Tuesday, 25 April 2017

On This Day in Math - April 25

Pure mathematics is the world's best game.
It is more absorbing than chess,
more of a gamble than poker,
and lasts longer than Monopoly.
It's free.
It can be played anywhere -
Archimedes did it in a bathtub.
~Richard J. Trudeau, Dots and Lines

The 115th day of the year; 115 is the 26th "Lucky" number. Lucky numbers are produced by a sieve method created by Stan Ulam around 1955. The term was introduced in 1955 in a paper by Gardiner, Lazarus, Metropolis and Ulam. They suggest also calling its defining sieve, "the sieve of Josephus Flavius" because of its similarity with the counting-out game in the Josephus problem. They are interesting explorations for both elementary and advanced students. Whether there are an infinite number of primes in the lucky numbers is still an open question.

115 (or 5! - 5) is the smallest composite number of the form p! - p, where p is prime.

\( \pi (115) = 30 \) occurs at the 115th decimal digit of pi. It is the smallest integer n, in which the number of primes less than n occurs at the nth decimal place of pi. Once more for the HS students, there are 30 prime numbers less than 115, and the 115th &116th decimal digits of pi are 3, 0, so the two digit value beginning at the 115th decimal place counts the number of primes less than 115. There is no smaller number for which this is true. You may want to find the next one.

1611 Galileo (1564 1642) visited Rome at the height of his fame in 1611 and was made the sixth member of the Accademia dei Lincei (Lynx Society) at a banquet on (14 Apr/25Apr). The word 'telescopium' was first applied to his instrument at this dinner. He showed sunspots to several people. The term “telescope” was introduced by Prince Federico Cesi at a banquet given in Galileo’s honor. It derives from the Greek “tele” meaning “far away” and “skop´eo” meaning “to look intently.” For a change, a term which derives from the Greek was actually coined by a Greek, namely Ioannes Demisiani. [Willy Ley, Watchers of the Skies, p. 112]*VFR Thony Christie at the Renaissance Mathematicus blog has an enjoyable review of the telescope and how it got its name.

1661 Two days after attending the Coronation of Charles II, John Evelyn attends another spectacular, "to the Society where were many diverse experiments in Mr. Boyle's Pneumatic Engine." *Lisa Jardine, Ingenious Pursuits, pg 54

1832 In a debate over the apportionment of the House, Senator Dickerson of New Jersey invoked the language of Berkeley’s Analyst when he railed against using Jefferson’s apportionment method wherein fractions are ignored: “These quasi-representitives, these infinitesimal, evanescent Rep­resentatives, these ideal Representatives, these ghosts of Representatives, after being counted in order to give the favored States their full proportion of a House of 250, are dismissed the service.” *VFR (for my students.) Bishop Berkeley wrote a paper called "The Analyst" in which he tried to refute Newton's use of fluxions (derivatives). The idea that we treat "h" as not zero to cancel in the difference quotient, then dismiss it in the final limit disturbed him (and lots of others).. He wrote, "And what are these fluxions? The velocities of evanescent increments? They are neither finite quantities, nor quantities infinitely small, nor yet nothing. May we not call them ghosts of departed quantities?"

1810 Exactly a week after he was elected a member of the Berlin Academy of Sciences, Wilhelm von Humboldt sends Gauss an offer of 1500 Thalers a year to serve as ordentliches Mitglied of the Academy with the assurance that, "...you are only requested to lend your name as a full professor to the new university, and, as much as your leisure and health allow, to teach a course from time to time." *Dunnington, Gray & Dohse; Carl Friedrich Gauss: Titan of Science

1828 Christopher Hansteen, Director of the Observatory in Christiana, set out from Berlin to confirm his belief that the earth had more than one magnetic axis. 

1834 William Whewell In a single letter to Faraday on 25 April, 1834;  invented the terms cathode, anode and ion. The letter is on display at the Wren Library at Trinity College, Cambridge, UK. He is known for creating scientific words. He founded mathematical crystallography and developed Mohr's classification of minerals. He created the words scientist and physicist by analogy with the word artist. They eventually replaced the older term natural philosopher. (actually the use of scientist was a very slow process often not well received. see more of the interesting story here) Other useful words were coined to help his friends: biometry for Lubbock; Eocine, Miocene and Pliocene for Lyell; and for Faraday, anode, cathode, diamagnetic, paramagnetic, and ion (whence the sundry other particle names ending -ion).

In 1953, Francis Crick and James Watson reached their conclusion about the double helix structure of the DNA molecule. They made their first announcement on Feb 28, and their paper, A Structure for Deoxyribose Nucleic Acid, was published in the 25 Apr 1953 issue of journal Nature. *TIS
Greg Ross at Futility Closet posted a note Crick created to respond to the deluge of requests the discovery created:
Deluged with mail after his discovery of the double helix, Francis Crick began sending a printed card in response to invitations:
crick demurral

1961 Noyce patent issued for the semiconductor. *VFR ---nicknamed "the Mayor of Silicon Valley", co-founded Fairchild Semiconductor in 1957 and Intel in 1968. He is also credited (along with Jack Kilby) with the invention of the integrated circuit or microchip. While Kilby's invention was six months earlier, neither man rejected the title of co-inventor. Noyce was also a mentor and father-figure to an entire generation of entrepreneurs, including Steve Jobs at Apple, Inc

1990 The Hubble Space Telescope is released from the payload bay of Discovery *David Dickinson ‏ @Astroguyz

2038 The next time that Easter will occur on April 25, the latest possible date. The last time Easter was on April 25 was in 1943.


1769 Sir Marc Isambard Brunel French-born English engineer and inventor who solved the historic problem of underwater tunneling. A prolific inventor, Brunel designed machines for sawing and bending timber, boot making, stocking knitting, and printing. As a civil engineer, his designs included the Île de Bourbon suspension bridge and the first floating landing piers at Liverpool. In 1818, however, Brunel patented the tunneling shield, a device that made possible tunneling safely through waterbearing strata. On 2 Mar 1825 operations began for building a tunnel under the Thames River between Rotherhithe and Wapping. The Thames Tunnel was eventually opened on 25 Mar 1843. It has a twin horseshoe cross-section with height of 23-ft (7m), width of 37-ft (11m), and total length 1,506-ft (406m) *Wik

1849 Christian Felix Klein (25 April 1849 – 22 June 1925) was a German mathematician, known for his work in group theory, complex analysis, non-Euclidean geometry, and on the connections between geometry and group theory. His 1872 Erlangen Program, classifying geometries by their underlying symmetry groups, was a hugely influential synthesis of much of the mathematics of the day.*Wik He recommended the teaching of calculus in the German secondary schools. *VFR
[In mathematics, the Klein bottle is a non-orientable surface, informally, a surface (a two-dimensional manifold) in which notions of left and right cannot be consistently defined. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a surface with boundary, a Klein bottle has no boundary. (For comparison, a sphere is an orientable surface with no boundary.) The Klein bottle was first described in 1882 by the German mathematician Felix Klein. It is sometimes claimed that it was originally named the Kleinsche Fläche "Klein surface" and that this was incorrectly interpreted as Kleinsche Flasche "Klein bottle," which ultimately led to the adoption of this term in the German language as well.*Wik

1874 Guglielmo Marconi Italian inventor, born in Bologna. He was a physicist, who invented the wireless telegraph in 1935 known today as radio. Nobel laureate (1909). In 1894, Marconi began experimenting on the "Hertzian Waves" (the radio waves Hertz first produced in his laboratory a few years earlier). Lacking support from the Italian Ministry of Posts and Telegraphs, Marconi turned to the British Post Office. Encouraging demonstrations in London and on Salisbury Plain followed. Marconi obtained the world's first patent for a system of wireless telegraphy, in 1897, and opened the world's first radio factory at Chelmsford, England in 1898. In 1900 he took out his famous patent No. 7777 for "tuned or syntonic telegraphy." *TIS

1898 Pavel Sergeevich Aleksandrov  Soviet mathematician who made important contributions to the field of topology, the study of related physical or abstract elements that remain unchanged under certain distortions. *TIS

1879 Edwin Bidwell Wilson born. As a student of Willard Gibbs at Yale he codified the physicist’s lectures on vector analysis into a textbook (1901) that profoundly influenced the use and nota­tion of the subject. In 1912 he published a comprehensive text on advanced calculus that was the first really modern book of its kind in the U.S. *VFR

1900 Wolfgang Pauli, Austrian-born American winner of the Nobel Prize for Physics in 1945 for his discovery in 1925 of the Pauli exclusion principle, which states that in an atom no two electrons can occupy the same quantum state simultaneously. This principle clearly relates the quantum theory to the observed properties of atoms. Pauli was known for having an acid tongue. He was once challenged by another arrogant physicist, Lev Davidovich Landau who had explained his ideas to Pauli, whom he knew was skeptical of his ideas. Landau asked, "Well now do you think my ideas are nonsense?". Pauli's reply was, "No, not at all.; Your ideas are so confused I can't tell if they are nonsense, or not."

1903 Andrey Nikolayevich Kolmogorov  Russian mathematician whose basic postulates for probability theory that have continued to be an integral part of analysis. This work had diverse applications such as his study of the motion of planets (1954), or the turbulent air flow from a jet engine (1941). In topology, he investigated cohomology groups. He made a major contribution to answering the probability part of Hilbert's Sixth Problem, and completely resolved (1957) Hilbert's Thirteenth Problem. Kolmogorov was active in a project to provide special education for gifted children, not only by writing textbooks and in teaching them, but in expanding their interests to be not necessarily in mathematics, but with literature, music, and healthy activity such as on hikes and expeditions. *TIS
The theory of probability as mathematical discipline can and should be developed from axioms in exactly the same way as Geometry and Algebra."
*Foundations of the Theory of Probability
A nice article about him as at the Nautilus (issue 004)

1918 Gerard Henri de Vaucouleurs (25 Apr 1918; 7 Oct 1995 at age 77) French-born U.S. astronomer whose pioneering studies of distant galaxies contributed to knowledge of the age and large-scale structure of the universe. He produced three Reference Catalogues of bright galaxies (1964, 1976, 1991). Each was a homogenization of data from widely different sources, so that the catalogues would not be merely finding lists or data collection lists, but astrophysically useful databases. Using data in the Reference Catalogues, he was able to develop new distance indicators and refine others. His unique philosophy on distance matters was "spreading the risks," that is, applying as many different and independent techniques as possible to check for scale and zero-point errors. *TIS


1472 Leon Battista Alberti (Feb. 14, 1404 Genoa April 25, 1472 also given as April 20) Artist and geometrist. As an artist, he "wrote the book," the first general treatise Della Pictura (1434) on the the laws of perspective, establishing the scienceof projective geometry. Alberti also worked on maps (again involving his skill at geometrical mappings) and he collaborated with Toscanelli who supplied Columbus with the maps for his first voyage. He also wrote the first book on cryptography which contains the first example of a frequency table.*TIS
"When I investigate and when I discover that the forces of the heavens and the planets are within ourselves, then truly I seem to be living among the gods. "

1744 Anders Celsius (27 November 1701 – 25 April 1744) Swedish astronomer, physicist and mathematician who is famous for the temperature scale he developed. Celsius was born in Uppsala where he succeeded his father as professor of astronomy in 1730. It was there also that he built Sweden's first observatory in 1741. He and his assistant Olof Hiortner discovered that aurora borealis influence compass needles. Celsius' fixed scale (often called centigrade scale) for measuring temperature defines zero degrees as the temperature at which water freezes, and 100 degrees as the temperature at which water boils. This scale, an inverted form of Celsius' original design, was adopted as the standard and is still used in almost all scientific work. *TIS
There is a Plaque to Anders Celsius in the church at Gamla Uppsala

1840 Siméon-Denis Poisson ( 21 June 1781 – 25 April 1840) French mathematician known for his work on definite integrals, advances in Fourier series, electromagnetic theory, and probability. The Poisson distribution (1837) describes the probability that a random event will occur in a time or space interval under the conditions that the probability of the event occurring is very small, but the number of trials is very large so that the event actually occurs a few times. His works included applications to electricity and magnetism, and astronomy. He is also known for the Poisson's integral, Poisson's equation in potential theory, Poisson brackets in differential equations, Poisson's ratio in elasticity, and Poisson's constant in electricity.

1999 Sir William Hunter McCrea (13 Dec 1904, 25 Apr 1999 at age 94)
was an Irish theoretical astrophysicist whose early work was in quantum physics, relativity and pure mathmatics, but he gradually turned to applying theoretical physics in astronomy. He ranged from considering the stellar atmospheres, planet formation, cosmology and indeed, the formation of stars and the universe. He was an early advocate that stars have a high hydrogen content. He studied gas dynamics, as in the formation of hydrogen in molecular form in dusty interstellar clouds, and developed a theory of the transition from increasing density to conditions sufficient for gravitational collapse and possible star formation. Although he at first was open-minded to the steady state theory of the universe proposed by Hermann Bondi, Thomas Gold and Fred Hoyle, McCrea's work and others accumulated evidence for the Big Bang theory.*TIS
"Our experience shows that not everything that is observable and measurable is predictable, no matter how complete our past observations may have been. "

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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