## Friday, 25 December 2020

### On This Day in Math - December 25

God Bless Us, Everyone
Me, and Tiny Tim

The 360th day of the year; Bryant Tuckerman found the Mersenne prime M19937 (which has 6000 digits) using an IBM360. *Prime Curios

360 is also the number of degrees in a full circle, and there is a (rather new) word for two angles that sum to 360 degrees.  They are called "explementary" .

360 is a highly composite number, it has 24 divisors, more than any other number of the year, in fact any number that is below twice its size.

It is the smallest number that is divisible by nine of the ten numbers 1-10 (not divisible by 7) What is next, students?

There are 360 possible rook moves on a 6x6 chess board.*Derek Orr

360 is centered on the 360th digit of pi (Also from Derek)[However 360 does occur once earlier centered at position 286.]

EVENTS

1843 Sir Henry Cole British industrial designer, museum director and writer who produced the first commercial Christmas card. In 1843, wishing to save much handwriting of seasonal correspondence, Cole introduced the world's first commercial Christmas card. He commissioned artist John Callcott Horsley to make the artwork for 1000 hand-coloured lithographs. (Individuals' homemade Christmas cards had existed earlier.) (See Image at top)

1640 Fermat's theorem on sums of two squares states that an odd prime p can be expressed as:

p= x2 + y2 with x and y integers, if and only if $p\equiv 1mod4$

The prime numbers for which this is true are called Pythagorean primes. For example, the primes 5, 13, 17, 29, 37 and 41 are all congruent to 1 modulo 4,

Albert Girard was the first to make the observation, describing all positive integral numbers (not necessarily primes) expressible as the sum of two squares of positive integers; this was published in 1625.The statement that every prime p of the form 4n+1 is the sum of two squares is sometimes called Girard's theorem. For his part, Fermat wrote an elaborate version of the statement (in which he also gave the number of possible expressions of the powers of p as a sum of two squares) in a letter to Marin Mersenne dated December 25, 1640: for this reason this version of the theorem is sometimes called Fermat's Christmas theorem. *Wik

1656 Huygens (who was a bachelor) spent Christmas Day making the ﬁrst model of a pendulum clock. *VFR(And then he was visited by three spirits.... oops, wrong story)

In 1741, the Centigrade temperature scale was devised by astronomer Anders Celsius (1701-44) and incorporated into a Delisle thermometer at Uppsala in Sweden. Celsius divided the fixed-point range of the Fahrenheit scale (the freezing and boiling temperatures of water) into 100 equal divisions, but curiously set the freezing point at 100 and the boiling point at 0. This reverse scaling was changed to match the sense of the other temperature scales after Celsius's death.*TIS

1758 Halley’s comet ﬁrst sighted after he predicted its return. After Newton explained planetary motion, he suggested that comets could have elongated elliptical orbits. Halley’s comet has eccentricity 0.9675. [UMAP Journal, 4(1983), p. 162] *VFR
In 1758, the predicted return of Halley's comet was first sighted by German farmer and amateur astronomer, Johann Georg Palitzsch, as a faint object in Pisces. Edmund Halley had predicted in 1705 the return of the comet to the Earth's vicinity every 75.5 years. For the first time the scientific prediction had been proven. Halley himself had died 16 years before this new event. Palitzsch also observed the 6 Jun 1761 transit of Venus, when he saw a black band linking Venus and the Sun near the beginning and end of the transit ("black drop effect") and correctly interpreted this as evidence that Venus possessed an atmosphere. He also measured the period of the variation of the brightness of the star Algol. *TIS
The BAYEUX TAPESTRY (Tapisserie de la Reine Mathilde) includes a clear picture of Halley's Comet, as shown on the stamp below.
and here is a Blog regarding the return in 1758.

In 1780, Luigi Galvani recorded, "The electric fluid should be considered a means to the nervo-muscular force." He reached this conclusion from work in his laboratory in Bologna, Italy, after a series of experiments and his accidental discovery that muscles are operated by electrical stimulation of nerves. He worked diligently along these lines, but waited for eleven years before he published the results and an ingenious and simple theory. His theory was that of a nervous electric fluid, secreted by the brain, conducted by the nerves, and stored in the muscles. Though his ideas were abandoned by scientists on account of later discoveries, his work opened the way to new research in the physiology of muscle and nerve and pioneered the subject of electrophysiology. *TIS

1884 On the first Christmas after it was printed, the future classic, Flatland, was reviewed in the Times UK, which gave it a less than sterling review.

In 1999, space shuttle Discovery's astronauts finished their maintenance work on the Hubble Space Telescope, installing correcting optics to repair problems due to a design flaw in the mirror. The first images the Hubble Telescope took after its original launch were disappointingly fuzzy, but after this repair mission the instrument returned crisp images of a clarity never before possible from terrestrial observatories *TIS

BIRTHS

1642 Isaac Newton born on Julian Calendar. (5 January 1643 New style) *VFR
Born 25 Dec 1642; died 20 Mar 1727. English physicist and mathematician, who made seminal discoveries in several areas of science, and was the leading scientist of his era. His study of optics included using a prism to show white light could be split into a spectrum of colours. The statement of his three laws of motion are fundamental in the study of mechanics. He was the first to describe the moon as falling (in a circle around the earth) under the same influence of gravity as a falling apple, embodied in his law of universal gravitation. As a mathematician, he devised infinitesimal calculus to make the calculations needed in his studies, which he published in Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy, 1687)*TIS

1763 Claude Chappe (25 Dec 1763; 23 Jan 1805) French engineer who invented the semaphore visual telegraph. He began experimenting in 1790, trying various types of telegraph. An early trial used telescopes, synchronized pendulum clocks and a large white board, painted black on the back, with which he succeeded in sending a message a few sentences long across a 16km (10mi) distance. To simplify construction, yet still easily visible to read from far away, he changed to using his semaphore telegraph in 1793. Smaller indicators were pivoted at each end of large horizontal member. The two indicators could each be rotated to stand in any of eight equally spaced positions. By setting them at different orientations, a set of corresponding codes was used to send a message.*TIS

1900 Antoni Szczepan Zygmund (25 Dec 1900 in Warsaw, Russian Empire (now Poland)
- 30 May 1992 in Chicago, Illinois, USA) Zygmund's work in harmonic analysis has application in the theory of waves and vibrations. He also did major work in Fourier analysis and its application to partial differential equations.*SAU

1905 Gottfried Maria Hugo Köthe (born 25 December 1905 in Graz; died 30 April 1989 in Frankfurt) was an Austrian mathematician working in abstract algebra and functional analysis.*SAU Köthe's best known work has been in the theory of topological vector spaces. In 1960, volume 1 of his seminal monograph Topologische lineare Räume was published (the second edition was translated into English in 1969). It was not until 1979 that volume 2 appeared, this time written in English. He also made contributions to the theory of lattices. *Wik

DEATHS

1921 Piers Bohl (October 23, 1865 – December 25, 1921) was a Latvian mathematician, who worked in differential equations, topology and quasi-periodic functions.
He was born in 1865 in Walk, Livonia, in the family of a poor Baltic German merchant. In 1884, after graduating from a German school in Viljandi, he entered the faculty of physics and mathematics at the University of Tartu. In 1893 Bohl was awarded his Master's degree. This was for an investigation of quasi-periodic functions. The notion of quasi-periodic functions was generalised still further by Harald Bohr when he introduced almost-periodic functions. *Wik

1929 Percy Alexander MacMahon (b. 26 September 1854, Sliema, Malta – 25 December 1929, Bognor Regis, England) was a mathematician, especially noted in connection with the partitions of numbers and enumerative combinatorics. MacMahon was elected a Fellow of the Royal Society in 1890. He received the Royal Society Royal Medal in 1900, the Sylvester Medal in 1919, and the Morgan Medal by the London Mathematical Society in 1923. MacMahon was the President of the London Mathematical Society from 1894 to 1896.
MacMahon is best known for his study of symmetric functions and enumeration of plane partitions; see MacMahon Master theorem. His two volume Combinatory analysis, published in 1915/16, is the first major book in enumerative combinatorics. MacMahon also did pioneering work in recreational mathematics and patented several successful puzzles.*WIK

1930 Eugen Goldstein (5 Sep 1850, 25 Dec 1930) German physicist who discovered and named canal rays (1886) which emerge through holes in the anodes of low-pressure electrical discharge tubes (later shown to be positively charged particles). Earlier, he coined the term "cathode ray" (1876) emitted from a cathode. He was the first to see that they could cast a shadow, and were emitted at right angles to the surface. He also investigated the wavelengths of light emitted by metals and oxides when canal rays impinge on them. When the Berlin Urania, opened in 1889 it had five scientific departments and a "science theatre", it was Goldstein who had recommended the "hall of physics in which the visitor could experiment on his own". Students of his that continued his work included Wien and Stark. *TIS

1941 Theodor Molien​ or Fedor Eduardovich Molin​ (September 10, 1861 - December 25, 1941) was a Baltic-German mathematician. He was born in Riga, Latvia, which at that time was a part of Russian Empire. Molien studied associative algebras and polynomial invariants of finite groups.*Wik

1944 Wilhelm Kutta was a German engineer who is best known for his work on the numerical solution of differential equations (the Runge-Kutta method).*SAU Kutta was born in Pitschen, Upper Silesia (today Byczyna, Poland). He attended the University of Breslau from 1885 to 1890, and continued his studies in Munich until 1894, where he became the assistant of Walther Franz Anton von Dyck. From 1898, he spent half a year at the University of Cambridge.[1] From 1899 to 1909 he worked again as an assistant of von Dyck in Munich; from 1909 to 1910 he was adjunct professor at the Friedrich Schiller University Jena. He was professor at the RWTH Aachen from 1910 to 1912. Kutta became professor at the University of Stuttgart in 1912, where he stayed until his retirement in 1935.
In 1901, he co-developed the Runge-Kutta method, used to solve ordinary differential equations numerically. He is also remembered for the Zhukovsky-Kutta aerofoil, the Kutta-Zhukovsky theorem and the Kutta condition in aerodynamics. Kutta died in Fürstenfeldbruck, Germany in 1944. *Wik

2000 Willard Van Orman Quine (June 25, 1908 – December 25, 2000) (known to intimates as "Van")[1] was an American philosopher and logician in the analytic tradition. From 1930 until his death 70 years later, Quine was continuously affiliated with Harvard University in one way or another, first as a student, then as a professor of philosophy and a teacher of mathematics, and finally as a professor emeritus who published or revised several books in retirement. He filled the Edgar Pierce Chair of Philosophy at Harvard from 1956 to 1978. A recent poll conducted among philosophers named Quine one of the five most important philosophers of the past two centuries.[2] He won the first Schock Prize in Logic and Philosophy in 1993, for "his systematical and penetrating discussions of how learning of language and communication are based on socially available evidence and of the consequences of this for theories on knowledge and linguistic meaning.*Wik

2018 Nancy Grace Roman (May 16, 1925..Nashville, Tennessee, U.S.-December 25, 2018 (aged 93)) was an American astronomer and one of the first female executives at NASA. She is known to many as the "Mother of Hubble" for her role in planning the Hubble Space Telescope. Throughout her career, Roman was also an active public speaker and educator, and an advocate for women in the sciences.
When Roman was eleven years old, she showed interest in astronomy by forming an astronomy club among her classmates in Nevada. She and her classmates got together once a week and learned about constellations from books. Although discouraged by those around her, Roman knew by the time she was in high school that she wanted to pursue her passion for astronomy. She attended Western High School in Baltimore where she participated in an accelerated program and was graduated in three years. *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