When you can measure what you are talking about

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.

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

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

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

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)

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

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)

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

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

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*=*x*^{2}+*y*^{2}

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. *Wik1775 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, 7^{e}, was built in 26 months and opened in Mar 1889 for the Universal Exposition. it is 320.75 m (1051 ft) high and only**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".***weighs 7000 tons – less than the air around it!*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

**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

**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

**BIRTHS**

**1667 Abraham De Moivre**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 a^{b}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

*SAU

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.

**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**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 [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.]*SAUHérigone 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

**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 determinants. 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".**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

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