## Wednesday, 8 March 2017

### On This Day in Math - March 8

 sheet from Kepler's Harmonices Mundi

The teaching of Algebra in the early stages ought to consist of a gradual generalisation of Arithmetic; in other words, Algebra ought, in the first instance to be taught as Arithmetica Universalis in the strictest sense.
~George Chrystal

The 67th day of the year; 67 is the largest prime which is not the sum of distinct squares. It is the 19th prime number and the sum of five consecutive primes ending in 19 (7 + 11 + 13 + 17 + 19)

The maximum number of internal pieces possible if a circle is cut with eleven lines. These are sometimes called "lazy caterer's numbers."
$67 = \binom{11}{0} + \binom {11} {1} + \binom {11}{2}$

67 is the largest prime which is not the sum of distinct squares. It is also the smallest prime which contains all ten digits when raised to the tenth power. *Prime Curios

and Jim Wilder ‏@wilderlab sent 67 = 26 + 21+ 20 = 26 + 21 + 20 = 67

And one smoot is equal to 67 inches.
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EVENTS
1618 Kepler, On how he discovered his Third law:
...and if you want the exact moment in time, it was conceived mentally on 8th March in this year one thousand six hundred an eighteen, but submitted to calculation in an unlucky way, and therefore rejected as false, and finally returning on the 15th of May and adopting a new line of attack, stormed the darkness of my mind. So strong was the support from the combination of my labor of seventeen years on the observations of Brahe and the present study, which conspired together, that at first I believed I was dreaming, and assuming my conclusion among my basic premises. But it is absolutely certain and exact that the proportion between the periodic times of any two planets is precisely the sesquialterate proportion of their mean distances ...
* Harmonice mundi (Linz, 1619) Book 5, Chapter 3, trans. Aiton, Duncan and Field, p. 411.

1758 Euler's paper on the game of Rencontre,(A type of solitare card game, although it was sometimes played in a variation with two players) published in 1753, is E201, "Calcul de la probabilité dans le jeu de rencontre," Mémoires de l'académie de Berlin (1751), 1753, p. 255-270. Regarding this work, the editor says that a memoir entitled "Calcul des probabilités dans les jeux de hasard" was presented to the Academy of Berlin 8 March 1758. He asserts that it is probably memoir 201: "Calcul de la probabilité dans le jeu de rencontre." An analysis of it appeared in the Nova Acta eruditorum, Leipzig 1754, p, 179. Euler's paper can be found here

In 1775, Joseph Priestley, having discovered oxygen on 1 Aug 1774, experimented with mice in his home laboratory on whether it is necessary to support life. *TIS

1896 James Dewar responds in answer to questions about his cryogenic experiments and safety precautions from Heike Kamerlingh Onnes, the Dutch Physicist whose laboratory had been shut down in Leiden for being to dangerous. "I may say that I have made all my experiments with high pressure apparatus before the Prince of Wales and the Sister of your Queen Dowager the Duchess of Albany without the slightest hesitation and no suggestions of danger were even suggested." *archive of the Kamerlingh Onnes Laboratory

1945 A Patent is Filed for the Harvard Mark I: C.D Lake, H.H. Aiken, F.E. Hamilton, and B.M. Durfee file a calculator patent for the Automatic Sequence Control Calculator, commonly known as the Harvard Mark I. The Mark I was a large automatic digital computer that could perform the four basic arithmetic functions and handle 23 decimal places. A multiplication took about five seconds. *CHM

In 1976, the largest recovered single stony meteorite (1,774 kg) fell in Jilin, China, during a meteor shower that dropped more than 4,000 kg of extra-terrestrial rock. *TIS

2016 Ralph Bohun's, A Discourse Concerning the Origine and Properties of the Wind (1671), was Sold for $£562 (US 734)$ at auction by Bonhams. The Book is mentioned by John Wallis in a letter to Oldenburg of 24 January, 1672(NS) because the book's printing had been temporarily suspended over some wording that appeared "too favourable to the Royal Society" (*Beeley's correspondence of Wallis)

BIRTHS
1804 Alvan Clark (8 Mar 1804, 19 Aug 1887) American astronomer whose family became the first significant manufacturers of astronomical instruments in the U.S. His company manufactured apparatus for most American observatories of the era, including Lick and Pulkovo, and others in Europe. In 1862, while testing a telescope, Clark discovered the companion star to Sirius, which had previously been predicted but until then never sighted. The 18½-in objective telescope he used was subsequently delivered to the Dearborn Observatory, Chicago. His sons, Alvan Graham Clark and George Bassett Clark, continued the business. The unexcelled 40-in refractor telescopes for the 40-in Yerkes observatory was made by Alvan Graham Clark*TIS

1851 George Chrystal (8 March 1851 in Old Meldrum (near Aberdeen), Scotland
- 3 Nov 1911 in Edinburgh, Scotland)is best remembered today for Algebra: a two volume work which was completed by 1889. He was also involved in educational reform throughout his career and was a major figure in setting up an educational system in Scotland. He became one of the first honorary members of the EMS in 1883. *SAU Chrystal was (one of?) the first to use the inverted exclamation mark for the subfactorial notation.

1865 Ernest Vessiot (8 March 1865 in Marseilles, France-17 Oct 1952 in La Bauche, Savoie, France) applied continuous groups to the study of differential equations. He extended results of Drach (1902) and Cartan (1907) and also extended Fredholm integrals to partial differential equations. Vessiot was assigned to ballistics during World War I and made important discoveries in this area. He was honored by election to the Académie des Sciences in 1943. *SAU

1866 Pyotr Nikolayevich Lebedev (8 Mar 1866; 1 Apr 1912 at age 46) Russian physicist who, in experiments with William Crookes' radiometer, proved (1910) that light exerts a minute pressure on bodies (as predicted by James Clerk Maxwell's theory of electromagnetism), and furthermore that this effect is twice as great for reflecting surfaces than for absorbent surfaces. He had proposed that light pressure on small particles of cosmic dust could be greater than gravitational attraction, thus explaining why a comet's tail points away from the Sun (though it is now understood the solar wind has a greater influence). He built an extremely small vibrator source capable of generating 4-6 mm waves, which he used to demonstrate the first observation of douible refraction of electromagnetic waves in crystals of rhombic sulphur.*TIS

1879 Otto Hahn (8 Mar 1879; 28 Jul 1968 at age 89) German physical chemist who, with the radiochemist Fritz Strassmann, is credited with the discovery of nuclear fission. He was awarded the Nobel Prize for Chemistry in 1944 and shared the Enrico Fermi Award in 1966 with Strassmann and Lise Meitner. Element 105 carries the name hahnium in recognition of his work.*TIS

1920 George Keith Batchelor FRS (8 March 1920 – 30 March 2000) was an Australian applied mathematician and fluid dynamicist. He was for many years the Professor of Applied Mathematics in the University of Cambridge, and was founding head of the Department of Applied Mathematics and Theoretical Physics (DAMTP). In 1956 he founded the influential Journal of Fluid Mechanics which he edited for some forty years. Prior to Cambridge he studied in Melbourne High School.
As an applied mathematician (and for some years at Cambridge a co-worker with Sir Geoffrey Taylor in the field of turbulent flow), he was a keen advocate of the need for physical understanding and sound experimental basis.
His An Introduction to Fluid Dynamics (CUP, 1967) is still considered a classic of the subject, and has been re-issued in the Cambridge Mathematical Library series, following strong current demand. Unusual for an 'elementary' textbook of that era, it presented a treatment in which the properties of a real viscous fluid were fully emphasized. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1959.*Wik

DEATHS
1688 Honoré Fabri (8 April 1608 in Le Grand Abergement, Ain, France - 8 March 1688 in Rome, Italy) was a French Jesuit who worked on astronomy, physics and mathematics. His lectureson natural philosophy were published in 1646 as Tractatus physicus de motu locali. In this work he uses the parallelogram law for forces, correctly applying it to deduce the law of reflection and the motion of a body acted on simultaneously by two forces.*SAU (This seems to be one of the earlier statements of the law)

1974 Olive Clio Hazlett (October 27, 1890 - March 8, 1974) was an American mathematician who spent most of her career working for the University of Illinois. She mainly researched algebra, and wrote seventeen research papers on subjects such as nilpotent algebras, division algebras, modular invariants, and the arithmetic of algebras.*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 & Campbel