## Saturday, 20 October 2018

### On This Day in Math - October 20

The mathematician plays a game in which he himself invents the rules while the physicist plays a game in which the rules are provided by nature, but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which nature has chosen.
~Paul Dirac

The 293rd day of the year; 293 is a Sophie Germain Prime. (A prime number p such that 2p + 1 is also prime.) Sophie Germain used them in her investigations of Fermat's Last Theorem. It is an unproven conjecture that there are infinitely many Sophie Germain primes.

293 is also the sum of five cubes, $293 = 2^3 + 2^3 + 3^3 + 5^3 + 5^3$

and from Jim Wilder @Wilderlab : 293202 begins with the digits 202 and 202293 begins with the digits 293.

EVENTS

1698 Halley began a scientific voyage on HMS Paramore & set out to measure magnetic variation & search for Terra Incognita. His log entry from the 20th says "Wind WSW a Small Gale I sailed from Deptford about Noon " *Kate Morant‏@KateMorant (Deptford is a small area near Greenwich, east of London along the Thames)

1735 Benjamin Franklin’s paper “On the Usefulness of Mathematics,” appeared in the Pennsylvania Gazette. [NCTM yearbook # 32(1970), p. 20]*VFR
I have also seen the date given as October 30. Some historians also question whether or not this was actually written by Franklin.

1744 In Euler's missing letter of October 20, 1744, Euler announced that he had just discovered a simple curve that exhibited something called a cusp of the second kind or a ramphoid from the Greek for a bird’s beak. L'H^opital (1661-1704) is responsible for defining these two types of cusps. In 1740, Jean-Paul de Gua de Malves (1713- 1785) published a proof that no algebraic curve could have a cusp of the second kind in [Gua de Malves 1740]. Euler was familiar with Gua de Malves' work and had initially accepted his result, but in 1744 he discovered that there was a subtle flaw in the supposed proof. In this letter, he wrote to Cramer that even in the fourth order there is a curved line of this kind, whose equation is, y4- 2xy2 + x2 = x3+ 4yx, which simplifies to y = x(1/2) +/- x(3/4)

*Ed Sandifer, How Euler Did It, MAA

1881 In a letter to Newcomb dated Oct. 20, 1881, Sylvester writes to Charles S. Pierce, "Who is to be the new superintendent of the Coast Survey?
Why should you not allow it to be known that you would accept the appointment supposing you would be willing to do so!" Sylvester was the eminent British mathematician who served as the first chairman of the Department of Mathematics at the Johns Hopkins University (1876-1883). He returned to England in 1884 to occupy the chair of Savilian Professor of Geometry at Oxford. *THE CHARLES S. PElRCE-SIMON NEWCOMB CORRESPONDENCE

1958 Italy issued a stamp to celebrate the 350th anniversary of the birth of Evangelista Torricelli, mathematician and physicist. [Scott #754]. *VFR

1975 The Public Record office in London released information on the Colossus, one of the ﬁrst programmable electronic digital computers. It was built in 1943 for work on cryptography. The Colossus machines were electronic computing devices used by British codebreakers to help read encrypted German messages during World War II. They used vacuum tubes (thermionic valves) to perform the calculations.
Colossus was designed by engineer Tommy Flowers with input from Harry Fensom, Allen Coombs, Sidney Broadhurst and William Chandler at the Post Office Research Station, Dollis Hill to solve a problem posed by mathematician Max Newman at Bletchley Park. The prototype, Colossus Mark 1, was shown to be working in December 1943 and was operational at Bletchley Park by February 1944. An improved Colossus Mark 2 first worked on 1 June 1944, just in time for the Normandy Landings. Ten Colossi were in use by the end of the war. No information about the computer was released until this date. *Wik

1980, Carl Sagan appeared on the cover of TIME

1983, the length of the meter was redefined by the international body Conférence Générale des Poids et Mesures (GCPM) by a method to give greater accuracy. Originally based on one ten-millionth of the distance from the North Pole to the equator, the meter was re-established as the distance that light travels in a vacuum in 1/299,792,458 of a second *TIS (We adjusted the measure of distance by using wavelength of light which had been measured using that same distance scale???? Don't think about it, it will only make you crazy.)

2004 The First Ubuntu Linux Distribution Released. Ubuntu is a free computer operating system based on Debian GNU​/Linux. Its name loosely translated from the Zulu means "humanity," or "a person is a person only through other people." Ubuntu is intended to provide an up-to-date, stable operating system for the average user, with a strong focus on usability and ease of installation. Ubuntu has been rated the most popular Linux distribution for the desktop, claiming approximately 30 percent of desktop Linux installations, according to the 2007 Desktop Linux Market survey. Ubuntu is open source and free. It is sponsored by Canonical Ltd, which is owned by South African entrepreneur Mark Shuttleworth​.*CHM

BIRTHS
1616 Thomas Bartholin (20 Oct 1616; 4 Dec 1680) Danish anatomist and mathematician who was first to describe fully the entire human lymphatic system (1652). He was one of the earliest defenders of Harvey's discovery of the circulation of blood. He was a member of the mathematical faculty of the University of Copenhagen, 1647-49, and anatomy professor there, 1649-61. He published many works on anatomy, physiology and medicine, (1645-74) and in 1658 a general work on pharmacology. In 1654, along with the rest of the medical faculty at the university, Bartholin published advice to the people on how to take care of themselves during the plague. King Christian V named Bartholin as his personal physician, with an annual salary, although Bartolin rarely had to treat the king. *TIS

1632 Sir Christopher Wren (20 Oct 1632; 25 Feb 1723) Architect, astronomer, and geometrician who was the greatest English architect of his time whose famous masterpiece is St. Paul's Cathedral, among many other buildings after London's Great Fire of 1666. Wren learned scientific skills as an assistant to an eminent anatomist. Through astronomy, he developed skills in working models, diagrams and charting that proved useful when he entered architecture. He inventing a "weather clock" similar to a modern barometer, new engraving methods, and helped develop a blood transfusion technique. He was president of the Royal Society 1680-82. His scientific work was highly regarded by Sir Isaac Newton as stated in the Principia. *TIS (I love the message on his tomb in the Crypt of St. Pauls: Si monumentum requiris circumspice ...."Reader, if you seek his monument, look about you."

1863 William Henry Young (20 Oct 1863 in London, England - 7 July 1942 in Lausanne, Switzerland) discovered Lebesgue integration, independently but 2 years after Lebesgue. He studied Fourier series and orthogonal series in general.

1865 Aleksandr Petrovich Kotelnikov (20 Oct 1865 in Kazan, Russia - 6 March 1944 in Moscow, USSR) In 1927 he published one of his most important works, The Principle of Relativity and Lobachevsky's Geometry. He also worked on quaternions and applied them to mechanics and geometry. Among his other major pieces of work was to edit the Complete Works of two mathematicians, Lobachevsky and Zhukovsky. He received many honours for his work, being named Honoured Scientist in 1934, then one year before he died he was awarded the State Prize of the USSR. *SAU

1891 Sir James Chadwick (20 Oct 1891; 24 Jul 1974) English physicist who received the Nobel Prize for Physics (1935) for his discovery of the neutron. He studied at Cambridge, and in Berlin under Geiger, then worked at the Cavendish Laboratory with Rutherford, where he investigated the structure of the atom. He worked on the scattering of alpha particles and on nuclear disintegration. By bombarding beryllium with alpha particles, Chadwick discovered the neutron - a neutral particle in the atom's nucleus - for which he received the Nobel Prize for Physics in 1935. In 1932, Chadwick coined the name "neutron," which he described in an article in the journal Nature. He led the UK's work on the atomic bomb in WW II, and was knighted in 1945. *TIS

1904 Hans Lewy (October 20, 1904 – August 23, 1988) was an American mathematician, known for his work on partial differential equations and on the theory of functions of several complex variables.*Wik

1914 R. H. Bing (October 20, 1914, Oakwood, Texas – April 28, 1986, Austin, Texas) was an American mathematician who worked mainly in the areas of geometric topology and continuum theory. His first two names were just single letters that do not stand for anything. Bing's mathematical research was almost exclusively in 3-manifold theory and in particular, the geometric topology of R3. The term Bing-type topology was coined to describe the style of methods used by Bing.
Bing established his reputation early on in 1946, soon after completing his Ph.D. dissertation, by solving the Kline sphere characterization problem. In 1948 he proved that the pseudo-arc is homogeneous, contradicting a published but erroneous 'proof' to the contrary. In 1951 he proved results regarding the metrizability of topological spaces, including what would later be called the Bing-Nagata-Smirnov metrization theorem.*Wik

DEATHS
1631 Michael Maestlin (30 September 1550, Göppingen – 20 October 1631, Tübingen) was a German astronomer and mathematician, known for being the mentor of Johannes Kepler.
Maestlin studied theology, mathematics, and astronomy/astrology at the Tübinger Stift in Tübingen, a town in Württemberg. He graduated as Magister in 1571 and became in 1576 a Lutheran deacon in Backnang, continuing his studies there.
In 1580 he became a Professor of mathematics, first at the University of Heidelberg, then at the University of Tübingen where he taught for 47 years from 1583. In 1582 Maestlin wrote a popular introduction to astronomy.
Among his students was Johannes Kepler (1571-1630). Although he primarily taught the traditional geocentric Ptolemaic view of the solar system, Maestlin was also one of the first to accept and teach the heliocentric Copernican view. Maestlin corresponded with Kepler frequently and played a sizable part in his adoption of the Copernican system. Galileo Galilei's adoption of heliocentrism was also attributed to Maestlin.
The first known calculation [3] of the reciprocal of the golden ratio as a decimal of "about 0.6180340" was written in 1597 by Maestlin in a letter to Kepler.
He is also remembered for :
Catalogued the Pleiades cluster on 24 December 1579. Eleven stars in the cluster were recorded by Maestlin, and possibly as many as fourteen were observed.
Occultation of Mars by Venus on 13 October 1590, seen by Maestlin at Heidelberg. *Wik

1896 François-Félix Tisserand (13 Jan 1845, 20 Oct 1896) French astronomer whose 4-volume textbook Traité de mécanique céleste (1889-96; "Treatise on Celestial Mechanics") updated Pierre-Simon Laplace's work. At age 28, he was named Director at Toulouse Observatory (1873-78). He went to Japan to observe the 1874 transit of Venus. The 83-cm telescope he installed at the Toulouse Observatory in 1875 had a wooden base insufficiently stable for photographic work, but he was able to use it for observation of the satellites of Jupiter and of Saturn. From 1892 until his death he was director of the Paris Observatory, where he completed the major work, Catalogue photographique de la carte du ciel, and arranged for its publication.*TIS

1972 Harlow Shapley (2 Nov 1885, 20 Oct 1972) Astronomer, known as "The Modern Copernicus," who discovered the Sun's position in the galaxy. From 1914 to 1921 he was at Mt. Wilson Observatory, where he calibrated Henrietta S. Leavitt's period vs. luminosity relation for Cepheid variable stars and used it to determine the distances of globular clusters. He boldly and correctly proclaimed that the globulars outline the Galaxy, and that the Galaxy is far larger than was generally believed and centered thousands of light years away in the direction of Sagittarius. In the early 1920's, Shapley entered a "Great Debate" with Heber D. Curtis. They truly argued over the "Scale of the Universe."*TIS

1974 Harold Ruse graduated from Oxford and held a position at Edinburgh University. he later became a professor at Southampton and Leeds. He worked on Harmonic Spaces. He became Secretary of the EMS in 1930 and President in 1935. *SAU

1984 Paul A.M. Dirac (8 Aug 1902, 20 Oct 1984) English physicist and mathematician who originated quantum mechanics and the spinning electron theory. In 1933 he shared the Nobel Prize for Physics with the Austrian physicist Erwin Schrödinger.*TIS

1987 Andrey Nikolayevich Kolmogorov (25 Apr 1903, 20 Oct 1987) Russian mathematician whose basic postulates for probability theory that have continued to be an integral part of analysis. This work had diverse applications such as his study of the motion of planets (1954), or the turbulent air flow from a jet engine (1941). In topology, he investigated cohomology groups. He made a major contribution to answering the probability part of Hilbert's Sixth Problem, and completely resolved (1957) Hilbert's Thirteenth Problem. Kolmogorov was active in a project to provide special education for gifted children, not only by writing textbooks and in teaching them, but in expanding their interests to be not necessarily in mathematics, but with literature, music, and healthy activity such as on hikes and expeditions. *TIS

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

## Friday, 19 October 2018

### A Play on Words, that could really have happened!

In my youth I had a fortunate encounter with the book, Thirty Days to a More Powerful Vocabulary. Ever since then I have had an affection for etymology and word origins and the history of word usage (especially math terms, which spawned this blog site in the first place.) This old post was prompted by such thoughts. Enjoy:

It never happened, but it could have...

Student reading a medical Journal to Teacher: What is the meaning of ideopathic?

Teacher, without looking up: "I don't know."

Student: "Ok, I'll look it up."

He walks to the dicitionary and looks it up... moments later the dictionary is slammed shut, and as he passes the teacher..."That was NOT funny."

Teacher:"My personal feeling is that it would be, if you checked the etymology."

If you are curious, or confused, see here and don't forget to check the etymology.

### 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

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. 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

## Thursday, 18 October 2018

### Another Approach to Pythagorean Triangles, using graphing

Click on image to enlarge

I wrote a couple of posts a while back on the Barning Tree method of finding Pythagorean triples using matrices, and then a followup. I recently came across another approach to Pythagorean triples that involves a clever relationship between points on the positive y-axis, and points on the unit circle. (ok, maybe I should have known this, but I didn't.. and I think it is really a neat idea)
On the unit circle, x2 + y 2 = 1, if we draw a secant from the point (-1,0) through (0,t) on the y-axis, it turns out that if t is a rational number, then the coordinates of P=(x,y) where the secant intersects the circle, will also be rational. Since the slope of the line is also t, the equation is y=tx+t ... and so and t2= (1-x2)/(1+x)2. That means t = y/(x+1) which leads to x= (1-t^2)/(1+t^2) and y= (2t)/(1+t^2) If we pick some rational number to be t, say t=2/7,
then x= 45/53 and y= 28/53.... Then by similar triangles, there must be a circle with radius 53 and a point on the circle would be (28, 45) and in fact 282+452=532... and any such rational point will produce another Image of unit circle

### A Curious Property of Vulgar Fractions

Another from 2008, hope you enjoy:

John Farey was a geologist, not a mathematician, but he is better remembered today for a single short (four paragraphs) paper he wrote in 1816 than for all his good works in geology. In that year he sent a paper to the Philosophical Magazine (or at least it was published in that year) called On a curious property of vulgar fractions .and described a pattern that appears in sequences of what we would today call common (vulgar is the Latin term for common) fractions, like 3/8 etc, which are in simplest terms. They observation has almost NO practical use, not even to prove other things mathematically, and yet, it seems to have all kinds of interesting properties that tend to keep us fascinated with it. If you have never been introduced to it, here is a brief description, and some novel relationships that I think are interesting, with some links to places where they are made clearer than I could do in this brief space.

So First... What is it we are talking about? If you take ALL the fractions that could be written in simplest terms with a denominator less than some number n, say n=5 (since that is the one Farey used in his paper), and put them in order from lowest to highest... you get
The "curious" thing that Farey noticed is that if you ignore the way your fifth grade teacher taught you to add fractions, and do it the way YOU would have added them, "add the tops, add the bottoms", then each number in the sequence is the sum of the terms on each side of it... for example 1/4 and 2/5 are on each side of 1/3, and if you add by this approach you get (1+2)/(4+5) = 3/9 and that simplifies to 1/3 . The number obtained by adding two fractions in this fashion is often called the mediant .

OK, so that is how you make them. Our first question might be, how many of them are there? F(5) obviously has eleven terms (I counted). If we picked a value of N, what would be the number of fractions in the set F(N). A little investigation would show that F(1) = 2 (0 and 1); and F(2) = 3 (0, 1/2, and 1). So how many would be added to the next set... and the next... it turns out that each new set will have all the values of the previous set (of course) and will add one for every value of one through n that is co-prime (has no common divisors) to n. So the set for N=6 will have the eleven terms of F(5) plus 1/6 (one has no common factor with six), and 5/6. (notice that 2/6, 3/6, and 4/6 are already in the sequence in F(5) in simplified form)... thus F(6) has thirteen terms.. and in general we get a recursive formula that say the Order of F(N) = Order of F(n-1) + φ(n).
A second nice curiosity related to Farey Sequences are the Ford Circles. "Ford circles are named after American mathematician Lester R. Ford, Sr., who described them in an article in American Mathematical Monthly in 1938, volume 45, number 9, pages 586-601" (from Wikipedia). In fact, the wikipedia article is a nice place to see how they work, and I need say no more as it shows the circles for F(5). What is amazing is that each circle is tangent to every other circle for a fraction it will be adjacent to in ANY sequence.... ahhh, go on..say "cool".

I decided to mention this when I came across another curious property of Farey sequences that relates them to lines on the plane and Pick's Theorem. If you treated each fraction a/b as a point (b,a) then none of the lines cross. If you make a triangle with the origin and any two adjacent Farey fractions, since each of the triangles have a determinant of one (meaning the area is 1/2) and therefore, by PIck's theorem, they cannot contain any other lattice points in their interior. A nice explanation of this, including the photo below, is at the Cut-The-Knot web site

### On This Day in Math - October 18

All models are wrong, some models are useful.

~George Box

The 291st day of the year; 291 is the largest number that is not the sum of distinct non-trivial powers.

$\phi(291) = 192$  The number of integers less than, and relatively prime to 291 is equal to it's reversal, 192.

291 is also equal to the nth prime + n.... but for which n, children?

EVENTS
1092 Walcher, the Prior of the monastery in Great Malvern, U.K., carried out the first known Western Experiment to improve astronomical predictions when he pointed an astrolabe toward a lunar eclipse. At this time his astrolabe was one of only a few in Europe. *Jonathan Lyons, The House of Wisdom: How the Arabs Transformed Western Civilization.

1640 Pierre de Fermat (1601–1665) explains his ‘little theorem’ to Bernard Frenicle de Bessey in a follow up to two previous letters. ("On the subject of progressions, I have sent to you in advance the propositions that serve to determine the properties of powers minus one"). The theorem, which states that np−1 ≡ 1 (mod p) if p is prime and relatively prime to n, was proved by Euler in 1736 by induction on n.[Scientiﬁc American, December 1982]
1) When the exponent, n, is composite, 2n-1 is also composite,
2) When the exponent, n, is prime, 2n -2 is divisible by 2*n,
3) When the exponent, n, is prime, the number 2n -1 can not be divided by any number less than 2n+1

*Jacqueline Stedall, Mathematics Emerging

1740  In a letter to Johann Bernoulli, Euler uses imaginary in the exponent. exi + e-xi = 2 cos(x) {note Euler used squareroot of -1 rather than i. Euler would be the first to use i for the imaginary constant, but not until a paper he presents in St. Petersburg in 1777.} Cajori seems to imply, but does not state explicitly, that this is the first time an imaginary has been used as an exponent.

1954, Texas Instruments & Industrial Development Engineering Assoc launch the first transistor radio, Regency TR-1,  (Like many other people, I listened to the beep of Sputnick overhead on one of these straining to see it in the sky above me...."beep...beep....")

1955, a new atomic subparticle called a negative proton (antiproton) was discovered at U.C. Berkeley. The hunt for antimatter began in earnest in 1932, with the discovery of the positron, a particle with the mass of an electron and a positive charge. However, creating an antiproton would be far more difficult since it needs nearly 2,000 times the energy. In 1955, the most powerful "atom smasher" in the world, the Bevatron built at Berkeley could provide the required energy. Detection was accomplished with a maze of magnets and electronic counters through which only antiprotons could pass. After several hours of bombarding copper with protons accelerated to 6.2 billion electron volts of energy, the scientists counted a total of 60 antiprotons.*TIS

1962, Dr. James D. Watson of the U.S., Dr. Francis Crick and Dr. Maurice Wilkins of Britain won the Nobel Prize for Medicine and Physiology for their work in determining the double-helix molecular structure of DNA (deoxyribonucleic acid).*TIS

BIRTHS

1863 Alan Archibald Campbell-Swinton, FRS (October 18, 1863, Scotland - February 19, 1930, London) was a Scottish consulting electrical engineer. He was an earlier experimenter in cathode rays and after 1896 he was frequently called upon by the medical profession to take "Roentgen Pictures" of bones.
He described an electronic method of producing television in a June 18,1908 letter to Nature.
He gave a speech in London in 1911 where he described in great detail how distant electric vision could be achieved. This was to be done by using cathode ray tubes (CRTs) at both the transmitting and receiving ends.[4] This was the first iteration of the electronic television which is still in use today. When Swinton gave his speech others had already been experimenting with the use of cathode ray tubes as a receiver, but the use of the technology as a transmitter was unheard of. *Wik

1902 (Ernst) Pascual Jordan (18 October 1902 in Hanover, German Empire; d. 31 July 1980 in Hamburg, Federal Republic of Germany) German physicist who in the late 1920s founded (with Max Born and later Werner Heisenberg) quantum mechanics using matrix methods, showing how light could be interpreted as composed of discrete quanta of energy. Later, (with Wolfgang Pauli and Eugene Wigner), while it was still in its early stages of development, he contributed to the quantum mechanics of electron-photon interactions, now called quantum electrodynamics. He also originated (concurrently with Robert Dicke) a theory of cosmology that proposed to make the universal constants of nature, (such as the universal gravitational constant G), variable over time. *TIS

1919 George Edward Pelham Box (18 October 1919, March 28, 2013, Madison, WI) is a statistician, who has made important contributions in the areas of quality control, time-series analysis, design of experiments, and Bayesian inference.
Box has written research papers and published books. These include Statistics for experimenters (1978), Time series analysis: Forecasting and control (1979, with Gwilym Jenkins) and Bayesian inference in statistical analysis. (1973, with George C. Tiao). Today, his name is associated with important results in statistics such as Box–Jenkins models, Box–Cox transformations, Box–Behnken designs, and others. Box married Joan Fisher, the second of Ronald Fisher's five daughters. In 1978, Joan Fisher Box published a biography of Ronald Fisher, with substantial collaboration of Box. *Wik

In his obituary for Box, Brad Jones of JMP recounted the following, with another fascinating Box quote,
"The last time I saw him was at the JMP Discovery Summit conference in 2009 where I introduced him to give a speech. George got a standing ovation from a crowd of several hundred fans of design of experiments and particularly his work. I will never forget his remarks as the applause died slowly away.

He said, "I feel like the son of the sultan on his 21st birthday when presented with 21 virgins. I know what to do. I just don't know where to start!"

Box died on 28 March 2013. He was 93 years old

1938 Phillip Griffiths (October 18, 1938, Raleigh, North Carolina -  ) is an American mathematician, known for his work in the field of geometry, and in particular for the complex manifold approach to algebraic geometry. He was a major developer in particular of the theory of variation of Hodge structure in Hodge theory and moduli theory.*Wik

DEATHS
1786 Alexander Wilson FRSE (1714 – 16 October 1786) was a Scottish surgeon, type-founder, astronomer, mathematician and meteorologist. He was the first scientist to record the use of kites in meteorological investigations. Wilson noted that sunspots viewed near the edge of the Sun's visible disk appear depressed below the solar surface, a phenomenon referred to as the Wilson effect. When the Royal Danish Academy of Sciences and Letters announced a prize to be awarded for the best essay on the nature of solar spots, Wilson submitted an entry. On 18 February 1772 the Academy presented Wilson with a gold medal for his work on sunspots.*Wik

1793 John Wilson (6 Aug 1741 in Applethwaite, Westmoreland, England - 18 Oct 1793 in Kendal, Westmoreland, England) In 1764 Wilson was elected a Fellow of Peterhouse and he taught mathematics at Cambridge with great skill, quickly gaining an outstanding reputation for himself. However, he was not to continue in the world of university teaching, for in 1766 he was called to the bar having begun a legal career on 22 January 1763 when he was admitted to the Middle Temple. It was a highly successful career, too.
He is best known among mathematicians for Wilson's theorem which states that
... if p is prime then 1 + (p - 1)! is divisible by p
This result was first published by Waring, without proof, and attributed to Wilson. Leibniz appears to have known the result. It was first proved by Lagrange in 1773 who showed that the converse is true, namely
... if n divides 1 + (n - 1)! then n is prime.
Almost certainly Wilson's theorem was a guess made by him, based on the evidence of a number of special cases, which neither he nor Waring knew how to prove. *SAU

1845 Jean-Dominique Comte de Cassini (30 June 1748 in Paris, France - 18 Oct 1845 in Thury, France)  French mathematician and surveyor who worked on his father's map of France.  He was the son of César-François Cassini de Thury and was born at the Paris Observatory. In 1784 he succeeded his father as director of the observatory; but his plans for its restoration and re-equipment were wrecked in 1793 by the animosity of the National Assembly. His position having become intolerable, he resigned on September 6, and was thrown into prison in 1794, but released after seven months. He then withdrew to Thury, where he died fifty-one years later.
He published in 1770 an account of a voyage to America in 1768, undertaken as the commissary of the French Academy of Sciences with a view to testing Pierre Le Roy’s watches at sea. A memoir in which he described the operations superintended by him in 1787 for connecting the observatories of Paris and Greenwich by longitude-determinations appeared in 1791. He visited England for the purposes of the work, and saw William Herschel at Slough. He completed his father’s map of France, which was published by the Academy of Sciences in 1793. It served as the basis for the Atlas National (1791), showing France in departments.
Cassini’s Mémoires pour servir à l’histoire de l’observatoire de Paris (1810) embodied portions of an extensive work, the prospectus of which he had submitted to the Academy of Sciences in 1774. The volume included his Eloges of several academicians, and the autobiography of his great-grandfather, Giovanni Cassini.*Wik

1871 Charles Babbage,(26 Dec 1792-18 Oct 1871) computer pioneer. His obsession for mechanizing computation made him into an embittered and crotchety old man. He especially hated street musicians, whose activities, he ﬁgured, ruined a quarter of his working potential. *VFR   English mathematician and pioneer of mechanical computation, which he pursued to eliminate inaccuracies in mathematical tables. By 1822, he had a small calculating machine able to compute squares. He produced prototypes of portions of a larger Difference Engine. (Georg and Edvard Schuetz later constructed the first working devices to the same design which were successful in limited applications.) In 1833 he began his programmable Analytical Machine, a forerunner of modern computers. His other inventions include the cowcatcher, dynamometer, standard railroad gauge, uniform postal rates, occulting lights for lighthouses, Greenwich time signals, heliograph opthalmoscope. He also had an interest in cyphers and lock-picking. *TIS

1931 Thomas Alva Edison (11 Feb 1847-18 Oct 1931) Inventor, died in West Orange, NJ. He invented the first phonograph (1877) and the prototype of the practical incandescent electric light bulb (1879). His many inventions led to his being internationally known as "the wizard of Menlo Park", from the name of his first laboratory. By the late 1880s he was contributing to the development of motion pictures. By 1912 he was experimenting with talking pictures. His many inventions include a storage battery, a Dictaphone, and a mimeograph. Meanwhile, he had become interested in the development of a system for widespread distribution of electric power from central generating stations. He held over 1,000 patents.In 1962 his second laboratory and home in West Orange, NJ, would be designated a National Historic Site.*TIS

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

## Wednesday, 17 October 2018

### On This Day in Math - October 17

To parents who despair because their children are unable to master the first problems in arithmetic I can dedicate my examples. For, in arithmetic, until the seventh grade I was last or nearly last.

The 290th day of the year, 290 is a sphenic (wedge) number, the product of three distinct primes (290 = 2*5*29).

It is also the sum of four consecutive primes (67 + 71 + 73 + 79) [Students might try to construct and examine a list of numbers that can be written as the sum of two or more consecutive primes]

290 is conjectured to be the smallest number such that the Reverse and Add! algorithm in base 4 does not lead to a palindrome.

290 is the tenth prime(29) times ten

EVENTS

1604 In Prague, Kepler first observes the supernova now known as supernova 1604 and Kepler's Star. The first recorded observation of this supernova was in northern Italy on October 9, 1604. It was named after Kepler because his observations tracked the object for an entire year and because of his book on the subject, entitled De Stella nova in pede Serpentarii ("On the new star in Ophiuchus's foot", Prague 1606). Here is an image of Kepler's De Stella Nova, open to the foldout star map placing the supernova of 1604, from the twitter feed of @Libroantiguo . It was the second supernova to be observed in a generation (after SN 1572 seen by Tycho Brahe in Cassiopeia). No further supernovae have since been observed with certainty in the Milky Way, though many others outside our galaxy have been seen since S Andromedae. *Wik

1776 Euler read a paper to the St. Petersburg Academy of Science entitled “De quadratis magicis,” in which he gave a method of constructing magic squares by means of two orthogonal Latin squares. *Peter Ullrich, “An Eulerian square before Euler and an experimental design before R. A. Fisher: On the early history of Latin squares,” Chance, vol. 12, no. 1, Winter 1999, pp. 22–26.

1831 After discovering induced current on October 1st using two electrified coils,  on the 17th of October Michael Faraday  observers the same effect on the galvanometer when he inserts a permanent steel magnet into the electrified coil. *A history of physics in its elementary branches By Florian Cajori

1843 Hamilton Writes to his friend, John Graves, with a description of Quaternions. By December, Graves will have extended the idea to an eight dimensional algebra which will become "octonians".

Observatory, October 17, 1843
My dear Graves,|A very curious train of mathematical speculation occurred to me
yesterday, which I cannot but hope will prove of interest to you. You know that I have long
wished, and I believe that you have felt the same desire, to possess a Theory of Triplets,
analogous to my published Theory of Couplets, and also to Mr. Warren's geometrical representation
of imaginary quantities. Now I think that I discovered1 yesterday a theory of
quaternions which includes such a theory of triplets.

The complete letter is available at this site. *David R. Wilkins, *John Derbyshire, Unkown Quantity
In his preface to the ‘Lectures on Quaternions’ and in a prefatory letter to a communication to the Philosophical Magazine for December 1844 are acknowledgments of his indebtedness to Graves for stimulus and suggestion. *Wik

1858 DeMorgan writes a letter about Euler’s  prodigious output. *W W Rouse Ball, from The genius of Euler: reflections on his life and work, By William Dunham, pg 89

1933 Albert Einstein seeks asylum in the US, one of many Jewish/left-wing intellectuals fleeing the Nazi govt in Germany and Europe. The Nazi government put a bounty now worth £50,000 on his head while a German magazine included him in a list of the Nazis’ enemies who were 'not yet hanged'.

1952 D. H. Lehmer, University of California, announced that 2n − 1 for n = 2203 and 2281 are Mersenne primes. He was aided by a SWAC computing machine, the ﬁrst result taking 59 minutes. *VFR This may have been predated by Raphael Mitchel Robinson (November 2, 1911 – January 27, 1995) at Berkeley may have beaten him by a week or so on October 7th of the same year.
D. H. Lehmer continued his fathers interest in combinatorial computing and in fact wrote the article "Machine tools of Computation," which is chapter one in the book "Applied Combinatorial Mathematics," by Edwin Beckenbach, 1964. It describes methods for producing permutations, combinations etc. This was a uniquely valuable resource and has only been rivaled recently by Volume 4 of Donald Knuth's series. In 1950, Lehmer was one of 31 University of California faculty fired after refusing to sign a loyalty oath, a policy initiated by the Board of Regents of the State of California in 1950 during the Communist scare personified by Senator Joseph McCarthy. (see below)*Wik

1952 The California Supreme Court declared the state loyalty oath unconstitutional and declared that the eighteen faculty members who had refused to sign the oath be reinstated.*VFR

1978 James Burke's history of science series Connections first airs, on BBC Television in the United Kingdom (with accompanying book). *Wik

1983 Gerard Debreu, who holds a joint appointment in Mathematics and Economics at Berkeley, won a Nobel Prize for his work in mathematical economics. For a non-technical description of his work see The Mathematical Intelligencer, 6(1984), no. 2, pp. 61–62. *VFR

2012 Car size pieces of Halley's Comet lit up the skies over the Bay Area in California. Hundreds of residents from Oakland, San Francisco and Santa Cruz called ABC News station KGO-TV, reporting a loud boom, explosions and streaks of light around 7:45 p.m. local time. The Orionids are one of two annual meteor showers produced by icy pieces of Halley's Comet. The other shower, called the Eta Aquarids, peaks each year in early May, according to NASA. Video *ABC News

BIRTHS

1759 Jakob II Bernoulli (17 October 1759, Basel – 3 July 1789, Saint Petersburg), younger brother of Johann III Bernoulli. Having finished his literary studies, he was, according to custom, sent to Neuchâtel to learn French. On his return he graduated in law. This study, however, did not check his hereditary taste for geometry. The early lessons which he had received from his father were continued by his uncle Daniel, and such was his progress that at the age of twenty-one he was called to undertake the duties of the chair of experimental physics, which his uncle’s advanced years rendered him unable to discharge. He afterwards accepted the situation of secretary to count de Brenner, which afforded him an opportunity of seeing Germany and Italy. In Italy he formed a friendship with Lorgna, professor of mathematics at Verona, and one of the founders of the Società Italiana for the encouragement of the sciences. He was also made corresponding member of the royal society of Turin; and, while residing at Venice, he was, through the friendly representation of Nicolaus von Fuss, admitted into the academy of St Petersburg. In 1788 he was named one of its mathematical professors. *Wik
He drowned while bathing in the Neva in July 1789, a few months after his marriage with a granddaughter of Leonhard Euler.  (Can't tell your Bernoulli's without a scorecard?  Check out "A Confusion of Bernoulli's" by the Renaissance Mathematicus.)

1788 Paul Isaak Bernays (17 Oct 1888; 18 Sep 1977) Swiss mathematician and logician who is known for his attempts to develop a unified theory of mathematics. Bernays, influenced by Hilbert's thinking, believed that the whole structure of mathematics could be unified as a single coherent entity. In order to start this process it was necessary to devise a set of axioms on which such a complete theory could be based. He therefore attempted to put set theory on an axiomatic basis to avoid the paradoxes. Between 1937 and 1954 Bernays wrote a whole series of articles in the Journal of Symbolic Logic which attempted to achieve this goal. In 1958 Bernays published Axiomatic Set Theory in which he combined together his work on the axiomatisation of set theory. *TIS

1927 Friedrich Ernst Peter Hirzebruch (17 October 1927 – 27 May 2012) was a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure in his generation. He has been described as "the most important mathematician in the Germany of the postwar period.
Amongst many other honours, Hirzebruch was awarded a Wolf Prize in Mathematics in 1988 and a Lobachevsky Medal in 1989. The government of Japan awarded him the Order of the Sacred Treasure in 1996. He also won an Einstein Medal in 1999, and received the Cantor medal in 2004.*Wik

DEATHS

1817 John West (10 April 1756 in Logie (near St Andrews), Scotland - 17 Oct 1817 in Morant Bay, Jamaica) The achievements of the little-known Scottish mathematician, John West (1756–1817), deserve recognition: hisElements of Mathematics(1784) shows him to be a skilled expositor and innovative geometer while his manuscript,Mathematical Treatises,unpublished until 1838, reveal him also to be an accomplished exponent of “continental” analysis, familiar with works of Lagrange, Laplace, and Arbogast then little studied in Britain.
First an assistant at St. Andrews University in Scotland, West then worked in isolation in Jamaica, combining mathematics with the duties of an Anglican rector. His life and his pastoral and mathematical works are here described. *abstract for Geometry, Analysis, and the Baptism of Slaves: John West in Scotland and Jamaica, Alex D.D. Craik

1877 Gustav Robert Kirchhoff (12 Mar 1824, 17 Oct 1887) German physicist who, with Robert Bunsen, established the theory of spectrum analysis (a technique for chemical analysis by analyzing the light emitted by a heated material), which Kirchhoff applied to determine the composition of the Sun. He found that when light passes through a gas, the gas absorbs those wavelengths that it would emit if heated, which explained the numerous dark lines (Fraunhofer lines) in the Sun's spectrum. In his Kirchhoff's laws (1845) he generalized the equations describing current flow to the case of electrical conductors in three dimensions, extending Ohm's law to calculation of the currents, voltages, and resistances of electrical networks. He demonstrated that current flows in a zero-resistance conductor at the speed of light. *TIS

1923 August Adler (24 Jan 1863 in Opava, Austrian Silesia (now Czech Republic)-17 Oct 1923 in Vienna, Austria) In 1906 Adler applied the theory of inversion to solve Mascheroni construction problems in his book Theorie der geometrischen Konstruktionen published in Leipzig. In 1797 Mascheroni had shown that all plane construction problems which could be made with ruler and compass could in fact be made with compasses alone. His theoretical solution involved giving specific constructions, such as bisecting a circular arc, using only a compass.
Since he was using inversion Adler now had a symmetry between lines and circles which in some sense showed why the constructions needed only compasses. However Adler did not simplify Mascheroni proof. On the contrary, his new methods were not as elegant, either in simplicity or length, as the original proof by Mascheroni.
This 1906 publication was not the first by Adler studying this problem. He had published a paper on the theory of Mascheroni's constructions in 1890, another on the theory of geometrical constructions in 1895, and one on the theory of drawing instruments in 1902. As well as his interest in descriptive geometry, Adler was also interested in mathematical education, particularly in teaching mathematics in secondary schools. His publications on this topic began around 1901 and by the end of his career he was publishing more on mathematical education than on geometry. Most of his papers on mathematical education were directed towards teaching geometry in schools, but in 1907 he wrote on modern methods in mathematical instruction in Austrian middle schools. He produced various teaching materials for teaching geometry in the sixth-form in Austrian schools such as an exercise book which he published in 1908. *SAU

1937 Frank Morley (9 Sept 1860 in Woodbridge, Suffolk, England-17 Oct 1937 in Baltimore, Maryland, USA) wrote mainly on geometry but also on algebra.*SAU Morley is remembered most today for a singular theorem which bears his name in recreational literature.  Simply stated, Morley's Theorem says that if the angles at the vertices of any triangle (A, B, and C in the figure) are trisected, then the points where the trisectors from adjacent vertices intersect (D, E, and F) will form an equilateral triangle. In 1899 he observed the relationship described above, but could find  no  proof. It spread from discussions with his friends to become an item  of  mathematical gossip. Finally in 1909 a trigonometric solution was   discovered by M. Satyanarayana. Later an elementary proof was developed.   Today the preferred proof is to begin with the result and work   backward. Start with an equilateral triangle and show that the vertices   are the intersection of the trisectors of a triangle with any given set   of angles. For those interested in seeing the proof, check Coxeter's Introduction to Geometry, Vol 2, pages 24-25. Find more about this unusual man here.  *PB

1941 John Stanley Plaskett (17 Nov 1865, 17 Oct 1941) Canadian astronomer known for his expert design of instruments and his extensive spectroscopic observations. He designed an exceptionally efficient spectrograph for the 15-inch refractor and measured radial velocities and found orbits of spectroscopic binary stars. He designed and supervised construction of the 72-inch reflector built for the new Dominion Astrophysical Observatory in Victoria and was appointed its first director in 1917. There he extended the work on radial velocities and spectroscopic binaries and studied spectra of O and B-type stars. In the 1930s he published the first detailed analysis of the rotation of the Milky Way, demonstrating that the sun is two-thirds out from the center of our galaxy about which it revolves once in 220 million years.*TIS

1952 Ernest Vessiot (8 March 1865 in Marseilles, France-17 Oct 1952 in La Bauche, Savoie, France) applied continuous groups to the study of differential equations. He extended results of Drach (1902) and Cartan (1907) and also extended Fredholm integrals to partial differential equations.  Vessiot was assigned to ballistics during World War I and made important discoveries in this area. He was honoured by election to the Académie des Sciences in 1943. *SAU

1963 Jacques-Salomon Hadamard (8 Dec 1865, 17 Oct 1963) French mathematician who proved the prime-number theorem (as n approaches infinity, the limit of the ratio of (n) and n/ln(n) is 1, where (n) is the number of positive prime numbers not greater than n). Conjectured in the 18th century, this theorem was not proved until 1896, when Hadamard and also Charles de la Vallée Poussin, used complex analysis. Hadamard's work includes the theory of integral functions and singularities of functions represented by Taylor series. His work on the partial differential equations of mathematical physics is important. He introduced the concept of a well-posed initial value and boundary value problem. In considering boundary value problems he introduced a generalization of Green's functions (1932). *TIS

1978 Gertrude Mary Cox (January 13, 1900 – October 17, 1978) was an influential American statistician and founder of the department of Experimental Statistics at North Carolina State University. She was later appointed director of both the Institute of Statistics of the Consolidated University of North Carolina and the Statistics Research Division of North Carolina State University. Her most important and influential research dealt with experimental design; she wrote an important book on the subject with W. G. Cochran. In 1949 Cox became the first female elected into the International Statistical Institute and in 1956 she was president of the American Statistical Association.*Wik

2008 Andrew Mattei Gleason (November 4, 1921 – October 17, 2008) was an American mathematician and the eponym of Gleason's theorem and the Greenwood–Gleason graph. After briefly attending Berkeley High School (Berkeley, California) he graduated from Roosevelt High School in Yonkers, then Yale University in 1942, where he became a Putnam Fellow. He subsequently joined the United States Navy, where he was part of a team responsible for breaking Japanese codes during World War II. He was appointed a Junior Fellow at Harvard in 1946, and later joined the faculty there where he was the Hollis Professor of Mathematicks and Natural Philosophy. He had the rare distinction among Harvard professors of having never obtained a doctorate. (In graph theory, the Greenwood–Gleason graph (Image at top of page) is also known as the Clebsch graph. It is an undirected graph with 16 vertices and 40 edges. It is named after Alfred Clebsch, a German mathematician who discovered it in 1868. It is also known as the Greenwood–Gleason graph after the work of Robert M. Greenwood and Andrew M. Gleason (1955), who used it to evaluate the Ramsey number R(3,3,3) = 17 *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

## Tuesday, 16 October 2018

### On This Day in Math - October 16

I have often pondered over the roles of knowledge or experience, on the one hand, and imagination or intuition, on the other, in the process of discovery. I believe that there is a certain fundamental conflict between the two, and knowledge, by advocating caution, tends to inhibit the flight of imagination. Therefore, a certain naivete, unburdened by conventional wisdom, can sometimes be a positive asset.
~Harish-Chandra

The 289th day of the year; 289 is a Friedman number since (8 + 9)2 = 289 (A Friedman number is an integer which, in a given base, is the result of an expression using all its own digits in combination with any of the four basic arithmetic operators (+, −, ×, ÷) and sometimes exponentiation.)Students might try to find the first few multi-digit Friedman numbers.

289 is the square of the sum of the first four primes, 289 = (2 + 3 + 5 + 7)2

289 is the largest 3-digit square with increasing digits.

289 is the hypotenuse of a primitive Pythagorean triple. Find the legs students!

EVENTS

1707 Roger Cotes elected ﬁrst Plumian Professor of Astronomy and Experimental Philosophy at Cambridge at age 26. He is best known for his meticulous and creative editing of the second edition (1713) of Newton’s Principia. He was also an important developer of the integral calculus. *Ronald Gowing, Roger Cotes, Natural Philosopher, p. 14

1797 Gauss records in his diary that he has discovered a new proof of the Pythagorean Theorem. See Gray, Expositiones Mathematicae, 2(1984), 97–130. *VFR

1819  Thomas Young writes to Fresnel to thank him for a copy of his memoirs (sent to Young by Arago). "I return a thousand thanks, Monsieur, for the gift of your admirable memoir, which surely merits a very high rank amongst the papers which have contributed most to the progress of optics." *A history of physics in its elementary branches By Florian Cajori

1843 Hamilton discovered quaternions while walking along the Royal Canal in Dublin and immediately scratches the multiplication formulas on a bridge. Today a plaque on the bridge reads, "Here as he walked by on the 16th of October 1843 Sir William Rowan Hamilton in a ﬂash of genius discovered the fundamental formula for quaternion multiplication i2 = j2 = k2 = ijk = −1 & cut it in a stone on this bridge." Since 1989, the Department of Mathematics of the National University of Ireland, Maynooth has organized a pilgrimage, where scientists (including the physicists Murray Gell-Mann in 2002, Steven Weinberg in 2005, and the mathematician Andrew Wiles in 2003) take a walk from Dunsink Observatory to the Royal Canal bridge where no trace of Hamilton's carving remains, unfortunately.
Here is how Hamilton described his memory of the discovery of the Quaternions to his son, "Every morning in the early part of the above-cited month, on my coming down to breakfast, your (then) little brother, William Edwin, and yourself, used to ask me, Well, papa, can you multiply triplets?' Whereto I was always obliged to reply, with a sad shake of the head: No, I can only add and subtract them. But on the 16th day of the same month (Oct) - which happened to be Monday, and a Council day of the Royal Irish Academy - I was walking in to attend and preside, and your mother was walking with me along the Royal Canal, to which she had perhaps driven; and although she talked with me now and then, yet an undercurrent of thought was going on in my mind which gave at last a result, whereof it is not too much to say that I felt at once the importance. An electric circuit seemed to close; and a spark flashed forth the herald (as I foresaw immediately) of many long years to come of definitely directed thought and work by myself, if spared, and, at all events, on the part of others if I should even be allowed to live long enough distinctly to communicate the discovery. Nor could I resist the impulse - unphilosophical as it may have been - to cut with a knife on a stone of Brougham Bridge, as we passed it, the fundamental formula which contains the Solution of the Problem, but, of course, the inscription has long since mouldered away. A more durable notice remains, however, on the Council Books of the Academy for that day (October 16, 1843), which records the fact that I then asked for and obtained leave to read a Paper on Quaternions,' at the First General Meeting of the Session; which reading took place accordingly, on Monday, the 13th of November following.'' *from Hamilton By Sir Robert Stawell Ball.

The plaque says:
Here as he walked by
on the 16th of October 1843
Sir William Rowan Hamilton
in a flash of genius discovered
the fundamental formula for
quaternion multiplication
i2 = j2 = k2 = i j k = −1
& cut it on a stone of this bridge

(Quatenion was a Latin term before Hamilton used it.  Milton uses it in Paradise Lost to refer to the four elements of antiquity: air, earth, water, and fire. The last three are “the eldest birth of nature’s womb” because they are mentioned in Genesis before air is mentioned. *John Cook )

In 1982, Halley's Comet was observed on its 30th recorded visit to Earth, first detected using the 5-m (200-in) Hale Telescope at the Mount Palomar Observatory by a team of astronomers led by David Jewett and G. Edward Danielson. They found the comet, beyond the orbit of Saturn, about 11 AU (1.6 billion km) from the Sun. While 50 million times fainter than the faintest objects our eyes can see, they needed to use not only the largest American telescope but also special electronic equipment developed for the Space Telescope. In 1705, Halley used Newton's theories to compute the orbit and correctly predicted the return of this comet about every 76 years. After his death, for correctly predicting its reappearance, it was named after Halley. *TIS (The next predicted perihelion of Halley's Comet is 28 July 2061)
In 1982 the first image of the returning Halley's Comet was recorded with the 200-inch Hale telescope at Palomar Mountain. Caltech astronomers David Jewitt and G. Edward Danielson found the comet when it was still beyond the orbit of Saturn, more than 1.6 billion kilometers (960 million miles) from the Sun. *National Air and Space Museum

1988 Connect Four Solved first by James D. Allen (Oct 1, 1988), and independently by Victor Allis (Oct 16, 1988). First player can force a win. Strongly solved by John Tromp's 8-ply database (Feb 4, 1995). Weakly solved for all boardsizes where width+height is at most 15 (Feb 18, 2006). *Wik

2016 The 27th Hamilton walk takes place on this day. Students, professors, and math lovers in general will gather at the Dunsink Observatory around 3:30 pm and proceed to Broombridge in Cabra where he had his Eureka moment about Quaternions. (see 1843 in Events above) The annual event is part of Irish Math week.

BIRTHS
1689 Robert Smith (16 October,1689 – 2 February, 1768) was an English mathematician and Master of Trinity College.
Smith was probably born at Lea near Gainsborough, the son of the rector of Gate Burton, Lincolnshire. He entered Trinity College, Cambridge, in 1708, and becoming minor fellow in 1714, major fellow in 1715 and senior fellow in 1739. From 1716 to 1760 he was Plumian Professor of Astronomy,and was chosen Master in 1742, in succession to Richard Bentley.
Besides editing two works by his cousin, Roger Cotes, who was his predecessor in the Plumian chair, he published A Compleat System of Opticks in 1738, (which was the principal textbook on Optics in the 18th Century) , and Harmonics, or the Philosophy of Musical Sounds in 1749.
Smith never married but lived with his unmarried sister Elzimar (1683–1758) in the lodge at Trinity College. Although he is often portrayed as a rather reclusive character, John Byrom's journal shows that in the 1720s and 1730s Smith could be quite sociable. Yet ill health, particularly gout, took its toll and severely inhibited his academic work and social activities. He died at the lodge on 2 February 1768, and on 8 February he was buried in Trinity College Chapel.
In his will Smith left £3500 South Sea stock to the University of Cambridge. The net income on the fund is annually divided equally between the Smith's Prize and the stipend of the Plumian Professor. *Wik

1879 Philip Edward Bertrand Jourdain (16 October 1879 – 1 October 1919) was a British logician and follower of Bertrand Russell. He corresponded with Georg Cantor and Gottlob Frege, and took a close interest in the paradoxes related to Russell's paradox, formulating the card paradox version of the liar paradox. He also worked on algebraic logic, and the history of science with Isaac Newton as a particular study. He was London editor for The Monist. *Wik

1882 Ernst Erich Jacobsthal (16 October 1882, Berlin – 6 February 1965, Überlingen) was a German mathematician, and brother to the archaeologist Paul Jacobsthal.
In 1906, he earned his PhD at the University of Berlin, where he was a student of Georg Frobenius, Hermann Schwarz and Issai Schur; his dissertation, Anwendung einer Formel aus der Theorie der quadratischen Reste (Application of a Formula from the Theory of Quadratic Remainders), provided a proof that prime numbers of the form 4n + 1 are the sum of two square numbers. *Wik

1930 John Charlton Polkinghorne KBE FRS (born 16 October 1930) is an English theoretical physicist, theologian, writer, and Anglican priest. He was professor of Mathematical physics at the University of Cambridge from 1968 to 1979, when he resigned his chair to study for the priesthood, becoming an ordained Anglican priest in 1982. He served as the president of Queens' College, Cambridge from 1988 until 1996.*Wik

DEATHS

1937 William Sealy Gosset (13 June 1876 in Canterbury, England - 16 October 1937 in Beaconsfield, England) Gosset was the eldest son of Agnes Sealy Vidal and Colonel Frederic Gosset who came from Watlington in Oxfordshire. William was educated at Winchester, where his favourite hobby was shooting, then entered New College Oxford where he studied chemistry and mathematics. While there he studied under Airy. He obtained a First Class degree in both subjects, being awarded his mathematics degree in 1897 and his chemistry degree two years later.

Gosset obtained a post as a chemist with Arthur Guinness Son and Company in 1899. Working in the Guinness brewery in Dublin he did important work on statistics. In 1905 he contacted Karl Pearson and arranged to go to London to study at Pearson's laboratory, the Galton Eugenics Laboratory, at University College in session 1906-07. At this time he worked on the Poisson limit to the binomial and the sampling distribution of the mean, standard deviation, and correlation coefficient. He later published three important papers on the work he had undertaken during this year working in Pearson's laboratory.
Many people are familiar with the name "Student" but not with the name Gosset. In fact Gosset wrote under the name "Student" which explains why his name may be less well known than his important results in statistics. He invented the t-test to handle small samples for quality control in brewing. Gosset discovered the form of the t distribution by a combination of mathematical and empirical work with random numbers, an early application of the Monte-Carlo method.

McMullen says:-

To many in the statistical world "Student" was regarded as a statistical advisor to Guinness's brewery, to others he appeared to be a brewer devoting his spare time to statistics. ... though there is some truth in both these ideas they miss the central point, which was the intimate connection between his statistical research and the practical problems on which he was engaged. ... "Student" did a very large quantity of ordinary routine as well as his statistical work in the brewery, and all that in addition to consultative statistical work and to preparing his various published papers.

From 1922 he acquired a statistical assistant at the brewery, and he slowly built up a small statistics department which he ran until 1934.
Gosset certainly did not work in isolation. He corresponded with a large number of statisticians and he often visited his father in Watlington in England and on these occasions he would visit University College, London, and the Rothamsted Agricultural Experiment Station. He would discuss statistical problems with Fisher, Neyman and Pearson. *SAU

1983 Harish-Chandra (11 October 1923 – 16 October 1983) was an Indian mathematician, who did fundamental work in representation theory, especially Harmonic analysis on semisimple Lie groups.*Wik

1998 Jonathan Bruce Postel (6 Aug 1943, 16 Oct 1998) American computer scientist who played a pivotal role in creating and administering the Internet. In the late 1960s, Postel was a graduate student developing the ARPANET, a forerunner of the Internet for use by the U.S. Dept. of Defense. As director of the Internet Assigned Numbers Authority (IANA), which he formed, Postel was a creator of the Internet's address system. The Internet grew rapidly in the 1990s, and there was concern about its lack of regulation. Shortly before his death, Postel submitted a proposal to the U.S. government for an international nonprofit organization that would oversee the Internet and its assigned names and numbers. He died at age 55, from complications after heart surgery.*TIS

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

## Monday, 15 October 2018

### On This Day in Math - October 15

Many have argued that a vacuum does not exist, others claim it exists only with difficulty in spite of the repugnance of nature; I know of no one who claims it easily exists without any resistance from nature.
— Evangelista Torricelli in a Letter to Michelangelo Ricci

The 288th day of the year; 288 is the super-factorial of four. 1! x 2! x 3! x 4! =288. It is important that math students learn not to say this number in public as it is two gross. (I apologize for the really bad pun)

288 is also the sum of the first four integers raised to their own power $1^1 + 2^2 + 3^3 + 4^4 = 288$

288 is the smallest non-palindrome, non-square, that when multiplied by its reverse is a square: 288 x 882 = 254,016 = 5042.

EVENTS

1582 St Theresa of Avila died overnight on the night between the 4th and the 15th of October. On that day the Gregorian calendar went into effect in Spain and the day after the 4th, was the 15th in order to catch up for the misalignment of the Julian Calendar. *VFR

1698 King William III commissioned Edmund Halley as Royal Naval Captain of the HMS
Paramore and provided him with a complete set of instructions. The Admiralty’s instructions to Halley dated 15 October 1698 were :
Whereas his Maty. has been pleased to lend his Pink the Paramour for your proceeding with her on an Expedition, to improve the knowledge of the Longitude and variations of the Compasse, which Shipp is now compleatly Man’d, Stored and Victualled at his Mats. Charge for the said Expedition ... *Lori L. Murray, The Construction of Edmond Halley’s 1701 Map of Magnetic Declination

1759 Euler's paper "An arithmetic theorem proved by a new method" was presented at the Saint-Petersburg Academy. In This paper he introduces the idea that has come to be called Euler's Phi function, but did not include a symbol or name. Euler defined the function as "the multitude of numbers less than D, and which have no common divisor with it." (This is slightly different than the current definition which used Greatest Common Divisor is one). He revisited the idea in a paper read to the Academy on October 9, 1775 In the earlier papers he had not used a symbol, but in the 1775 paper he chose πD for symbol. In 1801 Gauss's Disquisitiones Arithmeticae introduced the Phi notation, although Gauss didn't use parentheses around the argument and wrote φA. The term Totient was applied by J J Sylvester in 1879. So it's not Euler's Phi, and it's not Euler's Totient, and in fact, the function is now not exactly Euler's function. *Wik

1783 The ﬁrst manned ascension in a balloon. After the ﬂight of September 19, 1783, Louis XVI forbade men to go aloft, making the adventurers furious. Later he extended the privilege to convicts, ﬁguring they were expendable. de Rozier’s loud fulmigations against such glory for “vile criminals” soon changed the king’s mind. The hydrogen balloon, Aerostat Reveillon, carrying Pilâtre, first man to leave the earth, rose to the end of its 250- ft tether. It stayed aloft for 15 minutes, then landed safely nearby.
On 21 Nov 1783, untethered, Pilâtre and Marquis d'Arlande made the first manned free flight, across Paris. On 15 Jun 1785, Pilâtre attempt the first east-to-west crossing of the English Channel with a hybrid balloon combining lift from both hydrogen and hot air. Within minutes of launch, the craft exploded, and plunged to the rocks on the coast of Wimereux. Neither Pilâtre nor his co-pilot, Romain, survived the crash. *TIS (American Scientist and U S emissary to the court of Louis XVI, Ben Franklin, was present for some of the Balloon ascensions in 1783. When asked what was the use of Ballooning, he replied, “Of what use is a newborn baby?”)

In 1827, Charles Darwin was accepted into Christ's College at Cambridge, but did not start until winter term because he needed to catch up on some of his studies. A grandson of Erasmus Darwin of Lichfield, and of Josiah Wedgwood, he had entered the University of Edinburgh in 1825 to study medicine, intending to follow his father Robert's career as a doctor. However, Darwin found himself unenthusiastic about his studies, including that of geology. Disappointing his family that he gave up on a medical career, he left Edinburgh without graduating in April 1827. His scholastic achievements at Cambridge were unremarkable, but after graduation, Darwin was recommended by his botany professor to be a naturalist to sail on HM Sloop Beagle. *TIS

1956 The first FORTRAN reference manual is released on October 15, 1956, six months before the first compiler's release. Only 60 pages long, with large print and wide margins, that first programming language was miniscule by today's standard. The original FORTRAN development team comprised John Backus, Sheldon Best, Richard Goldberg, Lois Mitchell Haibt, Harlan Herrick, Grace Mitchell, Robert Nelson, Roy Nutt, David Sayre, Peter Sheridan, and Irving Ziller.*CHM

In 2003, China became the third nation to send a man into space. Lieutenant Colonel Yang Liwei, 38, was launched on a Long March CZ-2F rocket in the Shenzhou-5 spacecraft at 9 am local time (1 am GMT). He completed 14 Earth orbits during a 21-hour flight which ended with a parachute-assisted landing in the on the grasslands of Inner Mongolia in northern China. The Shenzhou spacecraft was based on the three-seat Russian Soyuz capsule, but with extensive modifications. The country began planning manned spaceflight in 1992. Russia began providing advice on technology and astronaut training in 1995. The first of four unmanned test flights of a Shenzhou craft (took place in Nov 1999. The name Shenzhou translates as "divine vessel." *TIS

BIRTHS

1608 Evangelista Torricelli (15 Oct 1608; 25 Oct 1647) Born in Faenza, Italy, Torricelli was an Italian physicist and mathematician who invented the barometer and whose work in geometry aided in the eventual development of integral calculus. Inspired by Galileo's writings, he wrote a treatise on mechanics, De Motu ("Concerning Movement"), which impressed Galileo. He also developed techniques for producing telescope lenses. The barometer experiment using "quicksilver" filling a tube then inverted into a dish of mercury, carried out in Spring 1644, made Torricelli's name famous. The Italian scientists merit was, above all, to admit that the effective cause of the resistance presented by nature to the creation of a vacuum (in the inverted tube above the mercury) was probably due to the weight of air. *TIS He succeeded his teacher, Galileo as professor of mathematics at Florence. One of his most amazing discoveries was a solid which had inﬁnite length but ﬁnite volume. He also invented the mercury barometer.*VFR

1735 Jesse Ramsden FRSE (15 October 1735 – 5 November 1800) was an English astronomical and scientific instrument maker.
Ramsden created one of the first high-quality dividing engines. This machine permitted the automatic and highly accurate division of a circle into degrees and fractions of degrees of arc.The machine  led to mass production of precision octants and sextants and gave British manufacturers dominance in the field of marine instruments for decades.  His invention was so valuable to the nation’s maritime interests that he received a share of the Longitude Prize.
His most celebrated work was a 5-feet vertical circle, which was finished in 1789 and was used by Giuseppe Piazzi at Palermo in constructing his catalog of stars. He was the first to carry out in practice a method of reading off angles (first suggested in 1768 by the Duke of Chaulnes) by measuring the distance of the index from the nearest division line by means of a micrometer screw which moves one or two fine threads placed in the focus of a microscope.
Ramsden's transit instruments were the first which were illuminated through the hollow axis; the idea was suggested to him by Prof. Henry Ussher in Dublin. He published a Description of an Engine for dividing Mathematical Instruments in 1777.
Ramsden is also responsible for the achromatic eyepiece named after him, and also worked on new designs of electrostatic generators. He was elected to the Royal Society in 1786. The exit pupil of an eyepiece was once called the Ramsden disc in his honour. In 1791 he completed the Shuckburgh telescope, an equatorial mounted refractor telescope.
In about 1785, Ramsden provided a new large theodolite for General William Roy of the Royal Engineers, which was used for a new survey of the distance between Greenwich, London and Paris. This work provided the basis for the subsequent Ordnance Survey of the counties of Britain. For his part with Roy in this work he received the Copley Medal in 1795. He died five years later at Brighton, England.*Wik

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

1776 Peter Barlow (15 Oct 1776, 1 March 1862) Peter Barlow was self-educated but this education was sufficiently good that he was able to compete successfully to became an assistant mathematics master at the Royal Military Academy at Woolwich. He was appointed to the post in 1801 and he began publishing mathematical articles in the Ladies Diary and he became sufficiently well established as a leading authority on mathematics that after a while he was asked to contribute various articles on mathematics for encyclopedias.
In addition to these articles, Barlow also published several important books, for example in 1811 he published An elementary investigation of the theory of numbers and three years later he published A new mathematical and philosophical dictionary.
He is remembered most for two important contributions. In 1814 he produced a second book, in addition to the one described above, entitled New mathematical tables. These soon became known as Barlow's Tables and this work gives factors, squares, cubes, square roots, reciprocals and hyperbolic logarithms of all numbers from 1 to 10 000. The book "...was considered so accurate and so useful that it has been regularly reprinted ever since. "
In the mathematical library at the University of St Andrews we have several well worn copies of these tables which must have been used intensely for many years. Today, however, they are only of historical interest since they were made completely obsolete by calculators and computers.
Barlow's second major contribution makes his name still well known by amateur astronomers today. He invented the Barlow lens, a telescope lens consisting of a colorless liquid between two pieces of glass, the "Barlow lens", a modification of this telescope lens, is a negative achromatic combination of flint glass and crown glass.
In 1819 Barlow began work on the problem of deviation in ship compasses caused by the presence of iron in the hull. For his method of correcting the deviation by juxtaposing the compass with a suitably shaped piece of iron, he was awarded the Copley Medal ... *SAU
Barlow is quoted on SAU as saying, "230(231-1) is the greatest perfect number that will ever be discovered, for, as they are merely curious without being useful, it is not likely that any person will attempt to find a number beyond it."

1829 Asaph Hall (15 Oct 1829; 22 Nov 1907) American astronomer, discovered and named the two moons of Mars, Phobos and Deimos, and calculated their orbits.Born in Goshen, Conn. and apprenticed as a carpenter at age 16, he had a passion for geometry and algebra. Hall obtained a position at the Harvard Observatory in Cambridge, Mass. in 1857 and became an expert computer of orbits. In August 1862, he joined the staff of the Naval Observatory in Washington, D.C. where he made his discoveries, in mid- Aug 1877, using the Observatory's 26-inch "Great Equatorial" refracting telescope, then the largest of its kind in the world. He stayed there 30 years until 1891. His son, Asaph Hall, Jr., followed him and worked at the Observatory at various times between 1882-1929.*TIS

1837 Leo Königsberger (15 October 1837 – 15 December 1921) was a German mathematician, and historian of science. He is best known for his three-volume biography of Hermann von Helmholtz, which remains the standard reference on the subject. The biography of Helmholtz was published in 1902 and 1903. He also wrote a biography of C. G. J. Jacobi.
Königsberger's own research was primarily on elliptic functions and differential equations. He worked closely with Lazarus Fuchs, a childhood friend.*Wik

1867 Jacques Inaudi (October 15, 1867 – November 10, 1950) Born to a poor family in the Italian Piedmont, Jacques Inaudi began life as a shepherd but soon discovered a prodigious talent for calculation, and soon he was giving exhibitions in large cities.
Camille Flammarion wrote, “He was asked, for example, how many minutes have elapsed since the birth of Jesus Christ, or what the population would be if the dead from the past ten centuries were resurrected, or the square root of a number of twelve digits, and he gave the response accurately and in two or three minutes — while amusing himself with another activity.”
“The subtraction of numbers consisting of twenty-four figures is an easy matter for him,” reported Scientific American. “Problems for which logarithm tables are generally used he solves mentally with wonderful precision.”
Unlike other prodigies, Inaudi did not visualize his work. “I hear the figures,” he told Alfred Binet, “and it is my ear which retains them; I hear them resounding after I have repeated them, and this interior sensation remains for a long time.”
Inaudi’s father had approached Flammarion hoping that his son could be educated toward a career in astronomy. “It had been an error, whichever way one looked at it,” Flammarion wrote 10 years later. “In science, one cannot make use of his methods, of his adapted formulae, which are tailored to mental calculation.” It was just as well: “Regarding his financial position, he now has, as a result of the curiosity his ability has aroused, a salary, which is over three times that of the Director of the Paris Observatory.” *Greg Ross, Futility Closet

1905 Baron C(harles) P(ercy) Snow (15 Oct 1905; 1 Jul 1980) British former physicist, turned novelist and government administrator. In 1959, C.P. Snow gave a controversial lecture called The Two Cultures and the Scientific Revolution claiming there were two cultures - the literary intellectuals and the scientists, who didn't understand each other and didn't trust each other. The split was not new; Snow noted that in the 1930s, literary theorists had begun to use the word "intellectual" to refer only to themselves. He illustrated this gap by asking a group of literary intellectuals to tell him about the Second Law of Thermodynamics, which he called the scientific equivalent of Have you read a work of Shakespeare?'" Since then, debate about this polarization has continued.*TIS

1875 André-Louis Cholesky (October 15, 1875 – August 31, 1918,) a French military officer and mathematician. He worked in geodesy and map-making, was involved in surveying in Crete and North Africa before World War I. But he is primarily remembered for the development of a matrix decomposition known as the Cholesky decomposition which he used in his surveying work. He served the French military as engineer officer and was killed in battle a few months before the end of World War I; his discovery was published posthumously by his fellow officer in the "Bulletin Géodésique".*Wik

Bernhard Hermann Neumann (15 Oct 1909, 21 Oct 2002) Neumann is one of the leading figures in group theory who has influenced the direction of the subject in many different ways. While still in Berlin he published his first group theory paper on the automorphism group of a free group. However his doctoral thesis at Cambridge introduced a new major area into group theory research. In his thesis he initiated the study of varieties of groups, that is classes of groups defined which are by a collection of laws which must hold when any group elements are substituted into them. *SAU
(check the dates of birth and death between this entry and the next... I checked, it seems to be correct, PB)

1909 Jesse L. Greenstein (15 Oct 1909; 21 Oct 2002) American astronomer who was a co-discoverer of quasars. His interest in astronomy began at age 8 when his grandfather gave him a brass telescope. By age 16, he was a student at Harvard University, and later earned his Ph.D.(1937), then joined the Yerkes Observatory under Otto Struve. Thereafter, he spent most of his career at the California Institute of Technology.. He measured the composition of stars, through which he found less heavy elements in the stars of globular clusters, thus proving they are younger than our Sun. In 1963, he and Maarten Schmidt were the first to correctly describe the nature of quasars, by interpreting their red shift as compact, very distant and thus very old objects. With Louis Henyey he designed and constructed a new spectrograph and wide-view camera to improve astronomical observations. *TIS

1921 Lillian Katie Bradley (born October 15, 1921) is a mathematician and mathematics educator who in 1960 became the first African-American woman to earn a doctorate in any subject at the University of Texas at Austin. She accomplished this ten years after African-Americans were first admitted to the school, and despite the dominance of the mathematics department at Austin by R. L. Moore, known for his segregationist views and for his snubs of African-American students. (In 1973, UT had named its mathematics building in honor of Robert Lee Moore, an accomplished mathematician who was also a strong segregationist. He famously walked out of lectures by black speakers, and refused to teach any black students. *PB)
Bradley was born in Tyler, Texas. She earned a bachelor's degree in mathematics in 1938 from Texas College, and a master's degree in mathematics education in 1946 from the University of Michigan. She became a teacher at a segregated black high school in Hawkins, Texas, at Paul Quinn College, and at Texas College, before becoming an assistant professor of mathematics at Prairie View A&M College. There, in 1957–1958, she was awarded a National Science Faculty Fellowship, one of only 100 awarded in the inaugural year of the program.
She completed her doctorate at the University of Texas in July 1960. Her dissertation, in mathematics education, was An Evaluation of the Effectiveness of a Collegiate General Mathematics Course. In 1962 she moved from Prairie View to Texas Southern University, as an associate professor. *Wik

DEATHS

1959 Lipót Fejér (9 Feb 1880, 15 Oct 1959) Fejér's main work was in harmonic analysis working on Fourier series and their singularities. Fejér collaborated to produce important papers with Carathéodory on entire functions and with Riesz on conformal mappings. *SAU

1965 Abraham Halevi (Adolf) Fraenkel (February 17, 1891, Munich, Germany – October 15, 1965, Jerusalem, Israel) known as Abraham Fraenkel, was an Israeli mathematician born in Germany. He was an early Zionist and the first Dean of Mathematics at the Hebrew University of Jerusalem. He is known for his contributions to axiomatic set theory, especially his addition to Ernst Zermelo's axioms which resulted in Zermelo–Fraenkel axioms.*Wik

1980 Mikhail Alekseevich Lavrentev(19 Nov 1900 in Kazan, Russia, 15 Oct 1980 in Moscow) is remembered for an outstanding book on conformal mappings and he made many important contributions to that topic.*SAU

1990 Wilhelm Magnus (February 5, 1907, Berlin, Germany – October 15, 1990, New York City) made important contributions in combinatorial group theory, Lie algebras, mathematical physics, elliptic functions, and the study of tessellations.*Wik

2016 Marcel Berger, (14 April 1927 – 15 October 2016) one of the world’s leading differential geometers and a corresponding member of the French Academy of Sciences for half a century, passed away at the age of eighty-nine. Marcel Berger’s contributions to geometry were both broad and deep. The classification of Riemannian holonomy groups provided by his thesis has had a lasting impact on areas ranging from theoretical physics to algebraic geometry. His 1960 proof that a complete oriented even-dimensional manifold with strictly quarter-pinched positive curvature must be a topological sphere is the direct ancestor of a vast sector of subsequent research in global Riemannian geometry. Through his many students and collaborators, he created a school which carried the torch of differential geometry into a new era. *Notices of the AMS

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