## Wednesday 19 October 2022

### On This Day in Math - October 19

I am a great believer in the simplicity of things and as you probably know I am inclined to hang on to broad & simple ideas like grim death until evidence is too strong for my tenacity.
~Sir Ernest Rutherford

The 292nd day of the year; The continued fraction representation of pi  is [3; 7, 15, 1, 292, 1, 1, 1, 2...]; the convergent obtained by  truncating before the surprisingly large term 292 yields the excellent  rational approximation $\frac{355/}{113}$ for pi.
The approximation was found by Chinese mathematician and astronomer Zu Chongzhi(429–500 AD), using Liu Hui's algorithm which is based on the areas of regular polygons approximating a circle*Wik (My mnemonic for this, "1,1,3,3,5,5; divide in the niddle, put big over little."

292 is the number of ways to make change for 1 dollar (or for 1 Euro), using only 1, 5 and 25 cent coins (base five coins).

292! + 291! ± 1 are 595-digit twin primes. (Are there smaller sums of consecutive factorials like this that are twin primes?)

EVENTS

1698 Halley began a scientific voyage on HMS Paramore & set out to measure magnetic variation & search for Terra Incognita *Kate Morant‏@KateMorant
This was the first time a sea voyage had been planned for the sole purpose of scientific discovery.

1752 Franklin described his kite experiment in a letter written in Philadelphia and addressed to Peter Collinson, who had earlier provided Franklin with some simple apparatus for performing electrical experiments.  The kite was not struck by lightning, but Franklin notices the loose strands of the rain soaked  hemp rope  standing out straight and recognized the phenomena as indicating static electric charge, and reached out a finger and got a mild shock.
On the same date his experiment was described in the Pennsylvania Gazette.
A copy of the original letter is at present in the archives of the Royal Society in London. *Julian Rubin web site

1759 Gauss writes,in a letter to his former teacher, E. A. W. von Zimmermann, when he showed up at the Göttingen University library, "I cannot deny, that I found it very unpleasant that most of my beautiful discoveries in indefinite analysis were not original. What consoles me is this. All of Euler's discoveries that I have so far found, I have made also, and still more so. I have found a more general, and, I think, more natural viewpoint; yet I still see an immeasurable field before me..." *Animating Creativity, The LaRouche Youth Movement web page.

1892: The first long-distance telephone line opened between the cities of New York and Chicago, although it could only handle one call at a time.
Seated at a telephone in the American Telephone and Telegraph Company’s office in Quincy street, Chicago Mayor Washburne conducted Chicago’s end of the above conversation. At the. other end of the wire was Mayor Grant of New York. With this simple ceremony the long-distance telephone between Chicago and New York was formally placed in service.

Sixty persons were present to see it done. They were telephone men, merchants, and newspaper men. There were 150 people around Mayor Grant at the company’s office in Cortland street. New York, and the company so managed matters that everybody got a chance to test the workings of the line. They invited all to stand beneath two funnels fastened to the gas fixture and keep perfectly still. They did so and heard the “Star Spangled Banner” played by a cornetist in New York. Then the New York crowd gathered around similar funnels while cornetist Cobb of Johnny Hand’s orchestra played the national anthem for them. *chicagology.com

This was not the first long distance call in the US, that had happened fifteen years earlier in California. The world's first long-distance telephone line, established in 1877, connected French Corral with Bowman Lake (previously known as French Lake) at the headwaters of the Yuba River. It was strung across trees and poles for a distance of 60 mi (97 km) in Nevada County, California, passing through Birchville, Sweetland, North San Juan, Cherokee, North Columbia, Lake City, North Bloomfield, Moores Flat, Graniteville, and Milton.
The line was operated by the Ridge Telephone Company for the service of Milton Mining and Water Company, as well as other water companies. The line was an improvement over the system used in nearby Downieville, California The site is now a California Historical Landmark. *Wik Unfortunately, it seems no one made note of the first conversation.

1901 Alberto Santos-Dumont won the French Aero Club’s Deutsch Prize, rounding the Eiffel Tower and landing at Parc Saint Cloud in twenty-nine minutes and thirty seconds in his dirigible. Later it became common that a crowd would gather to see the aviator driving his Baladeuse (The Wanderer), a personal sized dirigible, over the streets as if it were a carriage or automobile.
A few years later, on October 23, 1906, Santos-Dumont won the Archdeacon prize by flying his Hargrave box kite inspired aircraft at Bagatelle in Paris. He was hailed by many in Europe as the first to fly, despite the fact that the Wright Brothers had achieved such a feat three years earlier in the United Sates. But Orville and Wilbur Wright kept their invention under wraps, avoiding any public exhibitions while they sought a patent. Most aeronauts in Europe considered them to be bluffing., *theappendix.net

1948 The National Bureau of Standards authorized construction of its Standards Western Automatic Computer. The machine, which would be built at the Institute for Numerical Analysis in Los Angeles, had an objective to compute using already-developed technology. This was in contrast to the machine’s cousin, the Standards Eastern Automatic Computer, which tested components and systems for computer *CHM

1965 The London Times reported that an archaeologist has located what he believes to be the tomb of Archimedes.*VFR

In 1973, a US Federal Judge signed his decision following a lengthy court trial which declared the ENIAC patent invalid and belatedly credited physicist John Atanasoff with developing the first electronic digital computer, the Atanasoff- Berry Computer or the ABC. Built in 1937-42 at Iowa State University by Atanadoff and a graduate student, Clifford Berry, it introduced the ideas of binary arithmetic, regenerative memory, and logic circuits. These ideas were communicated from Atanasoff to John Mauchly, who used them in the design of the better-known ENIAC built and patented several years later.*TIS

1994 The Pentium FDIV bug error was isolated to the Pentium Pro chip by Professor Thomas R. Nicely at Lynchburg College, Virginia, USA while working on Brun's constant (the sum of the reciprocals of the odd twin primes).   Nicely had noticed some inconsistencies in the calculations on June 13, 1994 shortly after adding a Pentium system to his group of computers, but was unable to eliminate other factors (such as programming errors, motherboard chipsets, etc.) until October 19, 1994. On October 24, 1994 he reported the issue to Intel.   The bug was rarely encountered by average users (Byte magazine estimated that 1 in 9 billion floating point divides with random parameters would produce inaccurate results) *Wik

2014 Small chance that Comet C/2013 A1 (Siding Spring), discovered in the beginning of 2013, might collide with Mars. At the moment, based on the observation arc of 74 days, the nominal close approach distance between the red planet and the comet might be as little as 0.00073 AU, that is approximately 109,200 km! Distance to Mars’ natural satellite Deimos will be smaller by 6000 km, making it 103,000 km. On the 19th October 2014, the comet might reach apparent magnitude of -8…-8.5, as seen from Mars! *Spaceobs.org

BIRTHS

1795 Arthur Jules Morin​ (19 October 1795 – 7 February 1880) was a French physicist. He conducted experiments in mechanics and invented the Morin dynamometer.
In 1850, he was elected a foreign member of the Royal Swedish Academy of Sciences. His name is one of the 72 names inscribed on the Eiffel Tower.*Wik (He was also the director of my favorite Paris Museum, Musee des Arts et Métiers.) In the issue of Nature which appeared on 5 February 1880 the following report appears:-
We regret to state that General Morin, the well-known director of the Conservatoire des Arts et Métiers, is lying in a very precarious state in consequence of a severe cold. Great anxiety is felt for him at the Institute, of which he is one of the most respected and popular members. The General is aged 85 years. In the following issue of Nature, his death in Paris on 7 February was reported. *SAU

1871 John Miller (19 Oct 1871 in Glasgow, Scotland - 14 July 1956 in Victoria Infirmary, Glasgow, Scotland) studied at Glasgow and Göttingen. He returned to Glasgow to the Royal College of Science and Technology (the precursor to Strathclyde University). He became President of the EMS in 1913. *SAU

1903 Jean Frédéric Auguste Delsarte (October 19, 1903, Fourmies – November 28, 1968, Nancy) was a French mathematician known for his work in mathematical analysis, in particular, for introducing mean-periodic functions and generalized shift operators. He was one of the founders of the Bourbaki group.*Wik

1910 Subrahmanyan Chandrasekhar (19 Oct 1910; 21 Aug 1995) Indian-born American astrophysicist who (with William A.Fowler) won the 1983 Nobel Prize for Physics for formulating the currently accepted theory on the later evolutionary stages of massive stars. He was one of the first scientists to combine the disciplines of physics and astronomy. Early in his career he demonstrated that there is an upper limit, now called the Chandrasekhar limit, to the mass of a white dwarf star. A white dwarf is the last stage in the evolution of a star such as the Sun. When the nuclear energy source in the center of a star such as the Sun is exhausted, it collapses to form a white dwarf. Further, it shows that stars much more massive than the Sun must either explode or form black holes. *TIS

DEATHS

1586 Egnatio Danti was an Italian Dominican who made contributions to architecture, geography and astronomy.Finally, among Danti's publications, we mention Trattato del radio latino (1586) which is Danti's work describing his surveying instrument. This book appeared in the year in which Danti died. The other task he undertook just before his death was to travel to Rome, at the request of Pope Sixtus, to assist the architect Domenico Fontana, who had become architect to the papacy when Sixtus was elected, in moving the Egyptian obelisk from its place in the circus of the Vatican. The obelisk had been brought to Rome in the 1st century AD and Danti and Fontana erected it in 1586 where it now stands in the centre of St Peter's Square in the Vatican. After his return from this trip to Rome, Danti contracted pneumonia from which he died. *SAU

1875 Sir Charles Wheatstone (6 Feb 1802, 19 Oct 1875) English physicist who popularized the Wheatstone bridge, a device that accurately measured electrical resistance and became widely used in laboratories. He didn't actually invent the "Wheatstone Bridge". His contemporary, Samuel Hunter Christie, came up with the idea of the bridge circuit, but Wheatstone set the precedent for using it in the way in which it has been most commonly used. Over time, the device became associated with him and took on his name. He did, however, invent the concertina (1829), the stereoscope (1838), and an early form of the telegraph. He also  developed a chronoscope (1842) to determine the velocity of projectiles at an English gunnery.*TIS (For students of discrete math, or interested in codes, Wheatstone was also the creator of the Playfair Cipher.) A story is told that among friends he was "the life of the party" however he was afraid to speak in public. It was not unlike Wheatstone to set up a speaking engagement and cancel at the very last minute due to an awful case of stage fright. As a result of this condition Michael Faraday commentated much of Whetstone's work to the Royal Society through Faraday's famous Friday night lectures. On one such occasion Wheatstone was scheduled to speak at the Royal society and of course literally ran out the back door of the conference hall at the last minute. Faraday stepped onto the stage and delivered one of his most famous lectures, which was on the discovery of the Electro-magnetic field.

1878 Irénée-Jules Bienaymé (28 August 1796 - 19 October 1878) was a French statistician. He built on the legacy of Laplace generalizing his least squares method. He contributed to the fields and probability, and statistics and to their application to finance, demography and social sciences. In particular, he formulated the Bienaymé-Chebyshev inequality concerning the law of large numbers and the Bienaymé formula for the variance of a sum of uncorrelated random variables.*Wik

1890 Émile Léonard Mathieu (15 May 1835 in Metz, France - 19 Oct 1890 in Nancy, France) is remembered especially for his discovery (in 1860 and 1873) of five sporadic simple groups named after him. These were studied in his thesis on transitive functions.*SAU

1937 Sir Ernest Rutherford (30 Aug 1871, 19 Oct 1937) (baron) New Zealand-born British physicist who laid the groundwork for the development of nuclear physics. He worked under Sir J. J. Thomson at Cambridge University (1895-98). Then he collaborated with Frederick Soddy in studying radioactivity. In 1899 he discovered alpha particles and beta particles, followed by the discovery of gamma radiation the following year. In 1905, with Soddy, he announced that radioactive decay involves a series of transformations. In 1907, with Hans Geiger and Ernest Marsden, he devised the alpha-particle scattering experiment that led in 1911 to the discovery of the atomic nucleus. In 1919 he achieved the artificial splitting of light atoms. In 1908 he was awarded the Nobel Prize for Chemistry. *TIS

1944 Denes König (21 Sept 1884 in Budapest, Hungary - 19 Oct 1944 in Budapest, Hungary) At Göttingen, König had been influenced by Minkowski's lectures on the four color problem. These lectures contributed to his growing interest in graph theory, on which he lectured in Budapest from 1911. His book, Theorie der endlichen und unendlichen Graphen, was published in 1936, and was a major factor in the growth of interest in graph theory worldwide. It was eventually translated into English under the title Theory of finite and infinite graphs (translated by R McCoart), Birkhauser, 1990; this also contains a biographical sketch by Tibor Gallai​.  König's work on the factorization of bipartite graphs relates closely to the marriage problem of Philip Hall. König's use of graphs to give a simpler proof of a determinant result of Frobenius seems to have led to some hostility between the two men.
After the Nazi occupation of Hungary, König worked to help persecuted mathematicians. This led to his death a few days after the Hungarian National Socialist Party took over the country. *SAU

1979 Marjorie Lee Browne (September 9, 1914 – October 19, 1979) was a notable mathematics educator, the second African-American woman to receive a doctoral degree in the U.S., and one of the first black women to receive a doctorate in mathematics in the U.S.*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