Tuesday, 19 June 2018

On This Day in Math - June 19

The more I see of men, the better I like my dog.
Blaise Pascal (over 350 years before Carrie Underwood)

The 170th day of the year; the start of a record-breaking run of consecutive integers (170-176) with an odd number of prime factors.

170 is the smallest number that can be written as the sum of the squares of 2 distinct primes, where each of these primes is the square of a prime added to another prime (170 = (22 + 3)2 + (32 + 2)2).
*Prime Curios

170 is the largest integer for which its factorial can be stored in double-precision floating-point format. This is probably why it is also the largest factorial that Google's built-in calculator will calculate, returning the answer as 170! = 7.25741562 × 10306. (For 171! it returns "infinity".)

170 is the smallest number n for which phi(n)(the number of integers relatively prime to 170=64=82) and sigma(n) (the sum of the divisors of 170=324=182) are both square.


In 240 BC, Eratosthenes, a Greek astronomer and mathematician, estimated the circumference of the earth. As the director of the great library of Alexandria, he read in a papyrus book that in Syene, approaching noon on the summer solstice, the longest day of the year, shadows of temple columns grew shorter. At noon, they were gone. The sun was directly overhead. However, a stick in Alexandria, far to the north, could cast a pronounced shadow. Thus, he realized that the surface of the Earth could not be flat. It must be curved. Not only that, but the greater the curvature, the greater the difference in the shadow lengths. By measurement on the ground and application of geometry, he calculated the circumference of the earth. *TIS

325 The early Christian church opened the council of Nicaea, which decided the rules for computing the date of Easter: The first Sunday after the first full moon on or after the vernal equinox *VFR

1934 Jerzy Neyman's paper before the Royal Statistical Society entitled "On the Two Different Aspects of the Representative Method: The Method of Stratified Sampling and the Method of Purposive Selection. This paper was the one first presenting the concept of a "confidence interval" (interval estimate). *David Bee

1934 1st motion picture of the solar surface was made using the McMath-Hulbert Spectroheliokinematograph :
K8MHO is the club radio station for the McMath-Hulbert Astronomical Society. The station is housed in the McGregor administration building of the McMath-Hulbert Solar Observatory which at one time was the second largest solar observatory in the world. The station is currently manned by Tom Hagen, NE9Y, and Dave Benham, K8TRF. Members of this radio club have a mutual interest in astronomy, ham radio and the preservation of the McMath-Hulbert Solar Observatory.
The McMath-Hulbert Solar Observatory was founded in 1929 by Francis McMath, his son Robert McMath and Henry Hulbert, neighbors who just had a mutual interest in astronomy. The first tower at this site was built with a 16 foot dome in 1930 and originally had a 10.5” equatorial telescope. As they gained more interest in observing the sun, this building became more exclusively devoted to solar observing. On June 19, 1934, they released the first ever motion picture film of the surface of the sun. *QRZ.Com with hat tip to David Dickinson ‏@Astroguyz

In 1963, Soviet cosmonaut Valentina Tereshkova returned to Earth after spending nearly three days as the first woman in space. She had been interested in parachute jumping when she was young, and that expertise was one of the reasons she was picked for the cosmonaut program. She became the first person to be recruited without experience as a test pilot. On 16 Jun 1963, Tereshkova was launched into space aboard Vostok 6, and became the first woman to travel in space. Her radio name was "Chaika," Russian for "seagull." Her flight made 48 orbits of Earth. Tereshkova never made a second trip into space. She became an important member of the Communist Party and a representative of the Soviet government.*TIS


1623 Blaise Pascal ( 19 June 1623 – 19 August 1662) born in Ferrand, Auvergne, France.  He laid the foundation for the modern theory of probabilities. In hydrodynamics he formulated what came to be known as Pascal's law of pressure, and invented the syringe and hydraulic press. Pascal invented the first digital calculator to help his father with his work collecting taxes. He worked on it for three years (1642-45). The device, called the Pascaline, resembled a mechanical calculator of the 1940s. This, almost certainly, makes Pascal the second person to invent a mechanical calculator for Schickard had manufactured one in 1624. He died at the young age of 39 having been sickly and physically weak through life. Autopsy showed he had been born with a deformed skull.*TIS

1669 Leonty Magnitsky (June 9, 1669, Ostashkov – October 19, 1739, Moscow) was a Russian teacher who wrote the first guide to mathematics published in Russia.*SAU

1771 Joseph Gergonne born. (19 June 1771 Nancy, France—4 May 1859 Montpellier, France)  He came under the influence of Gaspard Monge, the Director of the new École Polytechnique in Paris. In 1810, in response to difficulties he encountered in trying to publish his work, Gergonne founded his own mathematics journal, officially named the Annales de mathématiques pures et appliquées but generally referred to as the Annales de Gergonne. The most common subject of articles in his journal was geometry, Gergonne's specialty. Over a period of 22 years, the Annales de Gergonne published about 200 articles by Gergonne himself, and other articles by many distinguished mathematicians, including Poncelet, Servois, Bobillier, Steiner, Plücker, Chasles, Brianchon, Dupin, Lamé, even Galois.
Gergonne was appointed to the chair of astronomy at the University of Montpellier in 1816. In 1830, he was appointed Rector of the University of Montpellier, at which time he ceased publishing his journal. He retired in 1844.
Gergonne was the first mathematician to employ the word polar. In a series of papers beginning in 1810, he discovered the principle of duality in projective geometry, by noticing that every theorem in the plane connecting points and lines corresponds to another theorem in which points and lines are interchanged, provided that the theorem embodied no metrical notions. In 1816, he devised an elegant solution to the problem of Apollonius: find a circle which touches three given circles.
In 1813, Gergonne wrote the prize-winning essay for the Bordeaux Academy, Methods of synthesis and analysis in mathematics, unpublished to this day and known only via a summary. The essay is very revealing of Gergonne's philosophical ideas. He called for the abandonment of the words analysis and synthesis, claiming they lacked clear meanings. Surprisingly for a geometer, he suggested that algebra is more important than geometry, at a time when algebra consisted almost entirely of the elementary algebra of the real field. He predicted that one day quasi-mechanical methods would be used to discover new results.
In 1815, Gergonne wrote the first paper on the optimal design of experiments for polynomial regression. According to S. M. Stigler, Gergonne is the pioneer of optimal design as well as response surface methodology.

1846 Antonio Abetti (19 Jun 1846, 20 Feb 1928 at age 81) Italian astronomer who was an authority on minor planets. At first a civil engineer, he became an astronomer at the University of Padua (1868-93), with an interest in positional astronomy and made many observations of small planets, comets and star occultations. In 1874, Abetti went to Muddapur, Bengal, to observe the transit of Venus across the sun's disk where his use of a spectroscope was the first use of this kind. Later, he became director at the Arcetri Observatory and Professor of astronomy at the University of Florence (1894-1921). The observatory had been founded by G. B. Donati in 1872, and Abetti equipped it with a new telescope that he had built in the workshops at Padua. He was active after retirement, until his death, and was followed by his son Giorgio.*TIS

1851 Silvanus P. Thomson (19 June 1851 – 12 June 1916) In 1910 he published Calculus Made Easy, which was published anonymously until after his death in 1916. It is still in print. *VFR He was a noted physicist and engineer, and a celebrated teacher and writer on electricity and magnetism. He also wrote popular biographies of Faraday and Lord Kelvin. At his death he was professor at City and Guilds Technical College at Finsbury (London). Thompson’s particular gift was in his ability to communicate difficult scientific concepts in a clear and interesting manner. He attended and lectured at the Royal Institution giving the Christmas lectures in 1896 on Light, Visible and Invisible with an account of Röntgen Light. He was an impressive lecturer and the radiologist AE Barclay said that: “None who heard him could forget the vividness of the word-pictures he placed before them.”


1504 Bernhard Walther (1430 – June 19, 1504) was a German merchant, humanist and astronomer based in Nuremberg, Germany.
Walther was born in Memmingen, and was a man of large means, which he devoted to scientific pursuits. When Regiomontanus settled in Nuremberg in 1471, they worked in collaboration to build an observatory and a printing press. After the death of Regiomontanus in 1476 at Rome, Walther bought his instruments, after Hans von Dorn, commissioned by the Hungarian king, had tried in vain about it with the council of Nuremberg. Thenceforward, he continued the observation of planets till his death in Nuremberg. His house, purchased in 1509 by Albrecht Dürer, is nowadays a museum

1945 Stefan Mazurkiewicz (September 25, 1888 in Warsaw, then Russian Empire – June 19, 1945, Grodzisk Mazowiecki, Poland)one of the founders of Fundamenta Mathematicae, died.

*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

Monday, 18 June 2018

On This Day in Math - June 18

I began to understand that pure mathematics was more than a collection of random tools mainly fashioned for use in the Cambridge treatment of natural philosophy.
Andrew Forsyth

The 169th day of the year; 169 is the smallest square which is prime when rotated 180o (691)  What is the next one?

And from Jim Wilder, 169 is the reverse of 961. The same is true of their square roots... √169=13 and √961=31
or stated another way, 169 = 132 and in reverse order 312 = 961

An interesting loop sequence within Pi. If you search for 169, it appears at position 40. If you then search for 40, it appears at position 70. Search for 70, ... 96, 180, 3664, 24717, 15492, 84198, 65489, 3725, 16974, 41702, 3788, 5757, 1958, 14609, 62892, 44745, 9385, 169, *Pi Search page

169 is the only year day which is both the difference of consecutive cubes, and a square: \(8^3-7^3 =169=13^2\)

The first successful dissection of a square into smaller squares was of a square with 169 units on a side. 1907-1914 S. Loyd published The Patch Quilt Puzzle. A square quilt made of 169 square patches of the same size is to be divided into the smallest number of square pieces by cutting along lattice lines. The answer, which is unique, is composed of 11 squares with sides 1,1,2,2,2,3,3,4,6,6,7 within a square of 13. It is neither perfect nor simple. Gardner states that this problem first appeared in 1907 in a puzzle magazine edited by Sam Loyd. David Singmaster lists it as first appearing in 1914 in Cyclopedia by Loyd but credits Loyd with publishing Our Puzzle Magazine in 1907 - 08. This puzzle also appeared in a publication by Henry Dudeney as Mrs Perkins Quilt. Problem 173 in Amusements in Mathematics. 1917


1558 Robert Recorde’s will was admitted to probate, after he died in prison. He introduced the equals sign in The Whetstone of Witte (1557) with the words: “And to avoide the tediouse repetition of these woordes: is equalle to: I will sette as I doe often in woorke use, a pair of paralleles, or Gemowe lines of one lenghte, thus:  because noe .2. thynges, can be moare equalle.” “Gemowe” (think Gemini )is an old French work meaning “twin.”. *VFR  When they are asked what they would use if this was not available, it seems difficult for students to imagine a different symbol.  

Image from Wikipedia.

1584 Jacob Christmann appointed professor of Hebrew at Heidelberg. In 1595 he defended the view that the circle could only be approximately squared. *VFR

1864 Lewis Carroll finally decided to write up Alice’s Adventures in Wonderland. [Stuart Dodgson Collingwook, The Life and Letters of Lewis Carroll (1898), p. 96] 

1908  Alan Archibald Campbell Swinton took the first x-ray images in Britain in January 1896 and by a year later the medical professions were bringing him surgical cases for analysis. But "on this day he predicted exactly how another magic box would work, in a letter to Nature. He called it ‘Distant Electric Vision’, but we know it now as television." *Keith Moore, http://blogs.royalsociety.org

 1928, aviator Amelia Earhart became the first woman to fly across the Atlantic Ocean. She had accepted the invitation of the American pilots Wilmer Stultz (1900-29) and Louis Gordon to join them on the transatlantic flight. The crossing from Newfoundland to Wales took about 21 hours. Amelia Earhart went on to establish herself as a respected role model, tirelessly demonstrating that young women were as capable as men in succeeding in their chosen vocations. In 1935 she crossed the Atlantic solo in record time: 13 hr 30 min.  *TIS

1983 Sally Ride, astrophysicist, becomes the first American woman in space. The Soviets were ahead by twenty years and two days.*VFR


1799 William Lassell (18 June 1799 – 5 October 1880) was a wealthy amateur English astronomer. He set up an observatory at Starfield, near Liverpool. England, He built his own 24" diameter telescope, and devised steam-driven equipment for grinding an polishing the speculum metal mirror. This telescope was the first of its size to be mounted "equitorially" to allow easy tracking of the stars. He discovered Triton, a moon of Neptune, and Ariel and Umbriel, satellites of Uranus. Later, Lassell built a 48" diameter telescope with th same design and took it to Malta for observations with clearer skies.*TIS

1818 Pietro Angelo Secchi (18 Jun 1818, 26 Feb 1878 at age 59) Italian Jesuit priest and astrophysicist, who made the first survey of the spectra of over 4000 stars and suggested that stars be classified according to their spectral type. He studied the planets, especially Jupiter, which he discovered was composed of gasses. Secchi studied the dark lines which join the two hemispheres of Mars; he called them canals as if they where the works of living beings. (These studies were later continued by Schiaparelli.) Beyond astronomy, his interests ranged from archaeology to geodesy, from geophysics to meteorology. He also invented a meteorograph, an automated device for recording barometric pressure, temperature, wind direction and velocity, and rainfall.*TIS

1858 Andrew Russell Forsyth (18 June 1858, Glasgow – 2 June 1942, South Kensington) studied at Liverpool College and was tutored by Richard Pendlebury before entering Trinity College, Cambridge, graduating senior wrangler in 1881. He was elected a fellow of Trinity and then appointed to the chair of mathematics at the University of Liverpool at the age of 24. He returned to Cambridge as a lecturer in 1884 and became Sadleirian Professor of Pure Mathematics in 1895. *Wik 
In 1893 he published Theory of functions of a complex variable which had such an impact at Cambridge that function theory dominated there for many years. Whittaker writes... that this text:-
... had a greater influence on British mathematics than any work since Newton's Principia.
However the reputation of the book outside Britain was not high. In fact this is not surprising since the whole thrust of the book was to bring the great advances of Continental mathematics to Cambridge which Forsyth rightly saw as living in the past. He was well equipped to undertake this task for he traveled widely and, being a good linguist, was able to appreciate the advances made by authors writing in French and German.
On Cayley's death Forsyth was appointed to his chair in 1895 becoming the Sadleirian professor of Pure Mathematics. However his preference for technical mastery rather than rigorous analysis meant that he failed to inspire future pure mathematicians. In fact one would have to say that Forsyth was unlucky, for although he saw the importance of Continental mathematics, at the same time his greatest strengths lay in his ability to handle complex formulae. He therefore excelled at precisely the style of mathematics which he himself campaigned successfully to replace at Cambridge.

1884  Charles Weatherburn  (18 June, 1884 in Australia - 1974 in Australia) worked on vector analysis and differential geometry.*SAU

1884 Frieda Nugel (18 June 1884 in Cottbus, Brandenburg, Germany- 6 Nov 1966 in Bad Godesberg, Bonn, Germany) was a German mathematician who was one of the first women to receive a doctorate in Germany *SAU

1913  Oswald Teichmüller's (June 18, 1913 – September 11, 1943)  main contribution is in the area of geometric function theory.*SAU

1926 Allan Rex Sandage  (June 18, 1926 – November 13, 2010)  U.S. astronomer who (with Thomas A. Matthews) discovered, in 1960, the first optical identification of a quasi-stellar radio source (quasar), a starlike object that is a strong emitter of radio waves. Although a strange source of radio emission, in visible light, it looked like a faint star. Yet this object was emitting more intense radio waves and ultraviolet radiation than a typical star. He is best known for determining the first reasonably accurate value for the Hubble constant and the age of the universe.*TIS & Wik


1818 George Baron (?? , June 18, 1818) was a mathematician who emigrated from Northumberland, England to Hallowell, Maine in the United States, thereafter moving to New York. He was the first superintendent and mathematics professor at what would become the United States Military Academy in 1801 and the founder and editor-in-chief of the Mathematical Correspondent, which was the first American "specialized scientific journal" and the first American mathematics journal, first published May 1, 1804.
Baron was first offered the position at the fledgling academy at West Point, New York by the newly elected United States President Thomas Jefferson's Secretary of War Henry Dearborn, a friend of Baron's who had lived near him in Maine. After agreeing upon salary and perks, instruction began on September 21, 1801 employing the use of Charles Hutton's A Course in Mathematics and a blackboard, the first recorded use of the latter in America. In October, there was a disagreement between Baron and one of the cadets, Joseph Gardner Swift. Swift was called upon to apologize and was reprimanded for the language he employed against Baron, but went on to become the Military Academy's first graduate, and later a Brigadier General. For a variety of reasons, Baron was court-martialled in December, and Major Jonathan Williams became the supervisor and Captain William Amherst Barron became the instructor of mathematics.
Baron became a teacher of mathematics in New York City, there joining the Theistical Society of New York, a deist group led by Elihu Palmer that came to public attention in the course of a pamphlet war between supporters of United States Vice President Aaron Burr and supporters of then United States Senator from New York DeWitt Clinton. *Wik
Baron may have been one of the earliest users of a blackboard in the US as, "use of the blackboard was a favorite method of Baron." *Edward S Holden, The Centenial of the US Military Academy at West Point, New York

1922 Jacobus Cornelius Kapteyn, (January 19, 1851, Barneveld, Gelderland – June 18, 1922) Dutch astronomer who used photography and statistical methods in determining the motions and spatial distribution of stars. Such work was the first major step after the works of William and John Herschel. He tried to solve the questions of space density of stars as a function of distance from the sun, and the distribution of starts according to brightness per unit volume. Some of his results had lasting value, but some were superceded because he had failed to account for the interstellar absorption. In studies using proper motion to determine stellar distances, he discovered stellar motions are not random, as previously thought, but that stars move in two "star streams" (1904). He introduced absolute magnitude and colour index as standard concepts.*TIS

1935 Alexander von Brill (20 September 1842 – 18 June 1935) died. He worked on algebraic geometry and the theory of algebraic func­tions.  Born in Darmstadt, Hesse, he attended University of Giessen where he earned his doctorate under supervision of Alfred Clebsch. He held a chair at the University of Tübingen, where Max Planck was among his students.*Wik

1980 Kazimierz Kuratowski  (February 2, 1896 – June 18, 1980) He worked in the area of topology and set theory. He is best known for his theorem giving a necessary and sufficient condition for a graph to be planar.*SAU   
Kuratowski's theorem:  "A finite graph is planar if and only if it does not contain a subgraph that is a subdivision of K5 (the complete graph on five vertices) or K3,3 (complete bipartite graph on six vertices, three of which connect to each of the other three)."  (in simpler, but less exact terms,  it can be drawn in such a way that no edges cross each other."  The well-known recreational problem of connecting three houses to three utilities is not possible to draw because it is K3,3 (below).  The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any of the gas/water/electric lines/pipes pass over any other. (1913 Dudeney: first publication of Gas, Water and Electricity Problem. according to David Singmaster, Gardner says 1917)  (see June 21)

Kuratowski proved his theorem in 1930. Forty years later the dedication of Frank Harary’s classic Graph Theory was:
Who gave K5 and K3,3
To those who thought planarity
Was nothing but topology.
(In fact three other almost simultaneous discoveries of the theorem are recorded: Orrin Frink and Paul Althaus Smith; Lev Semenovich Pontrjagin; and Karl Menger!)  With thanks to *theoremoftheday@ theoremoftheday

*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

Sunday, 17 June 2018

On This Day in Math - June 17

By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I have made, I ended up in the domain of mathematics, Although I am absolutely without training in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists.

M. C. Escher, Quoted in To Infinity and Beyond, E Maor (Princeton 1991)

The 168th day of the year; there are 168 prime numbers less than 1000. *Prime Curios

168 is the product of the first two perfect numbers. *jim wilder ‏@wilderlab

\(2^{168} = 374144419156711147060143317175368453031918731001856 \) lacks the digit 2; no larger 2n exists for \(n \lt 10^{399}\) that is not pandigital.

There are 168 hours in a week.

168 is also the number of moves that it takes a dozen frogs to swap places with a dozen toads on a strip of 2(12) + 1=25 squares (or positions, or lily pads) where a move is a single slide or jump. This activity dates back to the 19th century, and the incredible recreational mathematician, Edouard Lucas *OEIS.
Prof. Singmasters Chronology of Recreational Mathematics suggests that this was first introduced in the American Agriculturalist in 1867, and I have an image of the puzzle below. The fact that they call it, "Spanish Game" suggests it has an older antecedent. (anyone know more?)


1713  Leibniz replies from Vienna to Johan (I) Bernoulli's letter of June 7th informing him of the book from London accusing Leibniz of "plagiary".  "I have not yet seen the little English book directed against me. .... it appears that he (Newton) no more knew our calculus than Apollonius knew the algebraic calculus of Viete and Descartes." In this letter he will deny being the author of a critical review of Newton's tracts in the Arcta Eruditorum. (A lie.) *The Correspondence of Isaac Newton

1867 Nobel invented dynamite. It is from this invention that he earned the fortune that he used to endow the Nobel Prizes.*VFR

1870  Benjamin Pierce, Superintendent U. S. Coast Survey, sends letter of introduction for his son to August De Morgan, "I presume upon the unseen brotherhood of science to introduce to you my son Charles S. Peirce Esq. who is a devoted student of Logic and I think that he has original thoughts which you may regard as deserving your consideration. He carries with him a memoir which he has written upon one of the subjects of your own learned investigations... " *Universidad de Navarra

1928,  Amelia Earhart  embarked on a trans-Atlantic flight from Newfoundland to Wales; she was  the first woman to fly across the Atlantic Ocean, though as a passenger  in a plane piloted by Wilmer Stultz. In 1932, she became the first  woman to fly solo across that ocean.


1714  César-François Cassini de Thury (17 June 1714 – 4 September 1784), French astronomer and geodesist (Cassini III), who continued surveying work he began while assisting his father, Jacques Cassini (Cassini II), resulting in the first topographical map of France produced by modern principles. His grandfather, Giovanni Domenico Cassini  (Cassini I) discovered four satellites of Saturn, a band on planet's  surface, and that its ring was subdivided. Cassini I was the first to  assume effective direction (1671) of the new observatory established by  the Académie Royale des Sciences in Paris, which his descendants in turn  continued. Cassini III was the first official director of the  observatory when the post was created by the king in 1771. His son was  Jean-Dominique Cassini (Cassini IV) *TIS

Victorian picture "Leviathan of Parsonstown" *Wik
1800  William Parsons class="st">(17 June 1800 – 31 October 1867), 3rd Earl of Rosse was an Irish astronomer  who built the largest reflecting telescope of the 19th century. He  learned to polish metal mirrors (1827) and spent the next few years  building a 36-inch telescope. He later completed a giant 72-inch  telescope (1845) which he named "Leviathan," It remained the largest  ever built until decades after his death. He was the first to resolve  the spiral shape of objects - previously seen as only clouds - which  were much later identified as galaxies independent of our own Milky Way  galaxy and millions of light-years away. His first such sighting was  made in 1845, and by 1850 he had discovered 13 more. In 1848, he found  and named the Crab Nebula (because he thought it resembled a crab), by which name it is still known.*TIS

1832 Sir William Crookes, OM, FRS (17 June 1832 – 4 April 1919) was a British chemist and physicist who attended the Royal College of Chemistry, London, and worked on spectroscopy. He was a pioneer of vacuum tubes, inventing the Crookes tube.*Wik

1898 Maurits Cornelius Escher (17 June 1898 – 27 March 1972)   an artist whose works have included a considerable mathematical content.  He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints. These feature impossible constructions, explorations of infinity, architecture, and tessellations. *Wik    

1903 Sir. William Valance Douglas Hodge Jun 17, 2011 – 1903born.*VFR  Hodge also wrote, with Daniel Pedoe, a three-volume work Methods of Algebraic Geometry, on classical algebraic geometry, with much concrete content — illustrating though what Élie Cartan  called 'the debauch of indices', in its component notation. According  to Atiyah, this was intended to update and replace H. F. Baker's Principles of Geometry. *Wik

1906 Samuel Stanley Wilks (June 17, 1906 – March 7, 1964) was an American mathematician and academic who played an important role in the development of mathematical statistics, especially in regard to practical applications.
Born in Little Elm, Texas (Little Elm was once a quiet farm town, and today is one of the fastest growing municipalities in Texas) and raised on a farm, Wilks was educated at the University of Iowa, where he acquired his Ph.D. under Everett F. Linquist; his thesis dealt with a problem of statistical measurement in education, and was published in the Journal of Educational Psychology. Wilks became an instructor in mathematics at Princeton University in 1933; in 1938 he assumed the editorship of the journal Annals of Mathematical Statistics in place of Harry C. Carver. Wilks assembled an advisory board for the journal that included major figures in statistics and probability, among them Ronald Fisher, Jerzy Neyman, and Egon Pearson.
Wilks was named professor of mathematics and director of the Section of Mathematical Statistics at Princeton in 1944, and became chairman of the Division of Mathematics at the University in 1958. He was noted for his work on multivariate statistics and unit-weighted regression.
From the start of his career, Wilks favored a strong focus on practical applications for the increasingly abstract field of mathematical statistics; he also influenced other researchers, notably John Tukey, in a similar direction. Drawing upon the background of his thesis, Wilks worked with the Educational Testing Service in developing the standardized tests like the SAT that have had a profound effect on American education. He also worked with Walter Shewhart on statistical applications in quality control in manufacturing.
During World War II he was a consultant with the Office of Naval Research. Both during and after the War he had a profound impact on the application of statistical methods to all aspects of military planning.
The American Statistical Association named its Wilks Memorial Award in his honor.
Wilks' lambda distribution is a probability distribution related to two independent Wishart distributed variables. It is important in multivariate statistics and likelihood-ratio tests. *Wik

1908 Gunnar Af Hallstrom born. He determined the congruence axioms which Hilbert used in his famous axiomatization of geometry. *VFR

1919  William Kaye Estas  (June 17, 1919 – August 17, 2011) American psychologist, a leader in bringing mathematical methods into  psychological research, who was awarded the National Medal of Science in  1997 for "his fundamental theories of cognition and learning that  transformed the field of experimental psychology. His pioneering methods  of quantitative modeling and an insistence on rigor and precision  established the standard for modern psychological science." In his early  professional research he partnered with another pioneering psychologist  B. F. Skinner in studying animal learning and behavior. The  quantitative method they devised to measure emotional reactions is still  widely used today. From 1979, Estes focused on investigating human  memory and classification learning. 


1994 Frank Yates FRS (May 12, 1902 – June 17, 1994) was one of the pioneers of 20th century statistics.   He was born in Manchester. He spent two years teaching mathematics to secondary school pupils before heading to Africa where he was mathematical advisor on the Gold Coast Survey. He returned to England due to ill health and met and married a chemist, Margaret Forsythe Marsden, the daughter of a civil servant.  This marriage was dissolved in 1933 and he later married Pauline Penn,  previously the partner of the well-known architect. After her death in  1976 he married Ruth Hunt, his long-time secretary.
In 1931 Yates was appointed assistant statistician at Rothamsted Experimental Station by R.A. Fisher. In 1933 he became head of statistics when Fisher went to University College London. At Rothamsted he worked on the design of experiments, including contributions to the theory of analysis of variance and originating Yates' algorithm and the balanced incomplete block design.
During World War II he worked on what would later be called operational research.
After the war he worked on sample survey design and analysis. He became an enthusiast of electronic computers, in 1954 obtaining an Elliott 401 for Rothamsted and contributing to the initial development of statistical computing. In he was awarded the Guy Medal in Gold of the Royal Statistical Society, and in 1966 he was awarded the Royal Medal of the Royal Society. He retired from Rothamsted to become a Senior Research Fellow at Imperial College London. He died in 1994, aged 92, in Harpenden.*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

Saturday, 16 June 2018

On This Day in Math - June 16

In a world in which the price of calculation
continues to decrease rapidly, but the price of theorem proving continues to hold steady or increase, elementary economics indicates that we ought to spend a larger and larger fraction of our time on calculation.
John Tukey

The 167th day of the year; 167 is the only prime requiring exactly eight cubes to express it. *Prime Curios (I find it amazing that there is only one such prime number)

167= 2 * 34 + 5

167 is the smallest number whose fourth power begins with four identical digits, 1674=777796321.

167 is an emirp, a prime whose reverse, 761 is also prime. The 167th prime is 991 and it is also an emirp. Wait! the 991st prime, 7841 is also an emirp.


1497   Amerigo Vespucci (1454-1512) was born in one of the Vespucci houses in Borgo Ognissanti.  He is said to have made four voyages to the New World.  He reported sighting the South American mainland on 16 Jun 1497, a week before Cabot reached North America, which led to his name being attached to the New World in Martin Waldseemüller's Cosmographiæ Introductio of 1507 – but many authorities doubt that Vespucci ever made this voyage.  Waldseemüller realised that he had overrated Vespucci's accomplishments and removed the name from later versions of his map, but it was too late.  Simonetta Vespucci, who married his distant cousin was a celebrated beauty, immortalised in Botticelli's paintings – his 'Mars and Venus' in the Uffizi shows little wasps ('vespucci') circling the head of Mars.  Florence's airport, in the NW suburb of Peretola, is named Amerigo Vespucci.

1641  In a letter to Fr. Marin Mersenne, Descartes states that no prime of the form 12n ± 1 will divide a number that is one more than a power of three. He adds that 12n ± 5 will always divide some 3X +1.  He gives a similar rule for five, and states he has one for all primes.  (History of the theory of numbers,  By Leonard Eugene Dickson)

1657, the first pendulum clock was patented  by its inventor, Christiaan Huygens. Although others may have worked in this field before him, Huygens made major advances in building a practical clock. He needed time accuracy for his astronomical measurements.*TIS

17   1799 Gauss awarded his Ph.D. at age 22, the usual requirement of an oral exam being dropped. His dissertation gave the first correct proof of the fundamental theorem of algebra. *VFR

1833 Janos Bolyai was retired as Captain in the cavalry for dueling with thirteen other officers. He accepted their challenge on the condition that he be allowed to play his violin between duels. [Bonola, Non-Euclidean Geometry, Appendix 1, p. xxix]*VFR

1825 Faraday’s account of his discovery of bicarburet of hydrogen (later called Benzene) was read to the Royal Society. *Jennifer Wilson, Celebrating Michael Faraday’s Discovery of Benzene, Ambix,Volume 59, Issue 3

1825 Benjamin Gompartz leter to Francis Baily in which he expounded his law of human mortality. Today the curve is expressed as \( N(t) = N(O) e^{-c(e^{at}-1)} \) *Philosophical Transactions of the Royal Society of London

(For those interested in mathematical notation, this paper makes frequent use of the overbar as a vincula or grouping symbol.

1854 For the first time in more than twenty years, Gauss left Gottingen. He went to see the railway between Cassel and Gottingen that was under construction. *VFR

1867 A Memorial to Leonardo Bigolli (Fibonacci) was erected in Pisa.  The monument includes a 1241 decree by the commune of Pisa that bestowed an annual salary to Leonardo,  "In consideration of the honor brought to the city and its citizens and their betterment by the teaching and zealous cooperation of that discrete and learned man."  *The Man of Numbers, Keith Devlin

1885 The first gravity-powered American roller coaster that was commercially successful was put in operation at Coney Island, N.Y., the invention of La Marcus Thompson (patent No. 310,966). Passengers rode a train on undulating tracks over a wooden structure 600-ft long. The train started at a height of 50-ft on one end and ran downhill by gravity until its momentum died. Passengers then left the train and attendants pushed the car over a switch to a higher level. The passengers returned to their sideways facing seats and rode back to the original starting point. Admission on the Thompson Switchback Railway was 5 cents and he grossed an average of $600 / day. Within 4 yrs he had built about 50 more across the U.S. and in Europe.

1893 Secretary of Agriculture J. Sterling Morton begins his attack on the U. S. Weather Bureau with a letter to Cleveland Abbe, "It seems to me that the disbursements of the Weather Bureau for scientists are altogether too extravagant." Within days he would also cut his salary by 25%. *Isaac's Storm, Erik Larson

1902 Bertrand Russell wrote Gottlob Frege that in his Grundgesetze der Arithmetik “there is just one point where I have encountered a difficulty.” The difficulty is the Russell Antinomy, a logical contradiction. See 22 June 1902.  Russell had found a class of contradictions to Frege's 1879 Begriffsschrift. This contradiction can be stated as "the class of all classes that do not contain themselves as elements".

1902 Albert Einstein formally appointed as Technical Expert at the Swiss Patent Office at Bern at a salary equivalent to about $3,000 a year.

1933   FDR signed the Banking Act, which separated commercial banking from investment banking and established the Federal Deposit Insurance Corporation. He also signed the Farm Credit Act, the Emergency Railroad Transportation Act, and the National Industrial Recovery Act (which created the Public Works Administration).

1963 Valentina Tereshkova became the first woman in space. She was aboard the Soviet Union’s Vostok 6. See 18 June 1983.

1973 Afghanistan issued a postage stamp commemorating the millennium of the birth of Ab'u Rayhan Muhammad ibn Ahmad Al Bırunı (born 4 September 973, died after 1050), author of books on arithmetic, geometry, trigonometry, astronomy and geography. [Scott #881].

1993 The 100th anniversary of Cracker Jack (called America's first junk food) was celebrated at Wrigley Field during the game between the Cubs and the expansion Florida Marlins. Before the game, Sailor Jack, the company's mascot, threw out the ceremonial first pitch. Cracker Jacks have been associated with baseball since the 1908 publication of "Take Me Out to the Ball Game", a song written by lyricist Jack Norworth and composer Albert Von Tilzer, with the line: "Buy me some peanuts and Cracker Jack!"
 1993 May have been a premature date for the 100th anniversary. Although rumors exist that a "candy coated popcorn" was sold by the Rueckheim brothers at the World's Columbian Exposition in 1893, there seems to be no supporting evidence of this. The first lot of Cracker Jack was produced and the name was registered in 1896.
The Sailor Jack in the logo was modeled after Robert Rueckheim, nephew of the Rueckheim brothers, who sadly died of pneumonia shortly after his image appeared at the age of 8. The dog in the image, Bingo, was a stray who lived on for another 17 years. *Wik


1640  Jacques Ozanam (16 June 1640, Sainte-Olive, Ain - 3 April 1718, Paris) was born in Sainte-Olive, Ain, France. All his books sold well and ran to many editions, especially his famous works Dictionnaire mathématique (1691), the five volume work Cours de mathématiques (1693) and Récréations mathématiques et physiques (1694). It is certainly for this last work on recreational mathematics that Ozanam will be most remembered. The precursor of books to follow for the next 200 years, he published it in four volumes in 1694 and it later went through at least ten editions. Ozanam based his book on earlier works by Bachet, Mydorge, Leurechon, and Schwenter. It was later revised and enlarged by Montucla, then translated into English by Hutton (1803, 1814).
Ozanam's original edition contained an early example of a problem about orthogonal Latin squares:-
Arrange the 16 court cards so that each row and each column contains one of each suit and one of each value.

1782 Olry Terquem (16 June 1782 – 6 May 1862) was a French mathematician. He is known for his works in geometry and for founding two scientific journals, one of which was the first journal about the history of mathematics. He was also the pseudonymous author (as Tsarphati) of a sequence of letters advocating radical Reform in Judaism. He was French Jewish.
Terquem translated works concerning artillery, was the author of several textbooks, and became an expert on the history of mathematics. Terquem and Camille-Christophe Gerono were the founding editors of the Nouvelles Annales de Mathématiques in 1842. Terquem also founded another journal in 1855, the Bulletin de Bibliographie, d'Histoire et de Biographie de Mathématiques, which was published as a supplement to the Nouvelles Annales, and he continued editing it until 1861. This was the first journal dedicated to the history of mathematics.

The three marked points that lie on the nine point circle and interior to the triangle were found by Terquem. The point of convergence of the three red lines through the triangle is its orthocenter. He is also known for naming the nine-point circle and fully proving its properties. This is a circle defined from a given triangle that contains nine special points of the triangle. Karl Wilhelm Feuerbach had previously observed that the three feet of the altitudes of a triangle and the three midpoints of its sides all lie on a single circle, but Terquem was the first to prove that this circle also contains the midpoints of the line segments connecting each vertex to the orthocenter of the triangle. He also gave a new proof of Feuerbach's theorem that the nine-point circle is tangent to the incircle and excircles of a triangle.
Terquem's other contributions to mathematics include naming the pedal curve of another curve, and counting the number of perpendicular lines from a point to an algebraic curve as a function of the degree of the curve. He was also the first to observe that the minimum or maximum value of a symmetric function is often obtained by setting all variables equal to each other.
He became an officer of the Legion of Honor in 1852. After he died, his funeral was officiated by Lazare Isidor, the Chief Rabbi of Paris and later of France, and attended by over 12 generals headed by Edmond Le Bœuf.

1801 Julius Plucker (16 June 1801 – 22 May 1868)  born in Elberfeld, Germany. He was a geometer who worked in analytic andprojective geometry, and on the theory of plane curves.*VFR  He  was a pioneer in the investigations of cathode rays that led eventually to the discovery of the electron. He also vastly extended the study of Lamé curves. *VFR (Lame curves are curves with equations  of the form (x/a)^n + (y/b)^n = 1.  He investigated n for both rational and irrational values Piet Hein's   "super-ellipse" is an example of a Lame curve.)

1830 Alfred Enneper (June 14, 1830, Barmen - March 24, 1885 Hanover) born. He worked on elliptic functions and differential geometry. *VFR

1839  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

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

1866 James P. Pierpont (June 16, 1866, New Have, Connecticut, USA – December 9, 1938) American mathematician. His father Cornelius Pierpont was a wealthy New Haven businessman. He did undergraduate studies at Worcester Polytechnic Institute, initially in mechanical engineering, but turned to mathematics. He went to Europe after graduating in 1886. He studied in Berlin, and later in Vienna. He prepared his PhD at the University of Vienna under Leopold Gegenbauer and Gustav Ritter von Escherich. His thesis, defended in 1894, is entitled Zur Geschichte der Gleichung fünften Grades bis zum Jahre 1858. After his defense, he returned to New Haven and was appointed as a lecturer at Yale University, where he spent most of his career. In 1898, he became professor. Initially, his research dealt with Galois theory of equations. After 1900, he worked in real and complex analysis.
In his textbooks of real analysis, he introduced a definition of the integral analogous to Lebesgue integration. His definition was later criticized by Maurice Fréchet. Finally, in the 1920s, his interest turned to non-Euclidean geometry. *Wik

1888  Alexander Alexandrovich Friedmann (June 16 (4 old style)  – September 16, 1925, Leningrad, USSR) Russian mathematician who was the first to work out a mathematical analysis of an expanding universe consistent with general relativity, yet without Einstein's cosmological constant. In 1922, he developed solutions to the field equations, one of which clearly described a universe that began from a point singularity, and expanded thereafter. In his article On the Curvature of Space received by the journal Zeitschrift für Physik on 29 Jun 1922, he showed that the radius of curvature of the universe can be either an increasing or a periodic function of time. In Jul 1925, he made a record-breaking 7400-m balloon ascent to make meteorological and medical observations. A few weeks later he fell ill and died of typhus. *TIS  (His date of birth is often given as 29 June. However this is an error which came about in converting the "Old Style" Russian date to the "New Style" date, which requires an addition of 12 days.)

1915  John Wilder Tukey (June 16, 1915 – July 26, 2000) was an American statistician.  He was awarded the IEEE Medal of Honor in 1982 "For his contributions to the spectral analysis of random processes and the fast Fourier transform (FFT) algorithm."
Tukey retired in 1985. He died in New Brunswick, New Jersey Tukey coined many statistical terms that have become part of common usage, but the two most famous coinages attributed to him were related to computer science.
While working with John von Neumann on early computer designs, Tukey introduced the word "bit" as a contraction of "binary digit". The term "bit" was first used in an article by Claude Shannon in 1948.
The term "software", which Paul Niquette claims he coined in 1953, was first used in print by Tukey in a 1958 article in American Mathematical Monthly, and thus some attribute the term to him;  He also is credited with the terms ANOVA, and boxplot. *Wik


1902 Friedrich Wilhelm Karl Ernst Schröder (25 November 1841 in Mannheim, Germany -16 June 1902 in Karlsruhe, Germany) Friedrich Wilhelm Karl Ernst Schröder (25 November 1841 in Mannheim, Baden, Germany – 16 June 1902 in Karlsruhe, Germany) was a German mathematician mainly known for his work on algebraic logic. He is a major figure in the history of mathematical logic (a term he may have invented)[citation needed], by virtue of summarizing and extending the work of George Boole, Augustus De Morgan, Hugh MacColl, and especially Charles Peirce. He is best known for his monumental Vorlesungen über die Algebra der Logik (Lectures on the algebra of logic), in 3 volumes, which prepared the way for the emergence of mathematical logic as a separate discipline in the twentieth century by systematizing the various systems of formal logic of the day. *Wik

1910 Julius Weingartnen (2 March 1836 in Berlin – 16 June 1910 in Freiburg im Breisgau) He worked on differential geometry. He received his doctorate in 1864 from Martin-Luther-Universität Halle-Wittenberg. He made some important contributions to the differential geometry of surfaces, such as the Weingarten equations *Wik

1948 Marcel Brillouin (19 December 1854 – 16 June 1948) worked on topics ranging from history of science to the physics of the earth and the atom. *SAU

1970 Sydney Chapman (29 January 1888 – 16 June 1970) English mathematician and physicist noted for his research in geophysics. After graduation (1910) he worked at the Greenwich Observatory, but returned to Cambridge upon the outbreak of WW I. Between 1915 and 1917 he completed a series of important papers on thermal diffusion and the fundamentals of gas dynamics. He developed systematic approximations to the Maxwell-Boltzmann formulation for the velocity distribution function for interacting particles under general force laws. During WW II he worked on military operational research and incendiary bomb problems. Chapman's main area of research was geomagnetism, beginning in 1913 and extending to terrestrial and interplanetary magnetism, the ionosphere and the aurora borealis.*TIS

1977 Wernher Magnus Maximilian von Braun (23 Mar 1912; 16 Jun 1977 at age 65) was a German-American rocket engineer who was one of the most important developers of rockets and their evolution to applications in space exploration. His interest began as a teenager in Germany, and during WW II he led the development of the deadly V–2 ballistic missile for the Nazis (which role remains controversial). After war, he was taken to use his knowledge to produce rockets for the U.S. Army. In 1960, he transferred to the newly formed NASA and became director of Marshall Space Flight Center and chief architect of the Saturn V launch vehicle used to put men on the moon. His contributions include the Explorer satellites; Jupiter, Pershing, Redstone and Saturn rockets, and Skylab. *TIS

1990 Thomas George Cowling (17 June 1906 in Hackney, London, England - 16 June 1990 in Leeds, England) Tom Cowling graduated from Oxford and worked at Imperial College London. He lectured at Swansea, Dundee and Manchester and became a professor at Bangor and Leeds. He worked on theoretical astronomy and stellar physics. *SAU

2001 Alessandro Faedo (18 November 1913 – 15 June 2001) (also known as Alessandro Carlo Faedo or Sandro Faedo) was an Italian mathematician and politician, born in Chiampo. He is known for his work in numerical analysis, leading to the Faedo–Galerkin method: he was one of the pupils of Leonida Tonelli and, after his death, he succeeded him on the chair of mathematical analysis at the University of Pisa, becoming dean of the faculty of sciences and then rector and exerting a strong positive influence on the development of the university. *Wik

2004 Herman Heine Goldstine (September 13, 1913 – June 16, 2004) was a mathematician and computer scientist, who was one of the original developers of ENIAC, the first of the modern electronic digital computers.
Herman Heine Goldstine was born in Chicago in 1913 to Jewish parents. He attended the University of Chicago, where he joined the Phi Beta Kappa fraternity, and graduated with a degree in Mathematics in 1933, a master's degree in 1934, and a PhD in 1936. For three years he was a research assistant under Gilbert Ames Bliss, an authority on the mathematical theory of external ballistics. In 1939 Goldstine began a teaching career at the University of Michigan, until the United States' entry into World War II, when he joined the U. S. Army. In 1941 he married Adele Katz, who was an ENIAC programmer and who wrote the technical description for ENIAC. He had a daughter and a son with Adele, who died in 1964. Two years later he married secondly Ellen Watson.
In retirement Goldstine became executive director of the American Philosophical Society in Philadelphia between 1985 and 1997, in which capacity he was able to attract many prestigious visitors and speakers.
Goldstine died on June 16, 2004 at his home in Bryn Mawr, Pennsylvania, after a long struggle with Parkinson's disease. His death was announced by the Thomas J. Watson Research Center in Yorktown Heights, New York, where a post-doctoral fellowship was renamed in his honor. *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