**Two seemingly incompatible conceptions can each represent an aspect of the truth ... They may serve in turn to represent the facts without ever entering into direct conflict.**

~Louis de Broglie

The 227th day of the year; 227 is a prime number, but it can also be written as the sum of the sum and the product of the first four primes: (2 + 3 + 5 + 7)+(2 x 3 x 5 x 7) = 227. In a similar way, the first two primes work (2+3)+(2x3)=11 is prime. Can you find another?

**EVENTS**

**1665**Robert Hooke writes to Boyle in Oxford about his newly devised reflecting quadrant, "My quadrant does to admiration for taking angles, so that thereby we are able from hence to tell the true distance between (St.) Paul's and any other church steeple in the city.... within the quantity of twelve foot." *Lisa Jardine, Ingenious Pursuits, pg 152

**1768**Lagrange, in a letter to D’Alembert, expressed his difficulty in solving the problem: Given a nonsquare positive integer n, to ﬁnd a square integer x

^{2}such that nx

^{2}+1 shall also be a square. *VFR

In the same letter, he showed that x

^{2/3}could be expanded in a trigonometric series. D'Alembert had often used the function as an example that could not be so expanded. *Mathematical thought from ancient to modern times, Volume 2 , Morris Kline

1951 The Soviet Union issued a postage stamp with a portrait of Sonya Kovalevskaya. *VFR

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2006, Voyager 1, the most distant man-made object, reached 100 astronomical units from the sun - meaning 100 times more distant from the sun than is Earth - about 15,000 million km (9,300 million miles) from the sun. At such great distance, the sun is a mere point of light, so solar energy is not an option, but having a nuclear power source, Voyager 1 continues to beam back information. The spacecraft, launched nearly 30 years earlier, on 5 Sep 1977, had flown beyond the outer planets and reached the heliosheath, the outer edge of our solar system, where the sun's influence wanes. Voyager 1 continues traveling at a speed of about one million miles per day and could cross into interstellar space before 10 years later.

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**BIRTHS**

**1795 Émile Léger**(Born: 15 Aug 1795 in Lagrange-aux-Bois, France; Died: 15 Dec 1838 in Paris, France)Léger only published four mathematical papers but one contains possibly the first mention of what today is a well known fact about the Euclidean algorithm,

Émile Léger appears to have been the first (or second, if the work of de Lagny ... is counted) to recognise that the worst case of the Euclidean algorithm occurs when the inputs are consecutive Fibonacci numbers. *SAU________________________________________________________________________

**1863 Aleksei N. Krylov,**(Born: 15 Aug 1863 in Visyaga, Simbirskoy [now Ulyanovskaya], Russia

Died: 26 Oct 1945 in Leningrad, USSR [now St Petersburg, Russia]) noted for mathematics, mechanics and engineering. *VFR Krylov made many mathematical advances in his applications of mathematics to shipbuilding. In hydrodynamics, among many advances, he made significant contributions to the theory of ships moving in shallow water. In 1904 he constructed a mechanical integrator to solve ordinary differential equations, being the first in Russia to make such an instrument. He improved Fourier's method for solving boundary value problems in a 1905 paper and gave many applications. *SAU

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**1865 Hantaro Nagaoka**(Born 15 Aug 1865; died 11 Dec 1950)Japanese physicist who was influential in advancing physics in Japan in the early twentieth century. In 1904, he published his Saturnian model of the atom, inspired by the rings around the planet Saturn. He placed discrete, negatively charged electrons of the same tiny mass, spaced in a ring revolving around a central huge positive spherical mass at its centre. Considering the electrostatic forces, hee made a mathematical analogy to Maxwell's model of the stability of the motion of Saturn's rings in a huge central gravitational field. However, Nagaoka's theory failed in other ways, and he sidelined it in 1908. *TIS

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**1892 Louis Victor Pierre Raymond duc de Broglie**(died 19 Mar 1987) was a French physicist best known for his research on quantum theory and for his discovery of the wave nature of electrons. De Broglie was of the French aristocracy - hence the title "duc" (Prince). In 1923, as part of his Ph.D. thesis, he argued that since light could be seen to behave under some conditions as particles (photoelectric effect) and other times as waves (diffraction), we should consider that matter has the same ambiguity of possessing both particle and wave properties. For this, he was awarded the 1929 Nobel Prize for Physics. *TIS

**1893 Leslie (John) Comrie**(died 11 Dec 1950) was a New Zealand astronomer and pioneer in the application of punched-card machinery to astronomical calculations. He joined HM Nautical Almanac Office (1926-36), where he replaced the use of logarithm tables with desk calculators and punched card machines for the production of astronomical and mathematical tables. This made scientific use of these machines, made originally for only business uses. In 1938, he founded the Scientific Computing Service Ltd., the first commercial calculating service in Great Britain, to further his ideas of mechanical computation for the preparation of mathematical tables. His use of card processing systems prepared the way for electronic computers.*TIS

**DEATHS**

**1758 Pierre Bouguer**died. In 1727 he won the prize competition of the Acad´emie Royal des Sciences on the masting of ships. In this competition Euler only received the “accessit.” *vfr

Two days before (Aug 13)Charles-Etienne-Louis Camas was elected to the French Academy of Sciences because he had earlier won half the prize money in their competition for the best manner of masting vessels. (did Bouguer get the other half? Did Euler get any? is one, or more of these three pieces of information incorrect?)

French physicist whose work founded photometry, the measurement of light intensity. He was a child prodigy, a professor at age 15, following his father, Jean Bouguer, in hydrography - the study of bodies of water, both salt and fresh. He participated on the expedition to Peru (1735-44) to measure an arc of the meridian near the equator. In 1729, he invented a photometer to compare the intensity of two light sources illuminating separate halves of translucent paper. The eye itself, he determined, could not be used as a meter, but could establish the equality of brightness of adjacent surfaces. He determined the sun was 300 times brighter the moon. Bouguer's law gives the attenuation of a beam of light by an optically homogeneous (transparent) medium.*TIS

**1789 Jakob II Bernoulli**, There seems to be confusion about his date of death, although it is well known that he drowned while swimming in the Neva River at the age of 29 and that he was married to one of Euler's granddaughters. Part of the confusion may be due to the fact that Russia did not switch to the modern Gregorian calendar until after the 1918 revolution. Alternate date given is July 2. Should be Aug 5 if converting the same day from Julian to Gregorian. Anyone?

**1798 Edward Waring**was an English mathematician who gave many results about decomposing numbers into sums of powers and sums of primes.*SAU

**1927 Bertram Borden Boltwood**(born 27 Jul 1870, Died 15 Aug 1927). was an American chemist and physicist whose work on the radioactive decay of uranium and thorium was important in the development of the theory of isotopes. Boltwood studied the "radioactive series" whereby radioactive elements sequentially decay into other isotopes or elements. Since lead was always present in such ores, he concluded (1905) that lead must be the stable end product from their radioactive decay. Each decay proceeds at a characteristic rate. In 1907, he proposed that the ratio of original radioactive material to its decay products measured how long the process had been taking place. Thus the ore in the earth's crust could be dated, and give the age of the earth as 2.2 billion years.*TIS

**1953 Ludwig Prandtl**(born 4 Feb 1875, Died 15 Aug 1953).German physicist who is remembered for his studies of both aerodynamics and hydrodynamics. He established the existence of the boundary layer adjoining the surface of a solid over which a fluid flows. The design of an efficient shape, weight, and mass for ships and aircraft owes much to his work, for which he is considered to be the father of aerodynamics. His made major studies on the effects of streamlining and the properties of aircraft wings. He made improvements to such constructions as wind tunnels. The Prandtl number is a dimensionless group used in the study of convection. The von Karman-Prandtl equation describes the logarithmic variation of water velocity within a channel from zero flow at the stream bed to a maximum velocity at the water surface.*TIS

2002 Heinz Bauer (31 January 1928 – 15 August 2002) was a German mathematician.

Bauer studied at the University of Erlangen-Nuremberg and received his PhD there in 1953 under the supervision of Otto Haupt and finished his habilitation in 1956, both for work with Otto Haupt. After a short time from 1961 to 1965 as professor at the University of Hamburg he stayed his whole career at the University of Erlangen-Nuremberg. His research focus was the Potential theory, Probability theory and Functional analysis

Bauer received the Chauvenet Prize in 1980 and became a member of the German Academy of Sciences Leopoldina in 1986. Bauer died in Erlangen. *Wik

Credits:

*VFR = V Frederick Rickey, USMA

*TIS= Today in Science History

*Wik = Wikipedia

*SAU=St Andrews Univ. Math History

*CHM=Computer History Museum