## Monday 6 May 2024

### On This Day in Math - May 6

 *Fermat's Library

The 126th day of the year; nine points around a circle form the vertices of $\binom{n}{k} = 126$  unique quadrilaterals.   That also means that if you draw all the diagonals of the nonagon, you would be using the same 126 sets of four vertices to get 126 intersections.

126 is the first of four consecutive numbers that are the sum of a cube and a square. 5³+ 1²

In non-leap  years, there are 126 days in which the day of the month is prime.

The prime gap that covers the first century with no primes (from 1671800 to 1671899) has length 126 (from 1671781 to 1671907).

There are 9 choose 5, or 126 ways for a random selection to pick the five spaces on a tic tac toe board for the "first player" in a random game.  36 of these configurations are a "win" for both players. They have both three x's and three O's in a line, since they don't have an order of play. Over 58% of those games are a win for the "first player". Geometrically, a student could think of each random game as a pentagon selected from nine points spaced around a circle.

EVENTS

1604 Longomontanus wrote to Kepler criticizing his attacks on Tycho's system using Tycho's data: "These and perhaps all other things that were discovered and worked out by Tycho during his restoration of astronomy for our eternal benefit, you, my dear Kepler, although submerged in shit in the Augean stable of old, do not scruple to equal." More detail at the Renaissance Mathematicus blog

1747 Euler to Goldbach, QED  Euler succeeded in proving Fermat's theorem on sums of two squares in 1747, when he was forty years old. He communicated this in a letter to Goldbach dated 6 May 1747. The proof relies on infinite descent.  Fermat's theorem on sums of two squares asserts that an odd prime number p can be expressed as
p = x2 + y2
with integer x and y if and only if p is congruent to 1 (mod 4). The statement was announced by Fermat in 1640, but he supplied no proof. *Wik

1775 After being driven out of Concord by an angry mob because of his Tory leanings, the American born Benjamin Thompson, later to become Count Rumford, sends the first invisible ink letter of the American Revolution  . Within a few days of the Battle of Lexington, British headquarters in Boston received a secret ink letter which revealed details of the military plans of the patriot forces in New England. Long suspected to have been from Thompson in his home town of Woburn, Mass, recent chemical and handwriting analysis have conclusively confirmed that it was from him. *American Journal of Police Science

1807 Bessel wrote to Gauss, "I saw with pleasure that you have calculated the orbit of Vesta; also the name chosen by you is splendid, and therefore certainly also pleasant to all your friends because it shows them to which goddess you sacrifice.". Carl Friedrich Gauss: Titan of Science  By Guy Waldo Dunnington, Jeremy Gray, Fritz-Egbert Dohse

1840, the adhesive postage stamp was first sold in Great Britain. The "penny black" and "twopenny blue" stamps showed the profile of Queen Victoria. *TIS

1889 The Eiffel Tower, 7e, was built in 26 months and opened in Mar 1889 for the Universal Exposition.  it is 320.75 m (1051 ft) high and only weighs 7000 tons – less than the air around it!  The tower was inaugurated on 31 March 1889, and opened on 6 May. I recently read that "Gustav Eiffel included a flat for himself at the top of the Eiffel Tower, and retired there at age 62 to conduct aerodynamic experiments".
Today, after being off limits for years, the apartment is on display for visitors to come and peer into. Much of the furnishings remain the same and there are a couple of rather wan looking mannequins of Eiffel and Edison. For the right type of architectural admirer Eiffel’s secret apartment could inspire as much jealousy today as it did when it was built.
In 2016 several stories below Gustave Eiffel’s private apartment, a second Eiffel Tower apartment opened temporarily in the summer of 2016. Vacation rental company HomeAway transformed an unused conference space on the first floor of the tower into a new pop-op designer apartment as a marketing promotion. Four contest winners got a chance to stay inside the tower in July, 2016. *Atlas Obscura

1896  Samuel Pierpont Langley became the third Secretary of the Smithsonian Institution in 1887. In 1891, he began experiments with large, tandem-winged models powered by small steam and gasoline engines he called aerodromes. After several failures with designs that were too fragile and under-powered to sustain themselves, Langley had his first genuine success on May 6, 1896, with his Aerodrome Number 5. It made the world's first successful flight of an unpiloted, engine-driven, heavier-than-air craft of substantial size. It was launched from a spring-actuated catapult mounted on top of a houseboat on the Potomac River near Quantico, Virginia. Two flights were made on May 6, one of 1,005 m (3,300 ft) and a second of 700 m (2,300 ft), at a speed of approximately 40 kph (25 mph). On both occasions, the Aerodrome Number 5 landed in the water, as planned, because, in order to save weight, it was not equipped with landing gear.

 *Wikimedia

1937  The Hindenburg disaster was an airship accident that occurred on May 6, 1937, in Manchester Township, New Jersey, U.S. The LZ 129 Hindenburg (Luftschiff Zeppelin #129; Registration: D-LZ 129) was a German commercial passenger-carrying rigid airship, the lead ship of the Hindenburg class, the longest class of flying machine and the largest airship by envelope volume.[1] It was designed and built by the Zeppelin Company (Luftschiffbau Zeppelin GmbH) and was operated by the German Zeppelin Airline Company (Deutsche Zeppelin-Reederei). It was named after Field Marshal Paul von Hindenburg, who was president of Germany from 1925 until his death in 1934. Filled with hydrogen, it caught fire and was destroyed during its attempt to dock with its mooring mast at Naval Air Station Lakehurst. The accident caused 35 fatalities (13 passengers and 22 crewmen) from the 97 people on board (36 passengers and 61 crewmen), and an additional fatality on the ground.

1950 A famous series begins on this day. Can you guess what it is? The ﬁrst terms are Nicky Hilton, Michael Wilding, Mike Todd, Eddie Fisher, Richard Burton, Richard Burton, John Warner, Larry Fortensky. Note that one term in the series repeats; that’s perfectly natural. Your are right, this is a Taylor series. More speciﬁcally, the Elizabeth Taylor series. These are her husbands (eight by last count (2010)). *VFR [sadly, Ms. Taylor has departed the matrimonial game... at least on this sphere. pb]

1949 British Computer EDSAC Performs First Calculation. The EDSAC performed its first calculation. Maurice Wilkes had assembled the machine -- the first practical stored-program computer -- at Cambridge University (an earlier machine at the University of Manchester was too small for practical purposes). His ideas grew out of the Moore School lectures he had attended three years earlier at the University of Pennsylvania. For programming the EDSAC, Wilkes established a library of short programs called subroutines stored on punched paper tapes. It performed 714 operations per second. *CHM
 *Computer History Museum, Mountain View, CA

1954 Roger Bannister deﬁed the general belief that it was impossible to run a mile in less than 4 minutes by running one in 3 minutes 59.4 seconds. *VFR  ..."the announcer at the Oxford University cinder track in England calmly gave the placings in the one mile race, and then started to announce the winning time, beginning with the word “three...” The small crowd erupted in delirious excitement, the rest of the announcement went unheard"*Runner's World
At the 1952 Olympics in Helsinki, Bannister set a British record in the 1500 metres and finished in fourth place. This achievement strengthened his resolve to become the first athlete to finish the mile run in under four minutes. He accomplished this feat on 6 May 1954 at Iffley Road track in Oxford, with Chris Chataway and Chris Brasher providing the pacing.
Bannister went on to become a neurologist and Master of Pembroke College, Oxford, before retiring in 1993. As Master of Pembroke, he was on the governing body of Abingdon School from 1986 to 1993. When asked whether the 4-minute mile was his proudest achievement, he said he felt prouder of his contribution to academic medicine through research into the responses of the nervous system. Bannister was patron of the MSA Trust. He was diagnosed with Parkinson's disease in 2011.  *HT Offer Pade’

1996, Volodymyr Petryshyn,a professor of mathematics at Rutgers University, killed his wife, Ukrainian-American painter Arcadia Olenska-Petryshyn, with a hammer. After making a mistake in a proof he feared that he would be ridiculed by his fellow mathematicians and while under the strain of this, he had a complete mental breakdown. He was found not guilty of murder by reason of insanity. He later published Development of mathematical sciences in the Ukraine in Ukrainian in 2004.   Petryshyn died on March 21, 2020

BIRTHS

1635 Johann Joachim Becher, (1635–1682),the German physician and alchemist who initiated the theory that became the phlogiston theory, born. William Cullen considered Becher as a chemist of first importance and Physica Subterranea as the most considerable of Bechers writings. He reintroduced Paracelsus’ tria prima in the form of three different types of Earth.
• terra fluida or mercurial Earth giving material the characteristics, fluidity, fineness, fugacity, metallic appearance
• terra pinguis or fatty Earth giving material the characteristics oily, sulphurous and flammable
• terra lapidea glassy Earth, giving material the characteristic fusibility
It was the second of these, terra pingus, that  was adopted into phlogisten theory.  For a longer, clearer, and more knowledgeable look at this development read this by The Renaissance Mathematicus. Like George Box's comment on statistical models, "Wrong, but useful".

1667 Abraham De Moivre ( 26 May 1667 – 27 November 1754) born in Vitry-le-Francois, Champagne, France. *VFR [.. a French mathematician famous for de Moivre's formula, which links complex numbers and trigonometry, and for his work on the normal distribution and probability theory. He was a friend of Isaac Newton, Edmund Halley, and James Stirling. Among his fellow Huguenot exiles in England, he was a colleague of the editor and translator Pierre des Maizeaux.
De Moivre wrote a book on probability theory, The Doctrine of Chances, said to have been prized by gamblers. De Moivre first discovered Binet's formula, the closed-form expression for Fibonacci numbers linking the nth power of φ (the so-called "golden ratio" to the nth Fibonacci number.](Wikipedia)

1769 Jean Nicolas Pierre Hachette (May 6, 1769 – January 16, 1834) worked on descriptive geometry, collected work by Monge and edited Monge's Géométrie descriptive which was published in 1799. He also published on a wide range of topics from his own major works on geometry, to works on applied mechanics including the theory of machines. His work on machines includes much in the area of applied mechanics, but he was also interested in applied hydrodynamics and steam engines. In fact he published interesting work on the history of steam engines. *SAU

1792 Martin Ohm (6 May 1792 in Erlangen, Bavaria (now Germany)- 1 April 1872 in Berlin, Prussia, German Empire) was a German mathematician and a younger brother of physicist Georg Ohm. He earned his doctorate in 1811 at Friedrich-Alexander-University, Erlangen-Nuremberg where his advisor was Karl Christian von Langsdorf. Ohm was the first to fully develop the theory of the exponential ab when both a and b are complex numbers in 1823. He is also often credited with introducing the name "golden section" (goldener Schnitt).
Ohm's students included Friedrich August, Friedrich Bachmann, Paul Bachmann, Joseph Brutkowski, Heinrich Eduard Heine, Rudolf Lipschitz, Leo Pochhammer, Friedrich Prym, Wilhelm Wagner, Hermann Waldaestel, Wilhelm Wernicke, Elena Gerz, Valentien Gerz, and Johanna Gerz. *Wik
Martin Ohm made a distinction between writing for mathematicians and writing for students, a distinction that many of his contemporaries, including Hermann Grassmann, did not consider appropriate. His colleagues Steiner and Kummer also ridiculed him for not following Alexander von Humboldt's firm belief in the unity of teaching and research. It is quite difficult to assess the importance of Ohm's mathematical contributions. The first thing to say is that they certainly weren't as important as he himself thought. He had a very high opinion of himself as the following quotation indicates. Niels Abel wrote to Christopher Hansteen, the professor of astronomy at the University of Christiania, while he was on a visit to Berlin in 1826

There is at [August Crelle's] house some kind of meeting where music is mainly discussed, of which unfortunately I do not understand much. I enjoy it all the same since I always meet there some young mathematicians with whom I talk. At Crelle's house, there used to be a meeting of mathematicians, but he had to suspend it because of a certain Martin Ohm with whom nobody could get along due to his terrible arrogance.
*SAU

1872 Willem de Sitter (6 May 1872 – 20 November 1934) Dutch mathematician, astronomer, and cosmologist who developed theoretical models of the universe based on Albert Einstein's general theory of relativity. He worked extensively on the motions of the satellites of Jupiter, determining their masses and orbits from decades of observations. He redetermined the fundamental constants of astronomy and determined the variation of the rotation of the earth. He also performed statistical studies of the distribution and motions of stars, but today he is best known for his contributions to cosmology. His 1917 solution to Albert Einstein's field equations showed that a near-empty universe would expand. Later, he and Einstein found an expanding universe solution without space curvature. *TIS

1906 André Weil  (6 May 1906 – 6 August 1998) was an influential mathematician of the 20th century, renowned for the breadth and quality of his research output, its influence on future work, and the elegance of his exposition. He is especially known for his foundational work in number theory and algebraic geometry. He was a founding member and the de facto early leader of the influential Bourbaki group. The philosopher Simone Weil was his sister.. *Wikipedia

1908 John Frank (Jack) Allen (6 May 1908; 22 Apr 2001 at age 92) was a Canadian physicist who codiscovered the superfluidity of liquid helium near absolute zero temperature. Working at the Royal Society Mond Laboratory in Cambridge, with Don Misener he discovered (1930's) that below 2.17 kelvin temperature, liquid helium could flow through very small capillaries with practically zero viscosity. Independently, P. L. Kapitza in Moscow produced similar results at about the same time. Their two articles were published together in the 8 Jan 1938 issue of the journal Nature. Superfluidity is a visible manifestation resulting from the quantum mechanics of Bose- Einstein condensation. By 1945, research in Moscow delved into the microscopic aspect, which Allen did not pursue.*TIS

1916 Robert Henry Dicke (6 May 1916 St. Louis, Missouri, USA - 4 Mar 1997 at age 80) American physicist who worked in such wide-ranging fields as microwave physics, cosmology, and relativity. As an inspired theorist and a successful experimentalist, his unifying theme was the application of powerful and scrupulously controlled experimental methods to issues that really matter. He also made a number of significant contributions to radar technology and to the field of atomic physics. His visualization of an oscillating universe stimulated the discovery of the cosmic microwave background, the most direct evidence that our universe really did expand from a dense state. A key instrument in measurements of this fossil of the Big Bang is the microwave radiometer he invented. His patents ranged from clothes dryers to lasers. *TIS

DEATHS

1643 Pierre Herigone, (1580–1643) the ﬁrst person to use the symbol for angle. *VFR   (He also introduced the upside-down "T" symbol (⊥) to express perpendicularity.) [Pierre Hérigone is actually a pseudonym for the Baron Clément Cyriaque de Mangin. In fact, just to make things even more confusing, Cyriaque de Mangin also used the pseudonym Denis Henrion. He was of Basque origin. Little is known of his life except that he taught for most of it in Paris.]*SAU
Hérigone used a symbol with an angle made by a flat line and an inclined line and also use one like the angle bracket in Cursus mathematicus. It was published in 1634 and a second edition the next year. (Cajori vol. 1, page 202) . It appears that he may have been the first to use the inverted T for perpendicular as well. {note to reader, I have frequently seen 1643 shown as his birth date but that must be an error. pb)

1856 William Stirling Hamilton (8 March 1788 in Glasgow, Scotland - 6 May 1856 in Edinburgh, Scotland) Hamilton became professor of logic and metaphysics at the University of Edinburgh, giving his inaugural lecture on 21 November. Hamilton was one of the first in a series of British logicians to create the algebra of logic and introduced the 'quantification of the predicate'. Boole, De Morgan and Venn followed him, but Hamilton helped begin this development and his work, although not of great depth, influenced Boole to produce a much more sophisticated system. Sadly, however, Hamilton claimed that De Morgan was guilty of plagiarism which was a ridiculous suggestion. *SAU

1859  Friedrich Wilhelm Heinrich Alexander von Humboldt (14 September 1769 – 6 May 1859) was a German polymath, geographer, naturalist, explorer, and proponent of Romantic philosophy and science. He was the younger brother of the Prussian minister, philosopher, and linguist Wilhelm von Humboldt (1767–1835). Humboldt's quantitative work on botanical geography laid the foundation for the field of biogeography. Humboldt's advocacy of long-term systematic geophysical measurement laid the foundation for modern geomagnetic and meteorological monitoring.
Between 1799 and 1804, Humboldt traveled extensively in the Americas, exploring and describing them for the first time from a modern Western scientific point of view. His description of the journey was written up and published in several volumes over 21 years. Humboldt was one of the first people to propose that the lands bordering the Atlantic Ocean were once joined (South America and Africa in particular).

Humboldt resurrected the use of the word cosmos from the ancient Greek and assigned it to his multivolume treatise, Kosmos, in which he sought to unify diverse branches of scientific knowledge and culture. This important work also motivated a holistic perception of the universe as one interacting entity, which introduced concepts of ecology leading to ideas of environmentalism. In 1800, and again in 1831, he described scientifically, on the basis of observations generated during his travels, local impacts of development causing human-induced climate change.

Humboldt is seen as "the father of ecology" and "the father of environmentalism".
Isothermal map of the world using Humboldt's data by William Channing Woodbridge

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

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

1916 Ágoston Scholtz (27 July 1844 in Kotterbach, Zips district, Austro-Hungary (now Rudnany, Slovakia) Died: 6 May 1916 in Veszprém, Hungary) From 1871 he was a teacher of mathematics and natural philosophy at the Lutheranian Grammar School of Budapest which at that time had been upgraded to become a so called 'chief grammar school', namely one which offered eight years of teaching. This was precisely the school which later was attended by several famous mathematicians such as Johnny von Neumann and Eugene Wigner (or Jenó Pál Wigner as he was called at that time). Scholtz became the school director of the Lutheranian Grammar School in 1875. Unfortunately this excellent school was closed in 1952, and most of its equipment was lost. Due to the initiative and support of its former well-known students, among others Wigner, it was reopened in 1989 after being closed for thirty-seven years. Scholtz's field of research was projective geometry and theory of de
terminants. His results were recorded by Muir in his famous work The history of determinants *SAU

1951 Élie Joseph Cartan  (9 April 1869 – 6 May 1951) worked on continuous groups, Lie algebras, differential equations and geometry. His work achieves a synthesis between these areas. He is one of the most important mathematicians of the first half of the 20C. *SAU  He was one of the earliest "Bourbaki".

1979 Karl Wilhelm Reinmuth (4 April 1892 in Heidelberg – 6 May 1979 in Heidelberg) was a German astronomer and a prolific discoverer of 395 minor planets.  He was the world's foremost asteroid hunter before automated search techniques. His discoveries (1914-1957) of 389 such minor planets include some of the first found outside of the Solar System's asteroid belt. His Ph.D. thesis was 'Photographische Positionsbestimmung von 356 Schultzschen Nebelflecken' (Photographic Location of 356 Schultz's Nebulae, 1916). He had started a few years earlier, in 1912, volunteering his time to assist Maximillian Wolf, director at the Königstuhl Observatory, Heidelberg. He learned how to study photographic plates to find asteroids, from Wolf, the first astronomer to utilize such technique. On 15 Oct 1914, the minor planet (796) Sarita was the first Reinmuth identified. In 1937, he named Hermes, the asteroid which made the closest then known approach to Earth.

1983 Yudell Leo Luke (26 June 1918 – 6 May 1983) was an American mathematician who made significant contributions to the Midwest Research Institute, was awarded the N. T. Veatch award for Distinguished Research and Creative Activity in 1975, and appointed as Curator's Professor at the University of Missouri in 1978, a post he held until his death. Luke published eight books and nearly 100 papers in a wide variety of mathematical areas, ranging from aeronautics to approximation theory. By his own estimation, Luke reviewed over 1800 papers and books throughout his career.*SAU

2009 Chuan-Chih Hsiung (15 Feb 1915 in Shefong, Jiangsi, China - 6 May 2009 in Needham, Massachusetts, USA), also known as Chuan-Chih Hsiung, C C Hsiung, or Xiong Quanzhi, is a notable Chinese-born American differential geometer. He was Professor Emeritus of Mathematics at Lehigh University, Bethleham PA USA.
He is the founder and editor-in-chief of the Journal of Differential Geometry, an influential journal in the domain. During his early age, he focused on projective geometry. His interests were largely extended after his research in Harvard, including two-dimensional Riemannian manifolds with boundary, conformal transformation problems, complex manifold, curvature and characteristic classes, etc. *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