Tuesday, 18 August 2015

On This Day in Math - August 18

The total number of Dirichlet's publications is not large: jewels are not weighed on a grocery scale.
~Karl F. Gauss

The 230th day of the year; 230 is the first number such that it and the next number are both sphenic numbers, the product of three distinct primes (230 = 2*5*23 and 231 = 3*7*11). *Prime Curios (can there be three consecutive numbers that are the product of three (or n) distinct primes

Their are 230 possible crystal shapes that can tile space. This is the analogy of the better known 17 "wallpaper groups" which tile the plane. Interestingly, both were proved by the same man, Evgraf Fedorov, in 1891. He did the plane problem the hard way, he proved the case for space first, then worked backwards to the plane.


1709 Cotes writes to Newton in hopes of prompting the revision of the Principia which Newton had promised to deliver in "a fortnights time.". The revised papers (through Prop XXXIII) would be delivered by Cotes neighbor Whiston in September when he returned from London. *Correspondence of Sir Isaac Newton and Professor Cotes, pg 3

1783 The 1783 Great Meteor was an unusually bright Bolide observed on August 18, 1783, from the British Isles at a time when such phenomena were not well understood. The meteor was the subject of much discussion in the Philosophical Transactions of the Royal Society and was the subject of a detailed study by Charles Blagden. *Wik Christopher Goulding reproduced this Paul Sandby watercolor of the meteor as seen from the terrace of Windsor Castle on 18 August 1783. Goulding lists the observers as James Lind, the Italian physicist Dr Tiberio Cavallo (1749-1809), Dr. Lockman (the Canon of St George's, Windsor), Thomas Sandby (the brother of the artist), and two unknown women.*GeoCosmo History

1813 On August 18, 1913, at the famous Monte Carlo casino, black came up 26 times in a row. Supposedly the house made a fortune against people betting that the long overdue red HAD to show up. *PB Personal notes

In 1868, Pierre Janssan discovered helium in the solar spectrum during eclipse, but did not recognize it as a new element. The first evidence of helium was observed on August 18, 1868 as a bright yellow line with a wavelength of 587.49 nanometers in the spectrum of the chromosphere of the Sun. The line was detected by French astronomer Janssen during a total solar eclipse in Guntur, India. This line was initially assumed to be sodium. English astronomer Norman Lockyer observed a yellow line in the solar spectrum during the same eclipse, which he named the D3 Fraunhofer line because it was near the known D1 and D2 lines of sodium. He concluded that it was caused by an element in the Sun unknown on Earth. Lockyer and English chemist Edward Frankland named the element with the Greek word for the Sun, Helios. Terrestrial helium was found about 10 years later by William Ramsay. *Wik

1877 Asaph Hall discovered Phobos, a satellite of Mars. The two moons of Mars, Phobos and Deimos, were found when American astronomer Hall identified them after a long search, although their existence had been a source of speculation before. The possibility of Martian moons had been speculated long before Hall's discovery. The astronomer Johannes Kepler (1571–1630) even predicted their number correctly, although with faulty logic: he wrote that since Jupiter had four known moons and Earth had one, it was only natural that Mars should have two.
Perhaps inspired by Kepler (and quoting Kepler's third law), Jonathan Swift's satire Gulliver's Travels (1726) refers to two moons in Part 3, Chapter 3 (the "Voyage to Laputa"), in which the astronomers of Laputa are described as having discovered two satellites of Mars orbiting at distances of 3 and 5 Martian diameters, and periods of 10 and 21.5 hours, respectively. The actual orbital distances and periods of Phobos and Deimos of 1.4 and 3.5 Martian diameters, and 7.6 and 30.3 hours, respectively.
Hall discovered Deimos on August 12, 1877 at about 07:48 UTC and Phobos on August 18, 1877, at the US Naval Observatory in Washington, D.C., at about 09:14 GMT (contemporary sources, using the pre-1925 astronomical convention that began the day at noon, give the time of discovery as August 11, 14:40 and August 17 16:06 Washington mean time respectively)*Wik In the words of Asaph Hall, "Of the various names that have been proposed for these satellites, I have chosen those suggested by Mr Madan of Eton, England, viz: Deimos for the outer satellite; Phobos for the inner satellite. These are generally the names of the horses that draw the chariot of Mars.”

1881 “The matter is so perfectly clear that we cannot be amazed enough how the mathematicians so stubbornly insist on mystifying it.” Comment of Friedrich Engels on a manuscript of Karl Marx on the differential calculus. *VFR

1913 On August 18, 1913, at the famous Monte Carlo casino, black came up 26 times in a row. Supposedly the house made a fortune against people betting that the long overdue red HAD to show up. *PB Personal notes

1978 Henri Cohen gives lecture to confirm Roger Apery's proof that Apéry's constant ζ(3) is irrational. In June 1978 Roger Apéry gave a talk entitled "Sur l'irrationalité de ζ(3)." During the course of the talk he outlined proofs that ζ(3) and ζ(2) were irrational, the latter using methods simplified from those used to tackle the former rather than relying on the expression in terms of π. Due to the wholly unexpected nature of the result and Apéry's blasé and very sketchy approach to the subject many of the mathematicians in the audience dismissed the proof as flawed. Three of the audience members suspected Apéry was onto something, though, and set out to confirm his proof.
Two months later these three—Henri Cohen, Hendrik Lenstra, and Alfred van der Poorten—finished their work, and on August 18 Cohen delivered a lecture giving full details of Apéry's proof. Following the talk Apéry himself took to the podium to explain the source of some of his ideas. *Wik


1685 Brook Taylor born (18 August 1685 – 29 December 1731). Remembered in introductory Calculus classes for Taylor's Theorem and Taylor series. His 1713 "Methodus.." was the first book published on the calculus of finite differences and also the first use of Taylor's Theorem.
In his 1715 essay Linear Perspective, Taylor set forth the true principles of the art in an original and more general form than any of his predecessors; but the work suffered from the brevity and obscurity which affected most of his writings, and needed the elucidation bestowed on it in the treatises of John Joshua Kirby (1754) and Daniel Fournier. *Wik

1832 Eugène Rouché (18 August 1832 at Sommières, Hérault, France, -19 August 1910 at Lunel, Hérault) French Geometer who edited Laguerre's "Collected Works". He also is known for Rouche's Theorem on Complex functions. *SAU

1861 William J Greenstreet (18 Aug 1861 in Milton, Kent, England
- 28 June 1930 in Burghfield Common, Reading, England) graduated from Cambridge and became headmaster of Marling School Stroud. He is best-known as the long-running editor of the Mathematical Gazette. *SAU

1897 Bern Dibner (18 Aug 1897; 6 Jan 1988 ) Ukrainian-American engineer and science historian. Dibner worked as an engineer during the electrification of Cuba. Realizing the need for improved methods of connecting electrical conductors, in 1924, he founded the Burndy Engineering Company. A few years later, he became interested in the history of Renaissance science. Subsequently, he began collecting books and everything he could find that was related to the history of science. This became a second career as a scholar that would run parallel with his life as a businessman. He wrote many books and pamphlets, on topics from the transport of ancient obelisks, to authorative biographies of many scientific pioneers, including Volta, inventor of the electric battery, and Roentgen, discoverer of the X ray. *TIS

1910 Paul Turán (18 Aug 1910,26 Sept 1976) Paul Erdos, who co-authored many papers with Turan wrote:
Probably the most important, most enduring and most original of Turán's results are in his power sum method and its applications. I was there when it originated in 1938. Turán mentioned these problems and told me that they were not only interesting in themselves but their positive solution would have many applications. Their importance first of all is that they lead to interesting deep problems of a completely new type; they have quite unexpectedly surprising consequences in many branches of mathematics - differential equations, numerical algebra, and various branches of function theory.
In fact Turán invented the power sum method while investigating the zeta function and he first used the method to prove results about the zeros of the zeta function.*SAU


1652 Florimond DeBeaune died (7 October 1601, Blois – 18 August 1652, Blois). His name is attached to one of the first problems ever posed in differential equations. *VFR DeBeaune was a friend of Descartes, and helped van Schooten write the Latin Translation of Descartes "Geometrie". De Beaune asked to find a curve for which the subtangent had a fixed length. De Beaune did not give this curve a name, but it has come to be called by his name. Leibniz solve De Beaune's question in his first paper on calculus in 1684. *Ed Sandifer, How Euler Did It. (Oct 2008)
In a 1638 letter to Descartes, de Beaune posed the problem of solving the differential equation

\( \frac{\operatorname{d}y}{\operatorname{d}x}=\frac{\alpha}{y-x} \)

now seen as the first example of the inverse tangent method of deducing properties of a curve from its tangents.
His Tractatus de limitibus aequationum was reprinted in England in 1807; in it, he finds upper and lower bounds for the solutions to quadratic equations and cubic equations, as simple functions of the coefficients of these equations. His Doctrine de l'angle solide and Inventaire de sa bibliothèque were also reprinted, in Paris in 1975. Another of his writings was Notae breves, the introduction to a 1649 edition of Descartes' La Géométrie. *Wik

1823 André-Jacques Garnerin (31 Jan 1769, 18 Aug 1823) French aeronaut, the first person to use a parachute regularly and successfully. He perfected the parachute and made jumps from greater altitudes than had been possible before. On 22 October 1797, at age 28, Garnerin made his first jump above the Parc Monceau in Paris. He dropped from a hot-air balloon at 3000 feet. His parachute, with 36 ribs and lines, was semi-rigid, somewhat resembling an umbrella. The descent was a success, except that he shook back and forth violently while falling. The physicist Lalande, who attended the event, suggested improving air flow with a small opening at the top of the canopy. Garnerin died aged 41. While preparing balloon equipment, a beam struck his head inflicting a mortal wound. *TIS

1960 Carlo Emilio Bonferroni (28 Jan 1892 in Bergamo, Italy - 18 Aug 1960 in Florence, Italy) His articles are more of a contribution to probability theory than to simultaneous statistical inference. He also had interests in the foundations of probability. He developed a strongly frequentist view of probability denying that subjectivist views can even be the subject of mathematical probability. *SAU He is best known for the Bonferroni inequalities, and gives his name to (but did not devise) the Bonferroni correction in statistics. *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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