## Thursday 29 August 2024

### On This Day in Math - August 29

 Jeannie at VLA

In most sciences one generation tears down what another has built,
and what one has established, another undoes.
In mathematics alone each generation adds a new story to the old structure.
~Hermann Hankel

The 241st day of the year; 241 is the larger of a pair of twin primes. The larger of a pair of twin primes is always one more than a multiple of six; the smaller is always one less than a multiple of six.

2+4+1 is prime. 241 is the 53rd prime. (53 is also prime) *Derek Orr

241 is also The smallest prime p such that p plus the reversal of p equals a palindromic prime.  241 + 142 = 383; which is a prime palindrome.

And it is the largest known prime p such that the reversal of (p! + p) is prime.  (241! + 241 ends with a string of fifty-five zeros, and then 241 :
980360372638941007038951797078339359751464353463061342202811
188548638347461066010066193275864531994024640834549254693776
854464608509281547718518965382728677985343589672835884994580
815417004715718468026937051493675623385569404900262441027874
255428340399091926993707625233667755768320823071062785275404
107485450075779940944580451919726756974354635829128751944137
27644867102380111026020691554782580923999494640500736
000000000000000000000000000000000000000000000000000000

P. Honaker at Prime Curios points out that the sequence of primes formed by n!+239 begins, 241, 263, 359... Maybe I mis-searched but I did not find this sequence in OEIS. Seems like a good computer programming project for students, pick a prime and find primes of the form n! + p
John Cook posted that "if k is relatively prime to b, there is a multiple of k whose base b representation contains all ones. If I understand that then since 241 is prime, it is relatively prime to ten. Can you find the base ten multiple of k that has all ones for its digits? Be the first to share the answer with me and get immortality by being listed here. I think it must be a very large multiple of 241.

241 = 15^2 + 4^2 which means 241 is a Pythagorean Prime.

241 is a palindrome in duodecimal, base 12 (181) and a repdigit in base 15(111)

EVENTS

1609 Galileo writes to his brother in Florence to tell him about his telescope presentation to the Doge on the 24th of August.

1654 Fermat to Pascal Saturday, August 29, 1654

Monsieur,
Our interchange of blows still continues, and I am well pleased that our thoughts are in such complete adjustment as it seems since they have taken the same direction and followed the same road. Your recent Trait´e du triangle arithmetique and its applications are an authentic proof and if my computations do me no wrong, your eleventh consequence went by post from Paris to Toulouse while my theorem, on figurate numbers, which is virtually the same, was going from Toulouse to Paris. I have not been on watch for failure while I have been at work on the problem and I am persuaded that the true way to escape failure is by concurring with you. But if I should say more, it would he of the nature of a Compliment and we have banished that enemy of sweet and easy conversation. It is now my turn to give you some of my numerical discoveries, but the end of the parliament augments my duties and I hope that out of your goodness you will allow me due and almost necessary respite.

In the same letter he states that, "Meditate however, if you find it convenient, on this theorem: The squared powers of 2 augmented by unity [I.e. 22n+1] are always prime numbers. [That is,] The square of 2 augmented by unity makes 5 which is a prime number;The square of the square makes 16 which, when unity is added makes 17, a prime number; The square of 16 makes 256 which, when unity is added, makes 257, a prime number; The square of 256 makes 65536 which, when unity is added, makes 65537, a prime number; and so to infinity. This is a property whose truth I will answer to you. The proof of it is very difficult (impossible, since the statement, as Euler would show later, is not true) and I assure you that I have not yet been able to find it fully." * York University Maths Dept

1692 For his services to the field of astronomy, Johann Philipp von Wurzelbauer was ennobled in 1692 by Leopold I, Holy Roman Emperor and added the von to his name. *Wik

1740 In a letter to Euler dated August 29th, 1740, Philippe Naudé (the Younger) asked Euler in how many ways a number n can be written as a sum of positive integers. In his answer written on September 12th (23rd), Euler explained that if we denote
this “partition number” by p(n), then

*Correspondence of Leonhard Euler with Christian Goldbach, Springer

1831 Michael Faraday discovered electrical induction. *VFR In 1831, Michael Faraday wound a thick iron ring on one side with insulated wire that was connected to a battery. He then wound the opposite side with wire connected to a galvanometer. He found that upon closing the battery circuit, there was a deflection of the galvanometer in the second circuit. Then he was astonished to see the galvanometer needle jump in the opposite direction when the battery circuit was opened. He had discovered that a current was induced in the secondary when a current in the primary was connected and an induced current in the opposite direction when the primary current was disconnected.*TIS

1859 Amateur English astronomers Richard Carrington and Richard Hodgson, independently observed a "white light flare" emanating from the surface of the sun. Less than a day later, Earth's magnetic field was knocked awry. Across America and Europe, telegraph wires sparked and failed.
Fewer than 18 hours elapsed between the flare and the geomagnetic storm on Earth. That meant whatever had exploded off the sun must have traveled at more than 5 million miles per hour. *NY Times

1899 Dedekind sends a letter to Georg Cantor that includes a proof of the Schroder-Bernstein Theorem (Let A and B be sets. If there is a 1-1 correspondence from A to B and a 1-1 corespondence from B to A, then the sets have the same cardinality.) *Cantorian Set Theory and Limitation of Size By Michael Hallett

The traditional name "Schröder–Bernstein" is based on two proofs published independently in 1898. Cantor is often added because he first stated the theorem in 1887, while Schröder's name is often omitted because his proof turned out to be flawed while the name of Richard Dedekind, who first proved it, is not connected with the theorem. According to Bernstein, Cantor had suggested the name equivalence theorem

On July 11, 1887,  Dedekind proves the theorem (not relying on the axiom of choice) but neither publishes his proof nor tells Cantor about it. Ernst Zermelo discovered Dedekind's proof and in 1908 he published his own proof based on the chain theory from Dedekind's paper

In 1896 Schröder announces a proof (as a corollary of a theorem by Jevons), and in 1897 Bernstein, a 19-year-old student in Cantor's Seminar, presents his proof.

In 1897 After a visit by Bernstein, Dedekind independently proves the theorem a second time. Then finally in 1899 he sends his proof to Cantor.

 Richard Dedekind

In 1940, Sir Henry Tizard led a mission of leading British and Canadia (without proof)n scientists to the USA to brief official American representatives on devices under active development for war use and to enlist the support of American scientists. Thus began a close cooperation of Anglo-American scientists in such fields as aeronautics and rocketry. His influence probably made the difference between defeat or victory at the Battle of Britain in 1940. *TIS

Tizard was an English chemist, inventor and Rector of Imperial College, who developed the modern "octane rating" used to classify petrol, helped develop radar in World War II, and led the first serious studies of UFOs. *Wik

1949 the USSR tested their first atomic device, "First Lightning." It was an an implosive type plutonium bomb, detonated at the Semipalatinsk test range, giving up to a 20 kiloton yield. In the U.S. it was called Joe No. 1 ("Joe" was nickname for Y. Stalin.) This event came five years earlier than anyone in the West had predicted, largely due to one man, the spy Klaus Fuchs. As a Los Alamos physicist, Fuchs had passed detailed blue prints of the original American Trinity bomb design to the Russians. With the emergence of the USSR as a nuclear rival, America's monopoly of atomic weaponry was ended giving the U.S. strong motivation for intensifying its program of nuclear testing. Thus the Cold War was launched.*TIS

After his conviction in 1950, he served nine years in prison in the United Kingdom, then migrated to East Germany where he resumed his career as a physicist and scientific leader.

1970 Oscar Morgenstern writes in his diary that Gödel would NOT publish his ontological proof for the existence of God. The first version of the ontological proof in Gödel's papers is dated "around 1941". Gödel is not known to have told anyone about his work on the proof until 1970, when he thought he was dying. In February, he allowed Dana Scott to copy out a version of the proof, which circulated privately. In August 1970, Gödel told Oskar Morgenstern that he was "satisfied" with the proof, but Morgenstern recorded in his diary entry for 29 August 1970, that Gödel would not publish because he was afraid that others might think "that he actually believes in God, whereas he is only engaged in a logical investigation (that is, in showing that such a proof with classical assumptions (completeness, etc.) correspondingly axiomatized, is possible) *Wik

 Kurt Gödel

1990 The British Computer Misuse Act goes into effect One of the earliest laws anywhere designed to address computer fraud, the Act resulted from a long debate in the 1980s over failed prosecutions of hackers -- in one well-publicized case, two men hacked into a British Telecom computer leaving messages in the Duke of Edinburgh's private mailbox. *CHM

BIRTHS

1756 Jan Śniadecki (August 29, 1756– November 9, 1830) was a Polish mathematician, philosopher and astronomer at the turn of the 18th and 19th centuries.
Born in Żnin, Śniadecki studied at Kraków University and in Paris. He was rector of the Imperial University of Vilnius, a member of the Commission of National Education, and director of astronomical observatories at Kraków and Vilnius. He died at Jašiūnai Manor near Vilnius.
Śniadecki published many works, including his observations on recently discovered planetoids. His O rachunku losów (On the Calculation of Chance, 1817) was a pioneering work in probability. *Wik He is considered as the best Polish mathematician born in the 18th century.

1876 Charles F. Kettering (29 Aug 1876; 25 Nov 1958) was an American engineer whose 140 patents included the electric starter, car lighting and ignition systems. In his early career, with the National Cash Register Co., Dayton (1904-09), he created the first electric cash register with an electric motor that opened the drawer. When he co-founded the Dayton Engineering Laboratories Company (DELCO, with Edward A. Deeds) he invented the key-operated self-starting motor for the Cadillac (1912) and it spread to nearly all new cars by the 1920's. As vice president and director of research for General Motors Corp. (1920-47) he developed engines, quick-drying lacquer finishes, anti-knock fuels, and variable-speed transmissions.*TIS

1881 Ferdinand Springer born, The founder of an important publishing house,. Today Springer-Verlag is one of the most important publishers of advanced work on mathematics. *VFR

1904 Leonard Roth (29 August 1904 Edmonton, London, England – 28 November 1968 Pittsburgh, Pennsylvania) British Mathematician who worked primarily in Algebraic Geometry. *SAU

DEATHS

1873 Hermann Hankel (14 February 1839 - 29 August 1873) He studied and worked with, among others, Möbius, Riemann, Weierstrass and Kronecker. His 1867 exposition on complex numbers and quaternions is particularly memorable. For example, Fischbein notes that he solved the problem of products of negative numbers by proving the following theorem: "The only multiplication in R which may be considered as an extension of the usual multiplication in R+ by respecting the law of distributivity to the left and the right is that which conforms to the rule of signs." *Wik

1930 James Bolam (1839 in Newcastle, England - 29 Aug 1930 in St Helen's, Drumchapel, Dumbartonshire, Scotland) was educated at Newcastle. He became head of the Government Navigation School (later the Leith Nautical College). He was a founder member of the EMS and became an honorary member in 1923. *SAU

1937 Otto Ludwig Hoelder (December 22, 1859 – August 29, 1937) worked on the convergence of Fourier series and in 1884 he discovered the inequality now named after him. He became interested in group theory through Kronecker and Klein and proved the uniqueness of the factor groups in a composition series. *SAU

1967 Charles Brace Darrow (10 Aug 1889, 29 Aug 1967) was an American inventor who designed the board game Monopoly. He had invented the game on 7 Mar 1933, though it was preceded by other real-estate board games. On 31 Dec 1935, a patent was issued for the game of Monopoly assigned to Parker Brothers, Inc., by Charles Darrow of Pennsylvania (No. 2,026,082). The patent titled it a "Board Game Apparatus" and described it as "intended primarily to provide a game of barter, thus involving trading and bargaining" in which "much of the interest in the game lies in trading and in striking shrewd bargains." Illustrations included with the patent showed not only the playing board and pieces, cards, and the scrip money. *TIS

The history of Monopoly can be traced back to 1903, when American anti-monopolist Lizzie Magie created a game that she hoped would explain the single-tax theory of Henry George. It was intended as an educational tool, to illustrate the negative aspects of concentrating land in private monopolies. She took out a patent in 1904. Her game, The Landlord's Game, was self-published, beginning in 1906.

According to an advertisement placed in The Christian Science Monitor, Charles Todd of Philadelphia recalled the day in 1932 when his childhood friend Esther Jones and her husband, Charles Darrow, came to their house for dinner. After the meal, the Todds introduced Darrow to The Landlord's Game, which they then played several times. The game was entirely new to Darrow, and he asked the Todds for a written set of the rules. After that night, Darrow went on to utilize this, and distribute the game himself as Monopoly.

The Parker Brothers bought the game's copyrights from Darrow. When the company learned Darrow was not the sole inventor of the game, it bought the rights to Magie's patent for \$500.

Parker Brothers began marketing the game on November 5, 1935 *Wik

 The Landlord Game *Wik

1975 Éamon de Valera (14 October 1882, 29 August 1975) was one of the dominant political figures in twentieth century Ireland, serving as head of government of the Irish Free State and head of government and head of state of Ireland. He also introduced the Constitution of Ireland.
De Valera was a leader of Ireland's struggle for independence from Britain in the Irish War of Independence and of the anti-Treaty forces in the ensuing Irish Civil War (1922–23). In 1926, he founded Fianna Fáil and was head of government from 1932–48, 1951–54 and 1957–59 and President of Ireland from 1959–73.
In his youth he had trained as a mathematician and taught mathematics prior to the Easter Rising. Throughout his life he maintained an interest in mathematics and returned to it with a passion in his later life. *Wik

2003 Horace Welcome Babcock (September 13, 1912 – August 29, 2003) was an American astronomer. Babcock invented and built a number of astronomical instruments, and in 1953 was the first to propose the idea of adaptive optics. He specialized in spectroscopy and the study of magnetic fields of stars. He proposed the Babcock Model, a theory for the magnetism of sunspots.

During World War II, he was engaged in radiation work at MIT and Caltech. After the war he began a productive collaboration with his father, Harold D. Babcock. His undergraduate studies were at Caltech and his doctorate from University of California, Berkeley.

Babcock's doctoral thesis contained one of the earliest indications of dark matter. He reported measurements of the rotation curve for Andromeda which suggested that the mass-to-luminosity ratio increases radially. He, however, attributed it to either absorption of light within the galaxy or modified dynamics in the outer portions of the spiral and not to any form of missing matter.

He was director of the Palomar Observatory for Caltech from 1964 to 1978.

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