Wednesday 11 July 2018

On This Day in Math - July 11

Ten decimal places of π are sufficient to give the circumference
of the earth to a fraction of an inch, 
and thirty decimal places would give the circumference of the visible universe
to a quantity imperceptible to the most powerful microscope.
~Simon Newcomb  

The 192nd day of the year; 192 is the smallest number that together with its double and triple contain every digit from 1-9 exactly once. There are three other values of n so that n, 2n, and 3n contain each non-zero digit exactly once. Can you find them?

192 is the sum of ten consecutive primes (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37)

192 is the number of edges on a 6th dimension hypercube, it is the last day of the year which is the number of edges of a hypercube.

Diophantus probably knew, and Lagrange proved, that every positive integer can be written as a sum of four perfect squares. Jacobi] proved the stronger result that the number of ways in which a positive integer can be so written equals 8 times the sum of its divisors that are not multiples of 4. Use this theorem to prove that there are 192 ways to express 14 as a sum of four squares.


1663 John Wallis, Savilian Professor of Geometry at Oxford, gave a specious proof of Euclid’s parallel postulate. See W. W. Rouse Ball, Mathematical Recreations and Essays, 6th edition, pp. 314– 315.*VFR

1686 Leibniz published his first paper on the integral calculus in Acta eruditorum.*VFR  This paper contains the first appearance in print of the elongated s integral notation used today. He had used the symbol earlier in a manuscript on Oct 29, 1675.

1699 Halley's final log entry for his first voyage of discovery commanding the Paramore, “The Gunns and Gunners Stores were delivered to the Tower Officers and that Same Evening we moord our Shipp at Deptford” *

1700 Royal Prussian Academy of Sciences at Berlin founded. Leibniz was primarily responsible for the founding and directed it for sixteen years. [HM 2, p. 310; American Journal of Physics, 34(1966), p. 22]*VFR

1731 Alexis-Claude Clairaut elected to the French academy. He was only eighteen. *VFR

1738 Isaac Greenwood, the first Hollis Professor at Harvard, was “ejected” from his chair for drunk­enness. [I. B. Cohen, Some Early Tools of American Science, p. 36.]  *VFR

1747 Benjamin Franklin writes to Peter Collinson, London Businessman and member of the Royal Society, to describe the, "wonderful effects of pointed bodies, both in drawing off and throwing off the electrical fire."* A history of physics in its elementary branches By Florian Cajori

1811 Italian scientist Amedeo Avogadro published his memoire about the molecular content of gases. *TIS

1814 Amp`ere submitted a paper on general solutions of differential equations. It contains thought-provoking remarks and interesting examples which had to wait several decades for proper under­standing and recognition. [Ivor Grattan-Guiness, Convolutions in French Mathematics, 1800– 1840, pp. 700ff, 1389]*VFR

1859 The Current Big Ben (the bell) is first heard ringing in the Westminster clock tower. Why Big Ben? After Benjamin Hall (1802-67). In Aug 1856 the bell, with Hall's name inscribed on it, was cast, but cracked after tests in October 1857. The substitute was also defective but worked sufficiently well to be hung in Oct 1858. Named Big Ben, it was first heard on 11 July 1859. Two months later it too cracked & fell silent for 4 years; it was repaired with help of Sir George Airy, astronomer royal, & rings to this day. *Oxford DNB@ODNB

1976 K&E produced its last slide rule, which it presented to the Smithsonian Institution. A common method of performing mathematical calculations for many years, the slide rule became obsolete with the invention of the computer and its smaller, hand-held sibling, the calculator. (*This Day in History-Computer History Museum)

1979  U.S. space station, Skylab, re-entered the Earth's atmosphere. It disintegrated, spreading fragments across the southeastern Indian Ocean and over a sparsely populated section of western Australia, where a cow died after being struck by a piece of falling debris. *TIS (Proving the potential effectiveness of weapons in space?)

In 1991, a solar eclipse cast a blanket of darkness stretching 9,000 miles from Hawaii to South America, lasting nearly seven minutes in some places. It was the so-called eclipse of the century. A total solar eclipse - the moon passing between the sun and the earth - is the moon's shadow cast on the casting its shadow on the earth's surface. Total eclipses occur almost once per year, but are often over an ocean or remote countries. The solar eclipse on July 11, 1991, was a thrill for scientists. It traveled over the several astronomical observatories on the top of Mauna Kea. Their 14,000 feet elevation was actually above the cloud level, which obstructed the view for those below. *TIS

On this day about "one year" ago German astronomer Johanne Galle discovered Neptune ... One Neptunian year that is! *rmathematicus, Thony Christie;
On July 11, 2011, Neptune completed its first full barycentric orbit since its discovery on September 23, 1846, *Wik


1732  Joseph Jérôme Le Français de Lalande, (11 July 1732 – 4 April 1807) was a an astronomer, born in Bourg-en-Bresse, France. He determined the Moon's parallax from Berlin for the French Academy (1751). He was appointed professor of Astronomy, Collège de France (1762), and subsequently, director of the Paris Observatory. He published his Traité d'astronomie in 1764 - tables of the planetary positions that were considered the best available for the rest of the century. In 1801 he also published a comprehensive star catalogue. He died in 1807, apparently of tuberculosis. *TIS

1811 Sir William Robert Grove, (11 July 1811 – 1 August 1896) British physicist and a justice of Britain's high court (from 1880), who first offered proof of the thermal dissociation of atoms within a molecule. He showed that steam in contact with a strongly heated platinum wire is decomposed into hydrogen and oxygen in a reversible reaction. In 1839, Grove mixed hydrogen and oxygen in the presence of an electrolyte, and produced electricity and water. This Grove Cell was the invention of the fuel cell. The technology was not seriously revisited until the1960s. Through the electrochemical process, the energy stored in a fuel is converted - without combusting fuel - directly into DC electricity.*TIS

1857 Sir Joseph Larmor (11 July 1857 Magheragall, County Antrim, Ireland – 19 May 1942 Holywood, County Down, Northern Ireland), Irish physicist, the first to calculate the rate at which energy is radiated by an accelerated electron, and the first to explain the splitting of spectrum lines by a magnetic field. His theories were based on the belief that matter consists entirely of electric particles moving in the ether. His elaborate mathematical electrical theory of the late 1890s included the "electron" as a rotational strain (a sort of twist) in the ether. But Larmor's theory did not describe the electron as a part of the atom. Many physicists envisioned both material particles and electromagnetic forces as structures and strains in that hypothetical fluid. *TIS

1857 Alfred Binet (July 11, 1857 – October 18, 1911) who introduced his famous IQ test in 1905. *VFR French experimental psychologist, the director of the psychological laboratory of the Sorbonne, Paris (1894). He made fundamental contributions to the measurement of intelligence.With Theodore Simon, Binet produced a series of graded tasks typical of the intellectual development of children of different ages (1905). This scale was extended (1908-11), and the tasks were assigned to the age level at which average children could manage them. Thus children could be scored for the level, or mental age, they reached. This test formed the basis for the Stanford-Binet Tests.*TIS (today in Science also gives Binet's birthdate on July 11th, with a different description:  French psychologist who was a pioneer in the field of intelligence testing of the normal mind. He took a different approach than most psychologists of his day: he was interested in the workings of the normal mind rather than the pathology of mental illness. He wanted to find a way to measure the ability to think and reason, apart from education in any particular field. In 1905 he developed a test in which he had children do tasks such as follow commands, copy patterns, name objects, and put things in order or arrange them properly. He gave the test to Paris schoolchildren and created a standard based on his data. From Binet's work, "IQ" (intelligence quotient), entered the vocabulary. The IQ is the ratio of "mental age" to chronological age, with 100 being average.)

1890 Giacomo Albanese (11 July 1890 – 8 June 1947) was an Italian mathematician known for his work in algebraic geometry. He took a permanent position in São Paulo, Brazil, in 1936. *Wik

1902 Samuel Abraham Goudsmit (The Hague, July 11, 1902 — Reno, December 4, 1978) Dutch-born U.S. physicist who, with George E. Uhlenbeck, a fellow graduate student at the University of Leiden, Neth., formulated (1925) the concept of electron spin. It led to recognition that spin was a property of protons, neutrons, and most elementary particles and to a fundamental change in the mathematical structure of quantum mechanics. Goudsmit also made the first measurement of nuclear spin and its Zeeman effect with Ernst Back (1926-27), developed a theory of hyperfine structure of spectral lines, made the first spectroscopic determination of nuclear magnetic moments (1931-33), contributed to the theory of complex atoms and the theory of multiple scattering of electrons, and invented the magnetic time-of-flight mass spectrometer (1948).*TIS

1922 John William Scott Cassels  (11 July 1922 in Durham - ) initially worked on elliptic curves. After a period when he worked on geometry of numbers and diophantine approximation, he returned in the later 1950s to the arithmetic of elliptic curves, writing a series of papers connecting the Selmer group with Galois cohomology and laying some of the foundations of the modern theory of infinite descent. His best-known single result may be the proof that the Tate-Shafarevich group, if it is finite, must have order that is a square; the proof being by construction of an alternating form. Cassels has often studied individual Diophantine equations by algebraic number theory and p-adic methods. 
His publications include 200 papers. His advanced textbooks have influenced generations of mathematicians; some of Cassels's books have remained in print for decades. *Wik

1382 Nicole Oresme (c. 1320–5 – July 11, 1382), was a French mathematician who invented coordinate geometry long before Descartes. He was the first to use a fractional exponent and also worked on infinite series. *SAU
Oresme was Bishop of Liseux and died there, but I was recently (2011) at the Cathedral and cold find no mark of his life there.
"His most important contributions to mathematics are contained in "Tractatus de figuratione potentiarum et mensurarum difformitatum", still in manuscript. An abridgment of this work printed as "Tractatus de latitudinibus formarum" (1482, 1486, 1505, 1515), has heretofore been the only source for the study of his mathematical ideas. In a quality, or accidental form, such as heat, the Scholastics distinguished the intensio (the degree of heat at each point) and the extensio (e.g., the length of the heated rod): these two terms were often replaced by latitudo and longitudo, and from the time of St. Thomas until far on in the fourteenth century, there was lively debate on the latitudo formæ. For the sake of lucidity, Oresme conceived the idea of employing what we should now call rectangular co-ordinates: in modern terminology, a length proportionate to the longitudo was the abscissa at a given point, and a perpendicular at that point, proportional to the latitudo, was the ordinate. He shows that a geometrical property of such a figure could be regarded as corresponding to a property of the form itself only when this property remains constant while the units measuring the longitudo and latitudo vary. Hence he defines latitudo uniformis as that which is represented by a line parallel to the longitude, and any other latitudo is difformis; the latitudo uniformiter difformis is represented by a right line inclined to the axis of the longitude. He proves that this definition is equivalent to an algebraical relation in which the longitudes and latitudes of any three points would figure: i.e., he gives the equation of the right line, and thus forestalls Descartes in the invention of analytical geometry. This doctrine he extends to figures of three dimensions.
Besides the longitude and latitude of a form, he considers the mensura, or quantitas, of the form, proportional to the area of the figure representing it. He proves this theorem: A form uniformiter difformis has the same quantity as a form uniformis of the same longitude and having as latitude the mean between the two extreme limits of the first. He then shows that his method of figuring the latitude of forms is applicable to the movement of a point, on condition that the time is taken as longitude and the speed as latitude; quantity is, then, the space covered in a given time. In virtue of this transposition, the theorem of the latitude uniformiter difformis became the law of the space traversed in case of uniformly varied motion: Oresme's demonstration is exactly the same as that which Galileo was to render celebrated in the seventeenth century. Moreover, this law was never forgotten during the interval between Oresme and Galileo: it was taught at Oxford by William Heytesbury and his followers, then, at Paris and in Italy, by all the followers of this school. In the middle of the sixteenth century, long before Galileo, the Dominican Dominic Soto applied the law to the uniformly accelerated falling of heavy bodies and to the uniformly decreasing ascension of projectiles." 
*Catholic Encyclopedia online

1733 Jakob Hermann (16 July 1678, Basel – 11 July 1733, Basel) was a Swiss mathematician who made contributions to dynamics. *SAU

1807 George Atwood was an English mathematician best known for his invention of a low-friction pulley system.*SAU He is the author of Phoronomia, an early treatise on Mechanics. In 1729, he proclaimed that it was as easy to graph a locus on the polar coordinate system as it was to graph it on the Cartesian coordinate system. However, no one listened. He was a distant relative of Euler. *Wik

1778 Joseph Stepling, (29 June 1716 in Regensburg; 11 July 1778 in Prague) His fields included astronomy, physics and mathematics. At the age of 17 he documented with great accuracy the 1733 lunar eclipse. Later Euler was among his long list of correspondents. He transposed Aristotelian logic into formulas, thus becoming an early precursor of modern logic. already adopted the atomistic conception of matter he radically refused to accept Aristotelian metaphysics and natural philosophy. In 1748, at the request of the Berlin Academy, he carried out an exact observation of a solar and lunar eclipse in order to determine the precise location of Prague. During Stepling's long tenure at Prague, he set up a laboratory for experimental physics and in 1751 built an observatory, the instruments and fittings of which he brought up to the latest scientific standard.
v Even though he passed up a professorship in philosophy in favor of a chair in mathematics, Empress Maria Theresa appointed him director of the faculty of philosophy at Prague as part of the reform of higher education. He was very interested in cultivating the exact sciences and founded a society for the study of science modeled on the Royal Society of London. In their monthly sessions. over which he presided until his death, the group carried out research work and investigations in the field of pure mathematics and its appiication to physics and astronomy. A great number of treatises of this academy were published.
Stepling corresponded with the outstanding contemporary mathematicians and astronomers: Christian Wolf. Leonhard Euler. Christopher Maire, Nicolas-Louis de Lacaille, Maximilian Heli, Joseph Franz, Rudjer Boskovic, Heinrich Hiss, and others. Also, Stepling was particularly successful in educating many outstanding scientists, including Johann Wendlingen, Jakob Heinisch, Johannes von Herberstein, Kaspar Sagner, Stephan Schmidt, Johann Korber, and Joseph Bergmann. After his death, Maria Theresia ordered a monument erected in the library of the University of Prague *Joseph MacDonnell, Fairfield Univ web page

1745 George Atwood (Baptized October 15, 1745, Westminster,London – 11 July 1807, London) was an English mathematician who invented a machine for illustrating the effects of Newton's first law of motion. He was the first winner of the Smith's Prize in 1769. He was also a renowned chess player whose skill for recording many games of his own and of other players, including François-André Danican Philidor, the leading master of his time, left a valuable historical record for future generations.

He attended Westminster School and in 1765 was admitted to Trinity College, Cambridge. He graduated in 1769 with the rank of third wrangler and was awarded the inaugural first Smith's Prize. Subsequently he became a fellow and a tutor of the college and in 1776 was elected a fellow of the Royal Society of London.

In 1784 he left Cambridge and soon afterwards received from William Pitt the Younger the office of patent searcher of the customs, which required but little attendance, enabling him to devote a considerable portion of his time to mathematics and physics.

He died unmarried in Westminster at the age of 61, and was buried there at St. Margaret's Church. Over a century later, a lunar crater was renamed Atwood in his honour. *Wik

1871 Germain Sommeiller (February 15, 1815 - July 11, 1871) French-Italian engineer who built the Mount Cenis (Fréjus) Tunnel (1857-70) through the Alps, the world's first important mountain tunnel. The two track railway tunnel unites Italian Savoy (north of the mountains) through Switzerland with the rest of Italy to the south. At 8 miles long and it was more than double the length of any previous tunnel. In 1861, after three years of tedious hand-boring a mere eight inches a day into the rock face, Sommeiller introduced the first industrial-scale pneumatics for tunnel digging. He built a special reservoir, high above the tunnel entrance, to produce a head of water that compressed air (to 6 atm.) for pneumatic drills, able to dig up to 20 times faster. Authorised on 15 Aug 1857, the tunnel opened on 17 Sep 1871, as a major triumph of engineering.*TIS Note his death was only a few months before the opening of his great project.

1909 Astronomer and mathematician Simon Newcomb (March 12, 1835 – July 11, 1909) died in Washington D.C. He was such a revered scientist that President Taft attended his funeral.*VFR  Canadian-American astronomer and and mathematician who prepared ephemerides (tables of computed places of celestial bodies over a period of time) and tables of astronomical constants. He was an astronomer (1861-77) before becoming Superintendent of the U.S. Nautical Almanac Office (1877-97). During this time he undertook numerous studies in celestial mechanics. His central goal was to place planetary and satellite motions on a completely uniform system, thereby raising solar system studies and the theory of gravitation to a new level. He largely accomplished this goal with the adoption of his new system of astronomical constants at the end of the century. *TIS
Newcomb is buried in Arlington National Cemetery 
Newcomb is often quoted as saying that heavier than air flight was impossible from a statement he made only two months before the Wright Brothers flight at Kitty Hawk, N.C.
"The mathematician of to-day admits that he can neither square the circle, duplicate the cube or trisect the angle. May not our mechanicians, in like manner, be ultimately forced to admit that aerial flight is one of that great class of problems with which men can never cope… I do not claim that this is a necessary conclusion from any past experience. But I do think that success must await progress of a different kind from that of invention."   He also is famously quoted for saying, "We are probably nearing the limit of all we can know about astronomy." 

1995 Andrzej Alexiewicz (11 February 1917, Lwów, Poland – 11 July 1995) was a Polish mathematician, a disciple of the Lwow School of Mathematics. Alexiewicz was an expert at functional analysis and continued and edited the work of Stefan Banach. *Wik

*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

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