## Monday, 12 June 2017

### On This Day in Math - June 12

My work always tried to unite the true
with the beautiful, but when I had to choose...
I usually chose the beautiful.
~ Hermann Weyl

The 163rd day of the year; $e^{\pi*\sqrt{163}}$ is an integer. Ok, not quite, see the bottom of  the blog for details.  *Prime Curios

Colin Beveridge ‏@icecolbeveridge pointed out that $(2+\sqrt{3})^{163}$ is also very, very close to an integer. (but it is very large,greater than 1093 , and was not, to my knowledge, ever the source of an April fools joke.)

163 is conjectured to be the largest prime that can be represented uniquely as the sum of three squares /( 163 = 1^2 + 9^2 + 9^2 /).

Most students know that the real numbers can be uniquely factored. . Some other fields can be uniquely factored as well, for instance, the complex field a+bi where i represents the square root of -1 is such a field.  In 1801, Gauss conjectured that there were only nine integers k such that $a + b\sqrt{-k}$ is a uniquely  factorable field.  The largest of these integers is 163.  Today they are called Heegner numbers after a proof by Kurt Heegner in 1952.

EVENTS

1493 First issue of Nuremberg Chronicles published in Latin (A German edition would be issued in December). The journal is said to have printed an image of the 684 passage of Halley's comet. Roberta Olsen and Jay Pasachoff of Wheaton College have written that the same woodblock was used to depict four other comets. They also said the Chronicles use three more prints to depict this same 684 comet in different editions. The one below, from the Library of Congress Collection, is the one which was in the Art Exhibit at the Smithsonian Air and Space Museum in Washington, D.C., entitled: "Fire and Ice - A History of Comets in Art"
For more detail about the Chronicles check out this post by the Renaissance Mathematicus.

1676   a partial solar eclipse which was to be viewed as something of an opening ceremony for the Royal Observatory in Greenwich: it was hoped that the King would attend but he did not, Lord Brouncker, President of the Royal Society, being the guest of honour instead. *Rebekah Higgitt, Telescopos

1689 Although they had corresponded, through Oldenburg, about optics sixteen years earlier (much to Newton’s grief), Newton ﬁrst met Christiaan Huygens at a Royal Society meeting in London.
[Newton, Mathematical Papers, 6, xxiii] *VFR

In 1837, British inventors William Cooke and Charles Wheatstone received a patent for their electromagnetic telegraph. Their invention was put in public service in 1839, five years before the more famous Morse telegraph.*TIS Wheatstone's telegraph was a five wire/five needle telegraph that had a receiver that pointed out the message letter by letter without a code such as Morse used for his one and two wire models. (Wheatstone was very capable of creating codes as well. He was the creator of the Playfair cipher; an ingenious system which prevented frequency analysis by substituting two letters at a time.)

 1891, the Swiss Army Soldier Knife
In 1897, the Swiss Army Knife was patented by Carl Elsener *TIS It was in Ibach, in 1884, where Karl Elsener and his mother, Victoria, opened a cutlery cooperative that would soon produce the first knives sold to the Swiss Army. The original model, called the Soldier Knife, was made for troops who needed a foldable tool that could open canned food and aid in disassembling a rifle. The Soldier Knife included a blade, a reamer, a can opener, a screwdriver, and oak handles. *gearjunkie.com

In 1908, the Rotherhithe-Stepney tunnel beneath the Thames in South London was opened for road vehicle traffic. It was built by Sir Maurice Fitzmaurice between 1904 and 1908. With a length of 4860 feet (1481 metres) excluding the approaches, it remains the largest iron-lined subaqueous tunnel in the world. It was constructed partly by tunneling and partly by the cut and cover method. The area around the entrances was cleared resulting in 3,000 people being rehoused. It is located close to the Rotherhithe-Wapping Thames Tunnel built (1825-43) by Marc Brunel and his son, Isambad K. Brunel which was the world's first tunnel beneath a navigable river.*TIS

1973 Germany issued a postage stamp picturing a model of the calculator built by Wilhelm Schickard of the University of Tubingen 350 years before. [Scott #1123].

1979 Bryan Allen, age 26, of the U.S. pedaled the Gossamer Albatross on the ﬁrst human powered ﬂight across the English channel. This 21 mile ﬂight won him a £100,000 prize oﬀered by British industrialist Henry Kremer. Two years earlier Allen was the ﬁrst to ﬂy an aircraft around a one-mile ﬁgure eight course under human power alone. See “Human-powered ﬂight,” Scientiﬁc American, November 1985, p. 144. *VFR

BIRTHS

1577 Paul Guldin born (original name Habakkuk Guldin) (June 12, 1577 – November 3, 1643) was a Swiss Jesuit mathematician and astronomer. He discovered the Guldinus theorem to determine the surface and the volume of a solid of revolution. This theorem is also known as Pappus–Guldinus theorem and Pappus's centroid theorem, attributed to Pappus of Alexandria. ( simply stated: that the volume = area times distance traveled by the centroid, and surface = arclength times distance travelled by centroid. These nicely produce the surface area and volume of a torus, for example.) He was noted for his association with the German mathematician and astronomer Johannes Kepler. He was born in Mels, Switzerland and was a professor of mathematics in Graz and Vienna.
In Paolo Casati's astronomical work Terra machinis mota (1658), Casati imagines a dialogue between Guldin, Galileo, and Marin Mersenne on various intellectual problems of cosmology, geography, astronomy and geodesy. *Wik
Paul Guldin's critique of Bonaventura Cavalieri's indivisibles is contained in the fourth book of his De Centro Gravitatis (also called Centrobaryca), published in 1641. Cavalieri's proofs, Guldin argued, were not constructive proofs, of the kind that classical mathematicians would approve of. *Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, by Amir Alexander

1806 John A. Roebling ( June 12, 1806 – July 22, 1869), civil engineer and designer of bridges, was born in Mühlhausen, Prussia. The Brooklyn Bridge, Roebling's last and greatest achievement, spans New York's East River to connect Manhattan with Brooklyn. When completed in 1883, the bridge, with its massive stone towers and a main span of 1,595.5 feet between them, was by far the longest suspension bridge in the world. Today, the Brooklyn Bridge is hailed as a key feature of New York's City's urban landscape, standing as a monument to progress and ingenuity as well as symbolizing New York's ongoing cultural vitality. *Library of Congress

1843 Sir David Gill (12 June 1843 – 24 January 1914) Scottish astronomer known for his measurements of solar and stellar parallax, showing the distances of the Sun and other stars from Earth, and for his early use of photography in mapping the heavens. From his first training as a watchmaker, he progressed to the timekeeping requirements of astronomy. He designed, equipped, and operated a private observatory near Aberdeen. In 1877, Gill and his wife measured the solar parallax by observing Mars from Ascension Island. To determine parallaxes, he perfected the use of the heliometer, a telescope that uses a split image to measure the angular separation of celestial bodies. He later redetermined the solar parallax to such precision that his value was used for almanacs until 1968. *TIS

1851 Sir Oliver Joseph Lodge, FRS (12 June 1851 – 22 August 1940) was a British physicist and writer involved in the development of key patents in wireless telegraphy. In his 1894 Royal Institution lectures ("The Work of Hertz and Some of His Successors"), Lodge coined the term "coherer" for the device developed by French physicist Édouard Branly based on the work of Italian physicist Temistocle Calzecchi Onesti. In 1898 he was awarded the "syntonic" (or tuning) patent by the United States Patent Office. He was also credited by Lorentz (1895) with the first published description of the length contraction hypothesis, in 1893, though in fact Lodge's friend George Francis FitzGerald had first suggested the idea in print in 1889. *Wik

1855 Eduard Wiltheiss (12 June 1855 Worms, Germany – 7 July 1900 Halle) was a German mathematician who made major contributions to the theory of abelian functions *SAU

1888 Zygmunt Janiszewski, (June 12, 1888, Warsaw - January 3, 1920, Lviv) the father of Polish mathematics, born. At the end of World War I, Janiszewski was the driving force behind the creation of one of the strongest schools of mathematics in the world. This is all the more remarkable, given Poland's difficult situaltion at war's end.
Janiszewski devoted the family property that he had inherited from his father to charity and education. He also donated all the prize money that he received from mathematical awards and competitions to the education and development of young Polish students.
In mathematics, his main interest was topology.
He was the driving force, together with Wacław Sierpiński and Stefan Mazurkiewicz, behind the founding of the mathematics journal Fundamenta Mathematicae. Janiszewski proposed the name of the journal in 1919, though the first issue was published in 1920, after his death. It was his intent that the first issue comprise solely contributions by Polish mathematicians. It was Janiszewski's vision that Poland become a world leader in the field of mathematics—which she did in the interbellum.
His life was cut short by the influenza pandemic of 1918-19, which took his life at Lwów on 3 January 1920 at the age of 31. He willed his body for medical research, and his cranium for craniological study, desiring to be "useful after his death". *Wik

1937 Vladimir Arnold (12 June 1937 – 3 June 2010) won a Wolf prize for his work on dynamical systems, differential equations, and singularity theory.*SAU He died nine days before his birthdate in 2010.

DEATHS

1835 Edward Troughton  (October 1753 - June 12, 1835) English scientist and instrument maker. Troughton established himself as the leading maker of instruments in England. He began his instrument making career with instruments to aid navigation, for example, he designed the 'pillar' sextant, patented in 1788, the dip sector, the marine barometer and the reflecting circle built in 1796. Other instruments which he designed were for use in surveying. He designed the pyrometer, the mountain barometer and the large surveying theodolites. His famous instruments were astronomical ones. He made the Groombridge Transit Circle in 1805 and a six foot Mural Transit Circle in 1810 which was erected at the Observatory in Greenwich in 1812. *TIS  Troughton was awarded the Copley Medal of the Royal Society in 1809. He was elected a Fellow of the Royal Society in March 1810. *Wik

1885 (Henry Charles) Fleeming Jenkin (25 Mar 1833; 12 Jun 1885 at age 52) British engineer noted for his work in establishing units of electrical measurement. After earning an M.A. (1851), he worked for the next 10 years with engineering firms engaged in the design and manufacture of submarine telegraph cables and equipment for laying them. In 1861 his friend William Thomson (later Lord Kelvin) procured Jenkin's appointment as reporter for the Committee of Electrical Standards of the British Association for the Advancement of Science. He helped compile and publish reports that established the ohm as the absolute unit of electrical resistance and described methods for precise resistance measurements. *TIS

1900 Jean Frenet (7 February 1816 – 12 June 1900) was a French mathematician best remembered for the Serret-Frenet formulas for a space-curve and they were presented in his doctoral thesis at Toulouse in 1847. *SAU  He wrote six out of the nine formulas, which at that time were not expressed in vector notation, nor using linear algebra.*Wik

1980 Egon Sharpe Pearson, (Hampstead, 11 August 1895 – Midhurst, 12 June 1980) was the only son of Karl Pearson, and like his father, a leading British statistician.
He went to Winchester School and Trinity College, Cambridge, and succeeded his father as professor of statistics at University College London and as editor of the journal Biometrika.
Pearson is best known for development of the Neyman-Pearson lemma of statistical hypothesis testing.
He was President of the Royal Statistical Society in 1955–56, and was awarded its Guy Medal in Gold in 1955. He was awarded a CBE in 1946.
He was elected a Fellow of the Royal Society in Mar 1966. His candidacy citation read: "Known throughout the world as co-author of the Neyman-Pearson theory of testing statistical hypotheses, and responsible for many important contributions to problems of statistical inference and methodology, especially in the development and use of the likelihood ratio criterion. Has played a leading role in furthering the applications of statistical methods - for example, in industry, and also during and since the war, in the assessment and testing of weapons." *Wik

** Actually,  $e^{\pi*\sqrt{163}}$ is approximately 262537412640768743.9999999999992

In the April 1975 issue of Scientific American, Martin Gardner wrote (jokingly) that Ramanujan's constant (e^(pi*sqrt(163))) is an integer. The name "Ramanujan's constant" was actually coined by Simon Plouffe and derives from the above April Fool's joke played by Gardner. The French mathematician Charles Hermite (1822-1901) observed this property of 163 long before Ramanujan's work on these so-called "almost integers."

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