Simplicibus itaque verbis gaudet Mathematica Veritas, cum etiam per se simplex sit Veritatis oratio.
(So Mathematical Truth prefers simple words
since the language of Truth is itself simple.)
~ Tycho Brahe
The 114th day of the year; this day begins a string of thirteen consecutive day numbers that are composite. There is no string of more composite year day numbers. The next such string of composite day numbers will include Halloween.
The sum of the first 114 digits of e after the decimal point, is prime. This is the third consecutive day number with this property.
114 is another of D R Kaprekar's Harshad (Joy-Giver) numbers, divisible by the sum of its digits. Remembering that the famous Taxicab number of Ramanujan and Hardy, is also a Harshad number makes it easy to factor, since 1 + 7 + 2 + 9 = 19 is a factor.
114 is the sum of the first four hyperfactorials starting with zero, 0^0 + 1^1 + (2^2)(1^1) + (3^3)(2^2)(1^1) = 1+1+4+108 = 114.
The largest gap between two consecutive six digit primes is 114.
********Find more of these at Math Day of the Year Facts. *********************
EVENTS
1066 Halley's Comet heralded an invasion when it appeared over England. A monk spotted it and predicted the destruction of the country. The monk, Eilmer of Malmesbury (also known as Oliver due to a scribe's miscopying, or Elmer) was an 11th-century English Benedictine monk best known for his early attempt at a gliding flight using wings. He seems to have predicted the destruction of England when he saw the comet and wrote, "You've come, have you? – You've come, you source of tears to many mothers. It is long since I saw you; but as I see you now you are much more terrible, for I see you brandishing the downfall of my country." William of Malmesbury, who provides almost all the known information about Eilmer, writes that, in Eilmer's youth, he had read and believed the Greek fable of Daedalus. Thus, Eilmer fixed wings to his hands and feet and launched himself from the top of a tower at Malmesbury Abbey.*Wik (well, he got the invasion part right)
1610 Galileo comes to demonstrate his telescope but is poorly received.
from a Letter from Martin Horky to Kepler, April, 1610
Galileo Galilei, the mathematician of Padua, came to us in Bologna and he brought with him that spyglass through which he sees four fictitious planets. On the twenty-fourth and twenty-fifth of April I never slept, day and night, but tested that instrument of Galileo's in innumerable ways, in these lower as well as the higher [realms]. On Earth it works miracles; in the heavens it deceives, for other fixed stars appear double. Thus, the following evening I observed with Galileo's spyglass the little star that is seen above the middle one of the three in the tail of the Great Bear, and I saw four very small stars nearby, just as Galileo observed about Jupiter. I have as witnesses most excellent men and most noble doctors, Antonio Roffeni, the most learned mathematician of the University of Bologna, and many others, who with me in a house observed the heavens on the same night of 25 April, with Galileo himself present. But all acknowledged that the instrument deceived. And Galileo became silent, and on the twenty-sixth, a Monday, dejected, he took his leave from Mr. Magini very early in the morning. And he gave no thanks for the favors and the many thoughts, because, full of himself, he hawked a fable. Mr. Magini provided Galileo with distinguished company, both splendid and delightful. Thus the wretched Galileo left Bologna with his spyglass on the twenty-sixth.
Beneath the letter in German he has written, "Unknown to anyone, I have made an impression of the spyglass in wax, and when God aids me in returning home, I want to make a much better spyglass than Galileo's." *Timothy J. McGrew, Western Michigan Univ.
Len Fisher @LenFisherScienc sent a clip that pointed out that Galileo's fellow Pisano, was one of those who refused to look through the glass at all:
*from "Weighing the Soul"
1676 In a letter to the Royal Society, Leeuwenhock describes what happens after he put pepper water in his study for three weeks and then observed it through his scope, "I looked upon it the 24th of April, 1676 and discerned to my great wonder, an incredible number of very small animals of divers kinds." *Lisa Jardine, Incredible Pursuits, pg 92
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| HT to Greg Priest |
1800 The Library of Congress established . $5000 was appropriated for the purchase of such books as may be necessary for the use of Congress at the said city of Washington and for filling up a suitable apartment for containing them and for placing them therein." The first catalog, dated April 1802, listed 964 volumes and 9 maps. *VFR
In 1851, the first engineering society of importance in the U.S. was incorporated. The Boston Society of Civil Engineers was organized at an informal meeting on 26 Apr 1848, and its first regular meeting was held 3 Jul 1848. Its purpose was "promoting science and instruction in the department of civil engineering." In the following year, the national American Society of Civil Engineers and Architects was founded on 5 Nov 1852 in New York City. Earlier attempts in the U.S. to sustain an engineering society were unsuccessful, including those by the engineers of the Cincinnati & Charleston Railroad in 1836; engineers in Baltimore, Md. in 1839; and a society in Albany, N.Y. in 1841.
1897 The Chicago Section of the American Mathematical Society held its organizational meeting in Chicago under the chairmanship of E. H. Moore. It was the first section of the AMS. [Cajori, Historical Introduction to the Mathematical Literature, p. 34] *VFR
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| E H Moore |
In 1925, Darwin's theory of evolution was reputed to be taught in Dayton, Tennessee, by teacher John Scopes, who used the high school textbook, Civic Biology by George Hunter. For this, Scopes, 24, was prosecuted under the Butler Act, a state law enacted in the previous month, on 21 Mar 1925. It prohibited the teaching of evolution in public schools. The trial , which began 10 Jul 1925) was used as a platform to challenge the legality of the statute. Scopes was supported by the American Civil Liberties Union. At its end, on 21 Jul 1925, Scopes was convicted and fined $100. On appeal, the state supreme court upheld the constitutionality of the 1925 law but acquitted Scopes on the technicality that he had been fined excessively. The law was not repealed until 17 May 1967. *TIS
the Butler Act was passed in Tennessee, on March 25, 1925. Butler later stated, "I didn't know anything about evolution ... I'd read in the papers that boys and girls were coming home from school and telling their fathers and mothers that the Bible was all nonsense." Tennessee governor Austin Peay signed the law to gain support among rural legislators, but believed the law would neither be enforced nor interfere with education in Tennessee schools.William Jennings Bryan thanked Peay enthusiastically for the bill: "The Christian parents of the state owe you a debt of gratitude for saving their children from the poisonous influence of an unproven hypothesis." The Tennessee college in Clarksville is named for Governor Peay.
It would remain the law in Tennessee until repealed on September 1, 1967. *Wik
In 1928, the fathometer was patented by Herbert Grove Dorsey (No. 1,667,540). His invention was an electro-mechanical sounding instrument that measured underwater depths by using a series of electrical sounds signals and their echoes. He coined the name fathometer. The same instrument could measure both very shoal water and very deep water. His fathometers not only improved hydrographic surveying but also were valuable to the maritime shipping industry by saving time over line soundings. His instruments helped delineate much of the continental shelf and slope of the United States and its territories as well as much of the deep sea, in particular the northeast Pacific Ocean, the mid-Atlantic shelf and slope, and Gulf of Mexico.*TIS
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Dorsey and his fathometer
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| A model of 1862 Apollo viewed from the pole (top) and from the equator (bottom). The irregular shape of asteroids like 1862 Apollo means that photons adsorbed and re-emitted from the surface can produce a net torque that gradually makes the asteroids spin faster – what is known to astronomers as the "YORP" effect. Image credit: Mikko Kaasalainen and Josef Durech |
1932 Minor Planet Apollo Discovered on April 24 by K. Reinmuth at Heidelberg. This object is named for the god of the Sun. Patrick Poitevin @PatrickPoitevin
The prototype asteroid of the Apollo group. In 1932 it approached Earth to within 10.5 million km (0.07 AU), but was then lost until 1973. Apollo can come as close to Earth as 4.2 million km (0.028 AU) and also make near passes of Venus and Mars, whose orbits it crosses at perihelion and aphelion,respectively.*http://www.daviddarling.info
1949 Columbia issued a stamp honoring the mathematician Julio Garavito Armero (1865{1920). [Scott #573] *VFR [He is also on the 20,000 peso bank note] As an astronomer of the observatory, he did many useful scientific investigations such as calculating the latitude of Bogotá, studies about the comets which passed by the Earth between 1901 and 1910 (such as Comet Halley), and the 1916 solar eclipse (seen in the majority of Colombia). But perhaps the most important were his studies about celestial mechanics, which finally turned into studies about lunar fluctuations and their influence on weather, floods, polar ice, and the Earth's orbital acceleration (this was corroborated later). He worked also in other areas such as optics (this work was left unfinished at his death), and economics, by which he helped the country recover from the rough civil war. With this objective, he gave lectures and conferences in economics and the human factors which affected it, such as war or overpopulation. *Wik
1980 The winning number in the Pennsylvania lottery was 666. On this day a group of men bet some $20,000 on all combinations involving just 4 and 6. The state lost two million. In 1982 two men were convicted of a lottery fix. Ironically, on the day they went to prison, Delaware's daily number came up 555.
1981 first IBM personal computer was introduced.IBM's own Personal Computer (IBM 5150) was introduced in August 1981, only a year after corporate executives gave the go-ahead to Bill Lowe, the lab director in the company's Boca Raton, Fla., facilities. He set up a task force that developed the proposal for the first IBM PC. Early studies had concluded that there were not enough applications to justify acceptance on a broad basis and the task force was fighting the idea that things couldn't be done quickly in IBM. One analyst was quoted as saying that "IBM bringing out a personal computer would be like teaching an elephant to tap dance." During a meeting with top executives in New York, Lowe claimed his group could develop a small, new computer within a year. The response: "You're on. Come back in two weeks with a proposal." *IBM
1981 Apple Computer introduces its Apple IIc, a portable machine designed to have the same operating capacity as the standard IIe model. The machine came with 128 kilobytes of RAM and a 5 1/4 inch floppy disk drive. *CHM Perfect for its time! *PB
In 1990, space shuttle Discover was launched from Cape Canaveral, carrying the Hubble Space Telescope to be placed into orbit. *TIS The following day (4/25/90) the Hubble telescope would be deployed from Discoverer into orbit. It would be almost another month (5/20/90) before the first image ("first light") shows the 50% sharper images than Earth based images.
The image is of the 1/4 sized replica on the courthouse lawn in Hubble's birthplace, Marshfield Missouri.
BIRTHS
1562 Xu Guang-qi ( April 24, 1562 - November 8, 1633 ,aged 71) was a Chinese mathematician who made Western mathematics available by translating works into Chinese. *SAU
Xu Guangqi with Matteo Ricci (left) From Athanasius Kircher's China Illustrata, 1667
1620 John Graunt(24 April 1620 – 18 April 1674)His book Natural and Political Observations Made upon the Bills of Mortality (1662) used analysis of the mortality rolls in early modern London as Charles II and other officials attempted to create a system to warn of the onset and spread of bubonic plague in the city. Though the system was never truly created, Graunt's work in studying the rolls resulted in the first statistically-based estimation of the population of London. It was his only book but it was the foundations of both statistics and demography. *VFR [A nice essay on his "Bills of Mortality" and life is at the Rice University Stats Page by Thompson. Some personal history is at The Renaissance Mathematicus
1750 Simon Antoine Jean Lhuilier (24 April 1750 in Geneva, Switzerland - 28 March 1840 in Geneva, Switzerland) His work on Euler's polyhedra formula, and exceptions to that formula, were important in the development of topology. Lhuilier also corrected Euler's solution of the Königsberg bridge problem. He also wrote four important articles on probability during the years 1796 and 1797. His most famous pupil was Charles-François Sturm who studied under Lhuilier during the last few years of his career in Geneva. *SAU He won the mathematics section prize of the Berlin Academy of Sciences for 1784 in response to a question on the foundations of the calculus. The work was published in his 1787 book Exposition elementaire des principes des calculs superieurs. It was in this book that he first introduced the "lim." (the period would soon fall out use) notation for the limit of a function. he wrote, "lim.\( \frac{\delta x}{\delta x} \). The symbol reappeared in 1821 in Cours d'Analyse by Augustin Louis Cauchy. *Florian Cajori, The History of Notations on the Calculus.
1863 Giovanni Vailati (24 April 1863 – 14 May 1909) was an Italian proto-analytic philosopher, historian of science, and mathematician. Vailata's main historical interests concerned mechanics, logic, and geometry, and he was an important contributor to a number of areas, including the study of post-Aristotelian Greek mechanics, of Galileo's predecessors, of the notion and rôle of definition in the work of Plato and Euclid, of mathematical influences on logic and epistemology, and of the non-Euclidean geometry of Gerolamo Saccheri. He was particularly interested in the ways in which what might be seen as the same problems are addressed and dealt with at different times.
His historical work was interrelated with his philosophical work, involving the same fundamental views and methodology. Vailati saw the two as differing in approach rather than subject matter, and believed that there should be co-operation between philosophers and scientists in the pursuit of historical studies. He also held that a complete history demanded that one take into account the relevant social background. *Wik
1899 Oscar Zariski (24 April 1899 in Kobrin, Russian Empire (now Belarus) - 4 July 1986 in Brookline, Massachusetts, USA) Zariski's work was on foundations of algebraic geometry using algebraic methods. He worked on the theory of normal varieties, local uniformisation and the reduction of singularities of algebraic varieties. *SAU
1919 David H. Blackwell (April 24, 1919 – July 8, 2010) American Statistician, President of the Institute of Mathematical Statistics. Many more honours were to come his way. He was elected Vice President of the American Statistical Association, Vice President of the International Statistical Institute, and Vice President of the American Mathematical Society. In 1965 he was elected to the National Academy of Sciences. He received the John von Neumann Theory Prize from the Operations Research Society of America in 1979 for his work in dynamic programming and the R A Fisher Award from the Committee of Presidents of Statistical Societies in 1986.*SAU
and a nice links for more information, with thanks to Dave Bee:
For the extensive “An Oral History With David Blackwell”, conducted by Nadine Wilmot in 2002 and 2003.
1947 Ovide Arino (24 April 1947 - 29 September 2003) mathematician working on delay differential equations. His field of application was population dynamics. He was a quite prolific writer, publishing over 150 articles in his lifetime. He also was very active in terms of student supervision, having supervised about 60 theses in total in about 20 years. Also, he organized or coorganized many scientific events. But, most of all, he was an extremely kind human being, interested in finding the good in everyone he met. *euromedbiomath.com
DEATHS
1572 Petrus Ramus (1515, 24 Apr 1572 [Wik gives his death on 26 August]).
(Pierre de La Ramée) French mathematician and logician who challenged Aristotelian philosophy. As early as in his Master of Arts thesis (1536) he held that quaecumque ab Aristotle dicta essent, commentitia esse ("everything which Aristotle said is invented or contrived"). His book Aristotelicae animadversiones (1543) led to a decree from Francis I (Mar 1544) prohibiting such teachings. Though the decree was rescinded three years later by Henry II, Ramus continued to draw hostility from other scholars. He was an early adherent of the Copernican system. Ramus was murdered during the St. Bartholomew's Day massacre, but his theories remained influential after his death. *TIS
1656 Thomas Fincke (6 January 1561 – 24 April 1656) was a Danish mathematician and physicist, and a professor at the University of Copenhagen for more than 60 years. His lasting achievement is found in his book Geometria rotundi (1583), in which he introduced the modern names of the trigonometric functions tangent and secant.
His son in law was the Danish physician and natural historian, Ole Worm, who married Fincke's daughter Dorothea.*Wik
His most famous book Geometriae rotundi (1583), was intended as a textbook. Based on works of Ramus from whom he took the word 'radius', the book introduces the terms 'tangents' and 'secants' and Fincke devised new formulae such as the law of tangents.
Fincke's book was recommended by Clavius, Napier and Pitiscus all of whom adopted much from it. His other books on astronomy and astrology are of much less interest despite the fact that he was in touch with Brahe and Kepler. *SAU
1952 Hendrik Anthony Kramers (17 Dec 1894 - 24 Apr 1952 at age 57)Dutch physicist who, with Ralph de Laer Kronig, derived important equations relating the absorption to the dispersion of light. He also predicted (1924) the existence of the Raman effect, an inelastic scattering of light. Kramer's work covers almost the entire field of theoretical physics. He published papers dealing with mathematical formalism of quantum mechanics, and others on paramagnetism, magneto-optical rotation, ferro-magnetism, kinetic theory of gases, relativistic formalisms in particle theory, and on theory of radiation. His work shows outstanding mathematical skill and careful analysis of physical principles. *TIS
He worked with Niels Bohr to understand how electromagnetic waves interact with matter and made important contributions to quantum mechanics and statistical physics. *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
I was a little familiar with Prof. Hazard as I had leapfrogged off one of his old posts in the Mathematics Teacher on methods of solving a quadratic equation to write a little about the history of solving quadratics in twenty or so different ways, which I hope someday to reduce to blog posts, but not today. 
A natural question is, "So What?" But if we look at several of the points determined by the upper vertex, and select out only some "related" Pythagorean triples, we notice a pattern. In the image at right the points represent the set of triples 3-4-5; 5-12-13; 7-24-25; and 9-40-41. (Any teacher or student who is not aware, there is a simple trick to find an infinite number of these triangles with a longer side one less than the hypotenuse. Just take any odd number to be the short leg, square it, and then divide by two and round up to the next whole for the hypotenuse. For example, 11 is a good odd number, and its square is 121. If we divide 121 by 2 we get 60.5, which is between 60 and 61, and 11, 60, 61 is a Pythagorean triple.) 
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