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| Cover to Towers of Hanoi, *Wik |
If the Lord Almighty had consulted me before embarking upon his creation, I should have recommended something simpler.
Remarking on the complexity of Ptolemaic model of the universe after it was explained to him.
~Alfonso X of Castile
The 94th day of the year; 94!-1 is prime. The number 94!-1 ends in 21 consecutive nines. Students might inquire how they could have known this without being told.
93, 94, and 95 form the third string of three consecutive semiprimes (two distinct factors). In all the numbers up to 10^9, the longest string of semiprimes is 94.
Add the prime factors of 94 and the result is 49, 94 reversed. This is the only year day with this property, but there are two other smaller year days that when expressed as a product of two factors (not necessarily prime) the sum of the factors is the reverse of the product
The sum of digits of the distinct prime factors of 94 add up to 13, which is also the sum of the digit of 94. 94 = 2 x 47 and 2 + 4 + 7 = 13. Such numbers are called Hoax numbers. 94 is also a Smith number, which is the sum of the digits of all prime factors, including multiplicity, (see day 364 for more) There are 20 year days which are hoax numbers, and half of them have a digit sum of 13.
94 is the smallest even number greater than four which cannot be written as a sum of two twin primes (The inclusion of 6 suggests they need not be distinct) .
Most mathematicians know the story of 1729, the taxicab number which Ramanujan recognized as a cube that was one more than the sum of two cubes, or the smallest number that could be expressed as the sum of two cubes in two different ways. But not many know that 94 is part of the second such \(64^3 + 94^3 = 103^3 + 1^3 \)
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1597 Galileo writes to Kepler, "....Like you, I accepted the Copernican position several years ago and discovered from thence the causes of many natural effects which are doubtless inexplicable by the current theories. I have written up many of my reasons and refutations on the subject, but I have not dared until now to bring them into the open, being warned by the fortunes of Copernicus himself, our master, who procured immortal fame among a few but stepped down among the great crowd (for the foolish are numerous), only to be derided and dishonored. I would dare publish my thoughts if there were many like you; but, since there are not, I shall forebear.... " *Giorgio de Santillana, The Crime of Galileo (1955).
1615 In response to Galileo's assertion that Copernican cosmology was so scientifically confirmed that the Scriptures must be conformed to it, Cardinal Robert Bellarmine writes that, "I do not think there is any such proof, since none has been shown to me." He then cautions Galileo that without such evidence, teaching Copernicanism would be, "a very dangerous attitude, ...to injure our holy faith by contradicting the scriptures." *Timothy Ferris, Coming of Age in the Milky Way (Thony Christie has informed me that Bellermine's comments were in a letter to Paolo Antonio Foscarini, and not directly to Galileo.)
1687 Edmond Halley received Book Three of Newton's Masterpiece, the Principia. He would spend months pushing the publication to print, with a run of 250+ copies completed on July 5th of that year. The first edition sold out almost immediately. He writes to John Wallis that Newton "now falls in with Mr. Hooke." Newton had added Proposition XIX that the earth's diameter was greater at the equator than between the poles. Newton had previously argue for a spherical earth, and now agreed it was more oblate. *Stephen Inwood, Forgotten Genius The "now falls in with Mr. Hooke" is about the fact that Hooke had been writing about the Earth's geology and the shape as an oblate spheroid, among his many far sighted ideas, beginning in 1664. *Robert Hooke: Tercentennial Studies
1692 Acta eruditorum contained, under a pseudonym, Vincenzo Viviani’s problem of constructing in a hemispherical cupola four equal-sized windows such that the remaining area of the cupola is quadrable. The problem was solved by Leibniz (date?), Guido Grandi (1699), and Viviani himself (1692). *VFR
1803 C. F. Gauss in his letter on this day to Niklaus Fuss, the permanent secretary of the St. Petersburg Academy of Sciences, says that he cannot accept the employment offered there. At the same time he sends his observations of the asteroid Pallas as a token of his gratitude, and promises farther detail on the corrections of the elements of Ceres as he gets usable data. *Historia Matematica
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EVENTS
1615 In response to Galileo's assertion that Copernican cosmology was so scientifically confirmed that the Scriptures must be conformed to it, Cardinal Robert Bellarmine writes that, "I do not think there is any such proof, since none has been shown to me." He then cautions Galileo that without such evidence, teaching Copernicanism would be, "a very dangerous attitude, ...to injure our holy faith by contradicting the scriptures." *Timothy Ferris, Coming of Age in the Milky Way (Thony Christie has informed me that Bellermine's comments were in a letter to Paolo Antonio Foscarini, and not directly to Galileo.)
1687 Edmond Halley received Book Three of Newton's Masterpiece, the Principia. He would spend months pushing the publication to print, with a run of 250+ copies completed on July 5th of that year. The first edition sold out almost immediately. He writes to John Wallis that Newton "now falls in with Mr. Hooke." Newton had added Proposition XIX that the earth's diameter was greater at the equator than between the poles. Newton had previously argue for a spherical earth, and now agreed it was more oblate. *Stephen Inwood, Forgotten Genius The "now falls in with Mr. Hooke" is about the fact that Hooke had been writing about the Earth's geology and the shape as an oblate spheroid, among his many far sighted ideas, beginning in 1664. *Robert Hooke: Tercentennial Studies
1692 Acta eruditorum contained, under a pseudonym, Vincenzo Viviani’s problem of constructing in a hemispherical cupola four equal-sized windows such that the remaining area of the cupola is quadrable. The problem was solved by Leibniz (date?), Guido Grandi (1699), and Viviani himself (1692). *VFR
1803 C. F. Gauss in his letter on this day to Niklaus Fuss, the permanent secretary of the St. Petersburg Academy of Sciences, says that he cannot accept the employment offered there. At the same time he sends his observations of the asteroid Pallas as a token of his gratitude, and promises farther detail on the corrections of the elements of Ceres as he gets usable data. *Historia Matematica
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1820 On this day in 1820 Farkas Bolyai wrote to his son János about Euclid's 5th postulate:-
"Do not try the parallels in that way: I know that way all along. I have measured that bottomless night, and all the light and all the joy of my life went out there." *MacTutor
1870 Benjamin Peirce wrote in the introduction of his “Linear Associative Algebra,” doubtless his most original mathematical work: “This work has been the pleasantest mathematical effort of my life. In no other have I seemed to myself to have received so full a reward for my mental labor in the novelty and breadth of the results.” [MAA 32(1925); p. 15 of Benjamin Peirce, MAA offprint of 1925] *VFR
In 1930, the American Interplanetary Society was founded by G. Edward Pendray, David Lasser, Laurence Manning and others. Its was known as the American Rocket Society from 6 Apr 1934. Through the 1930s, the group designed an experimental test stand and tested liquid-fueled rockets. Their pioneering work led the way to the United States space program. Their ARS-4 rocket, was the first launched in America to break the sound barrier (9 Sep 1934). It was fired from from Marine Park, Staten Island, N.Y., reached a top speed of 700 mph, traveled to a maximum height of 400-ft and a horizontal range of 1,600-ft. In early 1963, it merged with the American Institute of Aeronautics and Astronautics *TIS The motor used gasoline and liquid oxygen.
Image : James Wyld with one of his rocket motors at an American Rocket Society test in Midvale, New Jersey, 1941. He helped design the Reaction Motors XLR-11 engine, which powered Chuck Yeager’s Bell X-1 airplane through the “sound barrier” in 1947. *Natl. Air and Space Museum
1994 Marc Andreesen Founds Netscape with Jim Clark:
Marc Andreessen and Jim Clark found Mosaic Communications Corp, later renamed Netscape Communications Corp. Andreessen developed the software used for browsing the World Wide Web while working at the National Center for Supercomputing Applications (NCSA) at the University of Illinois. Clark co-founded high-performance computer maker Silicon Graphics Inc.*CHM
BIRTHS
1809 Benjamin Peirce (4 Apr 1809, 6 Oct 1880) American astronomer, mathematician and educator who computed the general perturbations of the planets Uranus and Neptune. He was Harvard's Perkins Professor of Astronomy and Mathematics for nearly 40 years, and was largely responsible for introducing mathematics as a subject for research in American institutions. He is known especially for his contributions to analytic mechanics and linear associative algebra, but he is also remembered for his early work in astronomy and for playing a role in the discovery of Neptune. *TIS In number theory, he proved there is no odd perfect number with fewer than four prime factors. In algebra, he was notable for the study of associative algebras. He first introduced the terms idempotent and nilpotent in 1870 to describe elements of these algebras, and he also introduced the Peirce decomposition. *Wik He taught at Harvard for 49 years. Early on, he and the other young mathematics tutor, Charles W. Eliot, secured the innovation of written final examinations. Previously all exams were oral. Eliot later became president of Harvard. *VFR
1842 François Edouard Anatole Lucas (4 April 1842, 3 Oct 1891) Lucas is best known (to formal mathematicaticians) for his results in number theory, in particular he studied the Fibonacci sequence and the associated Lucas sequence is named after him. He gave the well-known formula for the Fibonacci numbers
Lucas also devised methods of testing primality, essentially those used today. In 1876 he used his methods to prove that the Mersenne number 2127 - 1 is prime. This remains the largest prime number discovered without the aid of a computer. (For recreational mathematicians), Lucas is also well known for his invention of the Tower of Hanoi puzzle and other mathematical recreations. The Tower of Hanoi puzzle appeared in 1883 under the name of M. Claus. Notice that Claus is an anagram of Lucas! His four volume work on recreational mathematics Récréations mathématiques (1882-94) has become a classic.*SAU Lucas is also remembered for his unusual death, caused by a waiter dropping a plate which shattered sending a piece of plate into his neck. Lucas died several days later from a deadly inflamation of the skin and subcutaneous tissue caused by streptococcus. The disease, officially listed as erysipelas (from the Greek for "red skin") was more commonly known as "Saint Anthony's Fire". *Pballew.net√5 fn = ((1 + √5)/2)n - ((1 - √5)/2)n.
1868 Philippa Garrett Fawcett (4 April 1868 - 10 June 1948) the first woman at Cambridge to come top in the Mathematical Tripos Examinations. A description of the event is recorded in the North Hall Diary of Newnham College:-
This blog from the Smithsonian has some nice detail about her.
The great event of the year was Philippa Garrett Fawcet's achievement in the Mathematical Tripos. For the first time a woman has been placed above the Senior Wrangler. The excitement in the Senate House when the lists were read was unparalleled. The deafening cheers of the throng of undergraduates redoubled as Miss Fawcett left the Senate House by the side of the Principal. On her arrival at the College she was enthusiastically greeted by a crowd of fellow-students, and carried in triumph into Clough Hall. Flowers, letters, and telegrams poured in upon her throughout the day. The College was profusely decorated with flags. In the evening the whole College dined in Clough Hall. After dinner toasts were proposed: the healths drunk were those of the Principal, Miss Fawcett, her Coach (Mr Hobson) and Senior and Junior Optimes. At 9.30 p.m. the College gardens were illuminated, and a bonfire was lighted on the hockey-ground, round which Miss Fawcett was three times carried amid shouts of triumph and strains of "For she's a jolly good fellow."
Photo: Ms Fawcett is front right in this photo of Newham College hockey team.
1884 Thomas Murray MacRobert FRSE (4 April 1884, Dreghorn, Ayrshire – 1 November 1962, Glasgow) was a Scottish mathematician. He became professor of mathematics at the University of Glasgow and introduced the MacRobert E function, a generalization of the generalized hypergeometric series.*Wik
1902 Eberhard Frederich Ferdinand Hopf (April 4, 1902, Salzburg, Austria-Hungary – July 24, 1983, Bloomington, Indiana) was a mathematician and astronomer, one of the founding fathers of ergodic theory and a pioneer of bifurcation theory who also made significant contributions to the subjects of partial differential equations and integral equations, fluid dynamics, and differential geometry. The Hopf maximum principle is an early result of his (1927) which is one of the most important techniques in the theory of elliptic partial differential equations.*Wik
1949 Shing-Tung Yau (4 Apr 1949, )Chinese-born mathematician who was awarded the Fields Medal in 1982 for his work in partial differential equations and differential geometry. His work also has applications in topology, algebraic geometry, representation theory and general relativity. Working collaboratively with Richard M. Schoen, Yau solved a long-standing open problem in relativity theory, by showing the positivity of mass for space-time. As a consequence, Schoen and Yau were able to give the first rigorous demonstration of how black holes can be formed because of the condensation of matter. A black hole possesses a gravitational field so intense that no matter or radiation can escape from it. Yau was the 1997 National Medal of Science winner. *TIS
DEATHS
1617 John Napier of Merchiston (1550 – 4 April 1617) – also signed as Neper, Nepair – named Marvellous Merchiston, was a Scottish mathematician, physicist, astronomer & astrologer, and also the 8th Laird of Merchistoun. He was the son of Sir Archibald Napier of Merchiston. John Napier is most renowned as the discoverer of the logarithm. Napier is the inventor of the so-called "Napier's bones". Napier also made common the use of the decimal point in arithmetic and mathematics. Napier's birthplace, the Merchiston Tower in Edinburgh, Scotland, is now part of the facilities of Edinburgh Napier University. After his death from the effects of gout, Napier's remains were buried in St Cuthbert's Church, Edinburgh.
His work, Mirifici Logarithmorum Canonis Descriptio (1614) contained fifty-seven pages of explanatory matter and ninety pages of tables of numbers related to natural logarithms. The book also has an excellent discussion of theorems in spherical trigonometry, usually known as Napier's Rules of Circular Parts. Modern English translations of both Napier's books on logarithms, and their description can be found on the web, as well as a discussion of Napier's Bones (see below) and Promptuary (another early calculating device). His invention of logarithms was quickly taken up at Gresham College, and prominent English mathematician Henry Briggs visited Napier in 1615. Among the matters they discussed was a re-scaling of Napier's logarithms, in which the presence of the mathematical constant e (more accurately, the integer part of e times a large power of 10) was a practical difficulty. Napier delegated to Briggs the computation of a revised table. The computational advance available via logarithms, the converse of powered numbers or exponential notation, was such that it made calculations by hand much quicker. The way was opened to later scientific advances, in astronomy, dynamics, physics; and also in astrology.
Napier made further contributions. He improved Simon Stevin's decimal notation.
In addition to his mathematical and religious interests, Napier was often perceived as a magician, and is thought to have dabbled in alchemy and necromancy. It was said that he would travel about with a black spider in a small box, and that his black rooster was his familiar spirit.
Napier used his rooster to determine which of his servants had been stealing from his home. He would shut the suspects one at a time in a room with the bird, telling them to stroke it. The rooster would then tell Napier which of them was guilty. Actually, what would happen is that he would secretly coat the rooster with soot. Servants who were innocent would have no qualms about stroking it but the guilty one would only pretend he had, and when Napier examined their hands, the one with the clean hands was guilty.
Another occasion which may have contributed to his reputation as a sorcerer involved a neighbor whose pigeons were found to be eating Napier's grain. Napier warned him that he intended to keep any pigeons found on his property. The next day, it is said, Napier was witnessed surrounded by unusually passive pigeons which he was scooping up and putting in a sack. The previous night he had soaked some peas in brandy, and then sown them. Come morning, the pigeons had gobbled them up, rendering themselves incapable of flight.
*Wik
1807 Joseph Jérôme Le Français de Lalande, (11 Jul 1732, 4 Apr 1807 at age 74)
He determined the Moon's parallax from Berlin for the French Academy (1751). He was appointed professor of Astronomy, Collège de France (1762), and subsequently, director of the Paris Observatory. He published his Traité d'astronomie in 1764 - tables of the planetary positions that were considered the best available for the rest of the century. In 1801 he also published a comprehensive star catalogue. He died in 1807, apparently of tuberculosis. *TIS
1919 Sir William Crookes, OM, FRS (17 June 1832 – 4 April 1919) was a British chemist and physicist who attended the Royal College of Chemistry, London, and worked on spectroscopy. He was a pioneer of vacuum tubes, inventing the Crookes tube. *Wik @LunarHeritage pointed out that Crookes also spectroscopically 1st discovered the element Thallium (1861) Tl atomic number 81 has two stable isotopes, one of which Tl-203, produces one of the workhorses of nuclear medicine.
Carl Ludwig Siegel (December 31, 1896 – April 4, 1981) was a mathematician specializing in number theory and celestial mechanics. He was one of the most important mathematicians of the 20th century.
Among his teachers were Max Planck and Ferdinand Georg Frobenius, whose influence made the young Siegel abandon astronomy and turn towards number theory instead. His best student was Jürgen Moser, one of the founders of KAM theory (Kolmogorov-Arnold-Moser), which lies at the foundations of chaos theory.
Siegel's work on number theory, diophantine equations, and celestial mechanics in particular won him numerous honours. In 1978, he was awarded the Wolf Prize in Mathematics, one of the most prestigious in the field.
Siegel's work spans analytic number theory; and his theorem on the finiteness of the integer points of curves, for genus greater than 1, is historically important as a major general result on diophantine equations, when the field was essentially undeveloped. He worked on L-functions, discovering the (presumed illusory) Siegel zero phenomenon. His work derived from the Hardy-Littlewood circle method on quadratic forms proved very influential on the later, adele group theories encompassing the use of theta-functions. The Siegel modular forms are recognised as part of the moduli theory of abelian varieties. In all this work the structural implications of analytic methods show through.
André Weil, without hesitation, named Siegel as the greatest mathematician of the first half of the 20th century. In the early 1970s Weil gave a series of seminars on the history of number theory prior to the 20th century and he remarked that Siegel once told him that when the first person discovered the simplest case of Faulhaber's formula then, in Siegel's words, "Es gefiel dem lieben Gott." (It pleased the dear Lord.) Siegel was a profound student of the history of mathematics and put his studies to good use in such works as the Riemann-Siegel formula.*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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