*For example*is not a proof.

**Jewish proverb**,

**EVENTS**

**1634**Gilles Personne de Roberval was proclaimed the winner of the triennial competition for the Ramus chair at the Coll`ege Royal in Paris. Thereafter, he kept his mathematical discoveries secret so that he could continue to win the competition and keep the chair. As a consequence he lost credit for many of his discoveries. *VFR

He worked on the quadrature of surfaces and the cubature of solids, which he accomplished, in some of the simpler cases, by an original method which he called the "Method of Indivisibles"; but he lost much of the credit of the discovery as he kept his method for his own use, while Bonaventura Cavalieri published a similar method which he independently invented.

Another of Roberval’s discoveries was a very general method of drawing tangents, by considering a curve as described by a moving point whose motion is the resultant of several simpler motions. He also discovered a method of deriving one curve from another, by means of which finite areas can be obtained equal to the areas between certain curves and their asymptotes. To these curves, which were also applied to effect some quadratures, Evangelista Torricelli gave the name "Robervallian lines."

**1644**In a letter to Torricelli, Fr. Marin Mersenne gives a method to find a number with any number of factors. He explained; since 60 = 2*2*3*5 subtract one from each factor (1,1,2, 4) and make them the exponents of any primes.. he used 2

^{4}*3

^{2}*5*7= 5040.. Of course Plato knew much earlier that 5040 had sixty factors.In

*Laws*, Plato suggests that 5040 is the optimal number of citizens in a state because a) It is the product of 12, 20, and 21; b) the 12th part of it can still be divided by 12; and c) it has 59 proper divisors, including all numbers for 1 to 12 except 11, and 5038--which is very close to 5040--is divisible by 11.

**1687**In a letter to Huygens, Fatio de Dullier used an integrating factor to solve the diﬀerential equation 3x dy − 2y dx = 0. No earlier instance of an integrating factor is known. The fundamental conception of integrating factors was due to Euler (1734) and further developed by Clairaut (1739). *VFR

In 1778, David Rittenhouse observed a total solar eclipse in Philadelphia. In a letter to him, dated 17 Jul 1778, Thomas Jefferson wrote that "We were much disappointed in Virginia generally on the day of the great eclipse, which proved to be cloudy." Rittenhouse (1732-1796) was not only an American astronomer, but also a mathematician and public official. He is reputed to have built the first American-made telescope and was the first director of the U.S. Mint (1792-1795).*TIS Jefferson was an excellent applied mathematician and had contacted Rittenhouse on another occasion. Travelling through France ten years later, " in 1788, he noticed peasants near Nancy ploughing, and fell to wondering about the design of the moldboard, that is, the surface which turns the earth: he spent the next ten years working on this, on and off, wondering how to achieve the most efficient design, both offering least frictional resistance, and which also would be easy for farmers out in the frontiers to construct, far from technical help. He consulted the Pennsylvania mathematician Robert Patterson (born in Ireland in 1743), and consulted also another Philadelphia luminary, the self-taught astronomer and mathematical instrument-maker David Rittenhouse (1732-1796)." Jefferson also communicated with Thomas Paine about bridge design, suggesting the use of catenary arches. Jefferson is believed to be the first person ever to use the term "catenary" in English.

**1847**The first observation with the Great Refractor at Harvard was of the Moon on the afternoon of June 24, 1847. A number of significant achievements quickly followed. The eighth satellite of Saturn was discovered in 1848 by W.C. Bond and his son, George P. Bond, who was to succeed his father as Director in 1859. In 1850, Saturn's crape, or inner, ring was first observed, again by the Bonds. That same year, the first daguerreotype ever made of a star, the bright Vega, was taken by J.A. Whipple working under W.C. Bond, following several years of experiments using smaller telescopes. One of the earliest photographs of a double star, Mizar and Alcor in the handle of the Big Dipper, was achieved in 1857, using the wet-plate collodion process. *Observatory web page... The 15 inch Great Refractor was "once the biggest and best telescope in the United States, perhaps the world." *Frederik Pohl, Chasing Science, pg 42.

**In 1898**, a U.S. commemorative stamp was first used that carried the design of a major engineering construction project, the Mississippi River Bridge, a triple-arch steel bridge between East St. Louis, Illinois and St. Louis,

Missouri. Each span was roughly 500 feet and rested on piers resting on bedrock some 100 feet beneath the river bottom. Opened on 4 Jul 1874, the bridge was named after its designer, the self-trained engineer, James Eads. The upper level road also carried streetcars, which are seen in the stamp design along with steam ships on the river below. The trains that ran on its lower level are hidden from view at this angle. (Although still in use, the bridge no longer carries rail traffic.) The design was reissued in 1998.*TIS

**In 1975**, a moon tremour, caused by a strike of Taurid meteors, was detected by the seismometer network left on the Moon's surface by American astronauts. The major series of lunar impacts between 22 - 26 Jun 1975 represented 5% of the total number of impacts detected during the eight years of the network's operation, and included numerous 1-ton meteorites. The impacts were detected only when the nearside of the Moon (where the astronauts landed) was facing the Beta Taurid radiant. At the same time, there was a lot of activity detected in Earth's ionosphere, which has been linked with meteor activity. The Taurid meteor storm crosses the Earth orbit twice a year, during the period 24 Jun to 6 Jul and the period 3 Nov to 15 Nov.*TIS

**BIRTHS**

**1880 Oswald Veblen**, American mathematician, born in Decorah, Iowa, who made important contributions to differential geometry and early topology. Many of his contributions found application to atomic physics and relativity. Along with his interest in the foundations of geometry he developed an interest in algebraic topology, or analysis situs as it was then called and by 1912 was writing papers on this subject. Gradually he became more interested in differential geometry. From l922 onward most of his papers were in this area and in its connections with relativity. His work on axioms for differentiable manifolds and differential geometry contributed directly to the field.*TIS

1909 William Penney (24 Jun 1909, 3 Mar 1991 at age 81)(Baron Penney of East Hendred) British nuclear physicist who led Britain's development of the atomic bomb. Penney was to Britain as Robert Oppenheimer was to the U.S. He was a prominent part of the British Mission at Los Alamos during WW II, where his principal assignment was studying the damage effects from the blast wave of the atomic bomb, but he became involved in implosion studies as well. Penney's combination of expertise, analytical skill, effective communication, and the ability to translate them into practical application soon made him one of the five members of the Los Alamos “brain trust” that made key decisions. He was the only Briton to be part of the ten man Target Committee that drew up the list of targets for the atomic bombing of Japan. *TIS

**1915 Sir Fred Hoyle**English mathematician and astronomer, best known as the foremost proponent and defender of the steady-state theory of the universe. This theory holds both that the universe is expanding and that matter is being continuously created to keep the mean density of matter in space constant. He became Britain's best-known astronomer in 1950 with his broadcast lectures on The Nature of the Universe, and he recalled coining the term "Big Bang" in the last of those talks. Although over time, belief in a "steady state" universe as Hoyle had proposed was shared by fewer and fewer scientists because of new discoveries, Hoyle never accepted the now most popular "Big Bang" theory for the origin of the universe.

**DEATHS**

**1832 Timofei Fedorovic Osipovsky**(February 2, 1766–June 24, 1832) was a Russian mathematician, physicist, astronomer, and philosopher. Timofei Osipovsky graduated from the St Petersburg Teachers Seminary.

He was to became a teacher at Kharkov University. Kharkov University was founded in 1805. The city of Kharkov, thanks to its educational establishments, became one of the most important cultural and educational centers of Ukraine. Osipovsky was appointed to Kharkov University in 1805, the year of the foundation of the University. In 1813 he became rector of the University. However in 1820 Osipovsky was suspended from his post on religious grounds.

His most famous work was the three volume book A Course of Mathematics (1801–1823). This soon became a standard university text and was used in universities for many years. *Wik

**1880 Jules Lissajous**was a French mathematician best known for the Lissajous figures produced from a pair of sine waves. *SAU The curves are also called Bowditch curves for the early American mathematician, Nathanial Bowditch, who worked with them earlier. In general, a parametric curve with equations x= A sin(k t ); y= B sin(m t), the curves can describe things as simple as a circle or ellipse to more complex open and closed curves. If the ratio of k/m is rational, the curve will eventually close.

Credits:

*VFR = V Frederick Rickey, USMA

*TIS= Today in Science History

*Wik = Wikipedia

*SAU=St Andrews Univ. Math History