 900 guilders Lippershey
received for his three instruments was large enough for him to buy his neighbor’s house in Middelburg, which he appropriately named ‘The Three Telescopes’ (the ‘Dry Vare Gesichten’). *Huib J. Zuidervaart, The ‘true inventor’ of the telescope. A survey of 400 years of debate, Royal Netherlands Academy of Arts and Sciences, Amsterdam 2010

1806 The French, under Napoleon, defeated the Prussians in the Battle of Jena. Killed was the Duke of Brunswick, patron of Gauss. *VFR

1863 Alfred Nobel was granted his first patent, a Swedish patent for the preparation of nitroglycerin. The end of the Crimean War (1856) brought bankruptcy for his father, Immanuel Nobel, whose factory manufactured war materiel. Studying chemistry, Alfred learned of the powerful new explosive, nitroglycerine. Around 1860, Alfred conducted repeated experiments involving great risks. He succeeded in manufacturing sufficient quantities of nitroglycerine without any mishaps. His father had been making similar experiments, but with less success. When his father realized his son's greater discoveries, he assisted Alfred patent the explosive that he aptly called "blasting oil." Later, in 1868, Nobel patented dynamite as a form for safer handling.*TIS

In 1885, after 15-year-old Jean Baptiste Jupille was severely bitten while with his bare hands he killed an attacking rabid dog to protect five other young shepherds in Villers-Farley, France. He shortly became the second person treated by Louis Pasteur's experimental vaccine for rabies. He was fortunate to be taken to Pasteur's laboratory. Pasteur's collaborator Emile Roux had thought of attenuating the power of the infection by exposing strips of fresh spinal marrow taken from a rabbit that had died of rabies to dry, sterile air for various lengths of time. The vaccine was a small piece of marrow ground up and suspended in sterilized broth. It had first been used on Joseph Meister on 6 Jul 1885. By 12 Apr 1886, 726 people had been treated.*TIS

1913 In letter to George Hale, Einstein sketched Sun's deflection of starlight (to be tested in eclipse) but got angle wrong (later revised)
*Paul Halpern‏ @phalpern

1947 Captain Charles E. Yeager was the first pilot to exceed the speed of sound, flying the exper-imental Bell XS-1 rocket-propelled research plane at Mach 1.06 (700 mph or 1,127 kph) at 43,000 feet. Previously, many felt that turbulence would prevent planes from breaking the sound barrier. *VFR

In 1960, the 4th legal definition of the meter was made to be 1,650,763.73 wavelengths in vacuum of the orange-red light radiation of the krypton-86 atom (transition between levels 2p10 and 5d5). This was now 100 times more accurate than the previous 3rd legal definition adopted in 1889. *TIS

1687 Robert Simson (14 October 1687 – 1 October 1768) was a Scottish mathematician and professor of mathematics at the University of Glasgow. The pedal line of a triangle is sometimes called the "Simson line" after him. Edmond Halley suggested to him that he might devote his considerable talents to the restoration of the work of the early Greek geometers, such as Euclid and Apollonius of Perga These are works that only survive in abbreviated accounts given by later mathematicians such as Pappus of Alexandria. He first studied Euclid's so-called porisms. Playfair's 1792 definition of porism is "a proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate, or capable of innumerable solutions."
Simson's work on Euclid's porisms was published in 1723 in the Philosophical Transactions of the Royal Society, and his restoration of the Loci Plani of Apollonius appeared in 1749. Further work of his on porisms and other subjects including logarithms was published posthumously in 1776 by Lord Stanhope at his own expense. Simson also set himself the task of preparing an edition of Euclid's Elements in as perfect a form as possible, and his edition of Euclid's books 1-6, 11 and 12 was for many years the standard text and formed the basis of textbooks on geometry written by other authors. The work ran through more than 70 different editions, revisions or translations published first in Glasgow in 1756, with others appearing in Glasgow, Edinburgh, Dublin, London, Cambridge, Paris and a number of other European and American cities. Recent editions appeared in London and Toronto in 1933 under the editorship of Isaac Todhunter and in São Paolo in 1944. Simson's lectures were delivered in Latin, at any rate at the beginning of his career. His most important writings were written in that language, however, his edition of Euclid, after its first publication in Latin, appeared in English, as did a treatise on conic sections that he wrote for the benefit of his students.
the Simson line does not appear in his work but Poncelet in Propriétés Projectives says that the theorem was attributed to Simson by Servois in the Gergonne's Journal. It appears that the theorem is due to William Wallace.
The University of St Andrews awarded Simson an honorary Doctorate of Medicine in 1746.
In 1753 Simson noted that, as the Fibonacci numbers increased in magnitude, the ratio between adjacent numbers approached the golden ratio, whose value is
(1 + √5)/2 = 1.6180 . . . . *SAU

1801 physicist J. Plateau (14 October 1801 – 15 September 1883)  Plateau’s problem asks for the minimal surface through a given curve in three dimensions. A minimal surface is the surface through the curve with the least area. Mathematically the problem is still unsolved, but physical solutions are easy: dip a curved wire in a soap solution. The “soap bubble” that results is the minimal surface for that curve. *VFR Jesse Douglas found a solution holding for an arbitrary simple closed curve. He was awarded the (one of the first two) Fields Medal in 1936 for his efforts.

In 1829 Joseph Plateau submitted his doctoral thesis to his mentor Adolphe Quetelet for advice. It contained only 27 pages, but formulated a great number of fundamental conclusions. It contained the first results of his research into the effect of colors on the retina (duration, intensity and color), his mathematical research into the intersections of revolving curves (locus), the observation of the distortion of moving images, and the reconstruction of distorted images through counter revolving
discs Prior to going blind was the first person to demonstrate the illusion of a moving image. To do this he used counter rotating disks with repeating drawn images in small increments of motion on one and regularly spaced slits in the other. He called this device of 1832 the phenakistoscope.
Plateau has often been termed a "martyr for science". . In many (popular) publications the blindness of Plateau is ascribed to his experiment of 1829 in which he looked directly into the sun for 25 seconds. Recent research definitely refutes this. The exact date of the blindness is difficult to formulate simply. It was a gradual process during the year 1843 and early 1844. Plateau publishes two papers in which he painstakingly describes the scientific observations of his own blindness. After 40 years of blindness he still has subjective visual sensations. For his experiments, as well as for the related deskwork colleagues and family help him. *Wik

1868 Alessandro Padoa​ (14 October 1868 – 25 November 1937) was an Italian mathematician and logician, a contributor to the school of Giuseppe Peano. He is remembered for a method for deciding whether, given some formal theory, a new primitive notion is truly independent of the other primitive notions. There is an analogous problem in axiomatic theories, namely deciding whether a given axiom is independent of the other axioms.*Wik

1890 Birth of Dwight D. Eisenhower. In high school, the math teacher took away Ike’s geometry book, telling him to work out the problems without benefit of the book. Eisenhower was told that unless the experiment was terminated by the teacher, he would receive an A+ in the course. “Strangely enough, I got along fairly well.” Wrote Eisenhower later. [From In Review: Pictures I’ve Kept by Dwight D. Eisenhower, 1969, p. 7]. (Morris Bishop, in a footnote to his biography of Pascal, makes an even stronger claim; he says Eisenhower was told to “construct his own geometry”.) *VFR

1900 W. Edwards Deming (14 Oct 1900; died 20 Dec 1993) was an American statistician, the father of "Total Quality Management." After WW II, he contributed to Japan's economic recovery by recommending statistical methods of quality control in industrial production. His method embraced carefully tallying product defects, examining their causes, correcting the problems, and then tracking the results of these changes on subsequent product quality. In his career before the war, he had developed statistical sampling techniques that were first used in the 1940 U.S. census. From the 1980's in the U.S. Deming taught quality control through the statistical control of manufacturing processes for companies such as Ford, Xerox, and GM.*TIS

1940 Heinrich Kayser (16 Mar 1853, 14 Oct 1940) Heinrich (Gustav Johannes) Kayser was a German physicist who discovered the presence of helium in the Earth's atmosphere. Prior to that scientists had detected helium only in the sun and in some minerals. Kayser's early research work was on the properties of sound. In collaboration with the physicist and mathematician Carl D.T. Runge, Kayser carefully mapped the spectra of a large number of elements. He wrote a handbook of spectroscopy (1901–12) and a treatise on the electron theory (1905).*TIS

1956 Jules Richard (12 August 1862 in Blet, France- 14 October 1956 in Châteauroux) worked on Geometry but is best known for Richard's paradox involving the set of real numbers which can be defined in a finite number of words.*SAU
Kurt Gödel considered his incompleteness theorem as analogous to Richard's paradox which, in the original version runs as follows:
Let E be the set of real numbers that can be defined by a finite number of words. This set is denumerable. Let p be the nth decimal of the nth number of the set E; we form a number N having zero for the integral part and p + 1 for the nth decimal, if p is not equal either to 8 or 9, and unity in the contrary case. This number N does not belong to the set E because it differs from any number of this set, namely from the nth number by the nth digit. But N has been defined by a finite number of words. It should therefore belong to the set E. That is a contradiction.
Richard never presented his paradox in another form, but meanwhile there exist several different versions, some of which being only very loosely connected to the original. For the sake of completeness they may be stated here.

1982 Edward Hubert Linfoot (8 June 1905, 14 Oct 1982)was a British mathematician, primarily known for his work on optics, but also noted for his work in pure mathematics. Linfoot's mathematical papers cover the period 1926–1939, all his subsequent work being on optics. These papers cover a wide range of areas in Fourier analysis, number theory, and probability, the first of these being applied later to his optical studies. His optics work was primarily concerned with synthesis, error balancing, assessment and testing. In particular he used his prodigious mathematical background to determine ways to improve and invent new optical configurations. *Wik

1984 Sir Martin Ryle (27 Sep 1918, 14 Oct 1984) British radio astronomer who developed revolutionary radio telescope systems and used them for accurate location of weak radio sources. With improved equipment, he observed the most distant known galaxies of the universe. Ryle and Antony Hewish shared the Nobel Prize for Physics in 1974, the first Nobel prize in the field of astronomy. Ryle helped develop radar for British defense during WW II. Afterward, he was a leader in the development of radio astronomy. Using interferometry he and his team located radio-emitting regions on the sun and pinpointed other radio sources so that they could be studied in visible light. Ryle’s catalogues of radio sources led to the discovery of numerous radio galaxies and quasars. He was Astronomer Royal 1972 to 1982.

1991 Walter M. Elsasser (20 Mar 1904, 14 Oct 1991) German-born American physicist notable for a variety of contributions to science. He is known for his explanation of the origin and properties of the Earth's magnetic field using a "dynamo model." Trained as a theoretical physicist, he made several important contributions to fundamental problems of atomic physics, including interpretation of the experiments on electron scattering by Davisson and Germer as an effect of de Broglie's electron waves and recognition of the shell structure of atomic nuclei. Circumstances later turned his interests to geophysics, where he had important insights about the radiative transfer of heat in the atmosphere and fathered the generally accepted dynamo theory of the earth's magnetism. *TIS

2010 Benoit Mandelbrot (20 November 1924 – 14 October 2010) was largely responsible for the present interest in Fractal Geometry. He showed how Fractals can occur in many different places in both Mathematics and elsewhere in Nature.*SAU He was a French American mathematician.
Mandelbrot worked on a wide range of mathematical problems, including mathematical physics and quantitative finance, but is best known as the father of fractal geometry. He coined the term fractal and described the Mandelbrot set. Mandelbrot also wrote books and gave lectures aimed at the general public.
Mandelbrot spent most of his career at IBM's Thomas J. Watson Research Center, and was appointed as an IBM Fellow. He later became a Sterling Professor of Mathematical Sciences at Yale University, where he was the oldest professor in Yale's history to receive tenure. Mandelbrot also held positions at the Pacific Northwest National Laboratory, Université Lille Nord de France, Institute for Advanced Study and Centre National de la Recherche Scientifique.
Mandelbrot died in a hospice in Cambridge, Massachusetts, on 14 October 2010 from pancreatic cancer, at the age of 85. Reacting to news of his death, mathematician Heinz-Otto Peitgen said "if we talk about impact inside mathematics, and applications in the sciences, he is one of the most important figures of the last 50 years." *Wik

2010 Wilhelm Paul Albert Klingenberg (28 January 1924 Rostock, Mecklenburg, Germany – 14 October 2010 Röttgen, Bonn) was a German mathematician who worked on differential geometry and in particular on closed geodesics. One of his major achievements is the proof of the sphere theorem in joint work with Marcel Berger in 1960: The sphere theorem states that a simply connected manifold with sectional curvature between 1 and 4 is homeomorphic to the sphere. *Wik

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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