## Saturday 24 December 2022

### On This Day in Math - December 24

 The travelers looked up to see an omen shining in the sky,Earthrise: See 1968 below

The 358th day of the year; 358 is twice a prime, and the sum of six consecutive primes, 47 + 53 + 59 + 61 + 67 + 71
The sum of the first 358 prime numbers is itself a prime number.

and in case you were curious, the 358th digit of pi (after the decimal point) is 3.

The product of the first 358 integers is not divisible by the sum of the first 358 integers.  That means that for any numbers x, y both greater than 1, there is no solution to the equation x + xy + y =158.  If this is not a leap year, then this is the last year day this year with this quality.  (younger students might try to show these interrelated ideas with a smaller number like 10.)

35+ 8 + 3 + 58 + 3 + 5 + 8 = 3 x 5 x 8 = 120

Derek Orr pointed out that 358 = 2 x 179, and 2+ 179 = 181 is prime, and 2 + 1 + 7 + 9 = 19 is also prime.

358 = 18^2 + 5^2 + 3^2 = 14^2 + 9^2 + 9^2

EVENTS

1734 A letter and drawing by Martha Gerrish, a woman of New England, described a Parhelion, (aka Sundog, an atmospheric optical phenomenon that consists of a bright spot to one or both sides of the Sun) a rare astronomical phenomenon. Gerrish comments ‘if this came from a masculine hand, I believe it would be an acceptable present to the Royal Society’. This is the first letter to the Royal Society known to be sent by a woman in her own name and demonstrates that women contributed to science even when their work was not made public.
The photograph shows very bright sun dogs in Fargo, North Dakota.*Wij
 *Royal Society Org

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1754 Euler writes to Muller in St Petersburg and describes d'Alembert as "the most argumentative man in the world," and calls him, "hated by everyone in Paris." *Thomas L. Hankins, Jean d'Alembert: science and the Enlightenment; pg 58

1819 Bernard Bolzano was dismissed from his theological chair at the University of Prague and put under police supervision for his unorthodox religious views. In mathematics he helped remove the scandal of inﬁnitesimals from the calculus. *VFR

1849 Gauss writes to the Astronomer Johann Franz Encke in response to Encke's remarks about the Frequency of Primes.
"Most Honored Friend!
. . .The kind communication of your remarks on the frequency of prime numbers
was interesting to me in more than one respect. You have reminded me of
my own pursuit of the same subject, whose first beginnings occurred a very long
time ago, in 1792 or 1793, when I had procured for myself Lambert’s supplement
to the table of logarithms. Before I had occupied myself with the finer
investigations of higher arithmetic, one of my first projects was to direct my
attention to the decreasing frequency of prime numbers, to which end I counted
them up in several chiliads (sets of a thousand) and recorded the results on one of the affixed white sheets. I soon recognized, that under all variations of this frequency, on average, it is nearly inversely proportional to the logarithm..."
Gauss never published his results. The first published version of the Prime Number Theorem was by Legendre in 1798. *John Derbyshire, Prime Obsession

1899 the Physico-Mathematic Society of Kazan (Russia) celebrated a Jubilee in honor of the twenty-fifth year of professional and scientific service of its President, Professor A. Vasiliev. It is also the fifteenth year of his presidency. Professor Vasiliev has been an extraordinarily important figure in Russian science. Outside of Russia he has chiefly been known for his remarkable discourse on Lobachevski. *The American Mathematical Monthly, Vol. 7, No. 1 (Jan., 1900), p. 30

1912 Irving Fisher (1867-1947), a Yale professor, patented an archiving system with index cards. On 1 Jul 1925, Fisher's own firm, the Index Visible Company, merged with its principal competitor to form Kardex Rand Co., later Remington Rand, still later Sperry Rand. Fisher earned about $1million$ for the invention, which grew to the princely sum of $9million$ before being lost in the stock market crash of 1929. Fisher is widely regarded as the greatest economist America has produced, who made much use of mathematics in his work.*TIS

1968 On Christmas Eve, the Apollo 8 astronauts saw the entirety of Earth for the first time. Turing their cameras to the Earth they took the first three pictures of the whole earth from space. The one above, by William Anders, has been called "the most influential environmental photograph ever taken." *Wik, NASA

In 2004, the Huygens probe began a 22-day descent towards Saturn's largest moon, Titan. It had been launched as part of the Cassini spacecraft in 1997, and together they entered Saturn's orbit in June 2004. As the paths of the spacecraft and Titan converged, Cassini ejected the Huygens probe, sending it on a 22-day coast toward the cloud-covered moon. It landed 14 Jan 2005, and sent back photographs of the moon's surface. Cassini will remain in orbit around Saturn until at least July 2008. The Cassini-Huygens mission to study Saturn and its 33 known moons resulted from an unprecedented cooperative effort between the NASA of the United States, the European Space Agency and Italy's space program, at a cost of \$3.3 billion. *TIS

BIRTHS

1740 Anders Johan Lexell (December 24, 1740 – December 11, 1784 (Julian calendar: November 30)) was a Swedish-born Russian astronomer, mathematician, and physicist who spent most of his life in Russia where he is known as Andrei Ivanovich Leksel.
Lexell made important discoveries in polygonometry and celestial mechanics; the latter led to a comet named in his honor. La Grande Encyclopédie states that he was the prominent mathematician of his time who contributed to the spherical trigonometry with new and interesting solutions, which he took as a basis for his research of comet and planet motion. His name was given to one of the theorems about spherical triangles.
Lexell was one of the most prolific members of the Russian Academy of Sciences at that time, having published 66 papers in 16 years of his work there. A statement attributed to Leonhard Euler expresses high approval of Lexell's works: "Besides Lexell, such a paper could only be written by D'Alambert or me". Daniel Bernoulli also praised his work, writing in a letter to Johann Euler "I like Lexell's works, they are profound and interesting, and the value of them is increased even more because of his modesty, which adorns great men".
Lexell did not have a family and kept up a close friendship with Leonhard Euler and his family. He witnessed Euler's death at his house and succeeded him to the chair of the mathematics department at the Russian Academy of Sciences, but died the following year. The asteroid 2004 Lexell is named in his honour, as is the lunar crater Lexell.*Wik

1818 James Prescott Joule (24 Dec 1818; 11 Oct 1889) English physicist who established that the various forms of energy - mechanical, electrical, and heat - are basically the same and can be changed, one into another. Thus he formed the basis of the law of conservation of energy, the first law of thermodynamics. He discovered (1840) the relationship between electric current, resistance, and the amount of heat produced. In 1849 he devised the kinetic theory of gases, and a year later announced the mechanical equivalent of heat. Later, with William Thomson (Lord Kelvin), he discovered the Joule-Thomson effect. The SI unit of energy or work , the joule (symbol J), is named after him. It is defined as the work done when a force of 1 newton moves a distance of 1 metre in the direction of the force.*TIS

1822 Charles Hermite (24 Dec 1822; 14 Jan 1901) French mathematician whose work in the theory of functions includes the application of elliptic functions to provide the first solution to the general equation of the fifth degree, the quintic equation. In 1873 he published the first proof that e is a transcendental number. Hermite is known also for a number of mathematical entities that bear his name, Hermite polynomials, Hermite's differential equation, Hermite's formula of interpolation and Hermitian matrices. Poincaré is the best known of Hermite's students.*TIS

1838 Thorvald Nicolai Thiele (24 December 1838 – 26 September 1910) was a Danish astronomer, actuary and mathematician, most notable for his work in statistics, interpolation and the three-body problem. He was the first to propose a mathematical theory of Brownian motion. Thiele introduced the cumulants and (in Danish) the likelihood function; these contributions were not credited to Thiele by Ronald A. Fisher, who nevertheless named Thiele to his (short) list of the greatest statisticians of all time on the strength of Thiele's other contributions.
Thiele also was a founder and Mathematical Director of the Hafnia Insurance Company and led the founding of the Danish Society of Actuaries. It was through his insurance work that he came into contact with fellow mathematician Jørgen Pedersen Gram. Asteroid 843 Nicolaia is named in his honor. *Wik

1868 Emanuel Lasker (24 Dec 1868 in Berlinchen, Prussia (now Barlinek, Poland) - 11 Jan 1941 in New York, USA) Lasker became World Chess Champion in 1894 and held the championship until 1921. In mathematics he introduced the notion of a primary ideal. *SAU

1904 Sir William Hunter McCrea FRS (13 December 1904, Dublin – 25 April 1999) was an English astronomer and mathematician. He went to Trinity College, Cambridge in 1923 where he studied Mathematics, later gaining a PhD in 1929 under Ralph H. Fowler. He was later appointed a lecturer of Mathematics at the University of Edinburgh in 1929. He also served as reader and assistant professor at Imperial College London. In 1936 he became head of the mathematics department at the Queen's University of Belfast. After serving in the war, he joined the mathematics department at Royal Holloway College in 1944 (the McCrea Building on Royal Holloway's campus is named after him). In 1965, McCrea created the astronomy centre of the physics department at the University of Sussex.
In 1928, he studied Albrecht Unsöld's hypothesis, and discovered that three quarters of the Sun is made of Hydrogen, and about one quarter is Helium, with 1% being other elements. Previous to this many people thought the Sun consisted mostly of Iron. After this, people realized most stars consist of Hydrogen.
McCrea was president of the Royal Astronomical Society from 1961-3 and president of Section A of the British Association for the Advancement of Science from 1965-6. He was knighted in 1985. He won the Gold Medal of the Royal Astronomical Society in 1976. McCrea died on April 25, 1999 in Lewes. *Wik

1910 William Hayward Pickering (24 Dec 1910; 15 Mar 2004) Engineer and physicist, head of the team that developed Explorer 1, the first U.S. satellite. He collaborated with Neher and Robert Millikan on cosmic ray experiments in the 1930s, taught electronics in the 1930s, and was at Caltech during the war. He spent the rest of his career with the Jet Propusion Laboratory, becoming its Director (1954) with responsibility for the U.S. unmanned exploration of the planets and the solar system. Among these were the Mariner spacecraft to Venus and Mercury, and the Viking mission to Mars. The Voyager spacecraft yielded stunning photographs of the planets Jupiter and Saturn.*TIS

DEATHS

(How sad to be one of these people who died on Christmas Eve)
1872 William John Macquorn Rankine (5 Jul 1820, 24 Dec 1872) Scottish engineer and physicist and one of the founders of the science of thermodynamics, particularly in reference to steam-engine theory. As the chair (1855) of civil engineering and mechanics at Glasgow, he developed methods to solve the force distribution in frame structures. Rankine also wrote on fatigue in the metal of railway axles, on Earth pressures in soil mechanics and the stability of walls. He was elected a Fellow of the Royal Society in 1853. Among his most important works are Manual of Applied Mechanics (1858), Manual of the Steam Engine and Other Prime Movers (1859) and On the Thermodynamic Theory of Waves of Finite Longitudinal Disturbance. *TIS (Many students are not aware there is a absolute temperature scale called the Rankine, named for him)

1882 Johann Benedict Listing (25 July 1808 in Frankfurt am Main, Germany - 24 Dec 1882 in Göttingen, Germany)wrote one of the earliest texts on Topology. he studied the figure of the earth in minute detail; he made observations in meteorology, terrestrial magnetism, and spectroscopy; he wrote on the quantitative determination of sugar in the urine of diabetics; he promoted the nascent optical industry in Germany and better street lighting in Göttingen; he travelled to the world exhibitions in London 1851, Vienna 1873 and London 1876 as an observer for his government; he assisted in geodetic surveys; ... he invented a good many terms [other than topology], some of which have became current: "entropic phenomenona", "nodal points", "homocentric light", "telescopic system", " geoid" ...he coined "one micron" for the millionth of a metre ...*SAU

1927 William Henry Dines (5 Aug 1855, 24 Dec 1927) was an English meteorologist (like his father) and inventor of related measurement instruments such as the Dines pressure tube anemometer (the first instrument to measure both the velocity and direction of wind, 1901), a very lightweight meteorograph, and a radiometer (1920). He joined the Royal Meteorological Society study of the cause of the disastrous Tay Bridge collapse of 1879. His measurements of upper air conditions, first with kites and later by balloon ascents (1907), brought an understanding of cyclones from dynamic processes in the lower stratosphere rather than thermal effects nearer to the ground.*TIS

1962 Wilhelm Friedrich Ackermann (29 March 1896 – 24 December 1962) was a German mathematician best known for the Ackermann function, an important example in the theory of computation.*Wik

1994 Alfred Leon Foster (13 July 1904 in New York City, New York, USA - 24 Dec 1994 in Berkeley, California, USA) Foster went on to define the concept of a primal algebra generalising a Boolean algebra within the theory of varieties of universal algebras. In 1953 showed that the variety generated by a primal algebra has the same essential structure as the variety of Boolean algebras. He continued devoting his efforts to the structure theory of algebras that are generalizations of Boolean algebras and, more than ten years down the line in 1966, he published Families of algebras with unique (sub-)direct factorization. Equational characterization of factorization in Mathematische Annalen.*SAU

2000 Laurence Chisholm Young (14 July 1905 – 24 December 2000) was a mathematician known for his contributions to measure theory, the calculus of variations, optimal control theory, and potential theory. He is the son of William Henry Young and Grace Chisholm Young, both prominent mathematicians.
The concept of Young measure is named after him. *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