**To call in the statistician after the experiment is done may be**

**no more than asking hm to perform a postmortem examination:**

**he may be able to say what the experiment died of.**

~Ronald Fisher

The 210th day of the year; (21, 20, 29) and (35, 12, 37) are the two least primitive Pythagorean triangles with different hypotenuses and the same area (=210). Students are challenged to find another pair of such PPTs

There are only two triangular numbers that are the product of consecutive integers that are year days. 210 = 14 x 15. The other is much smaller and should be easier to find. (**Well**???)

There are an infinite number of numbers that appear six or more times in Pascal's Arithmetic Triangle, but only three of them; 1, 120, and 210 are year dates.

7! hours is 210 days.

See More Math Facts for every Year Day here.

**EVENTS**

**1654** Pascal wrote a letter to Fermat agreeing to a result of Fermat on a probability problem about repeated rolls of a single die for a wager. "Impatience has seized me as well as it has you, and although I am still abed, I cannot refrain from telling you that I received your letter in regard to the problem of the points yesterday evening from the hands of M. Carcavi, and that I admire it more than I can tell you. I do not have the leisure to write at length, but, in a word, you have found the two divisions of the points and of the dice with perfect justice. I am thoroughly satisfied as I can no longer doubt that I was wrong, seeing the admirable accord in which I find myself with you." *York Univ Hist of Stats

**1698** In a letter to John Bernoulli, Leibniz introduces the dot for multiplication..(cajori 233; vol 1 pg 267) “The dot was introduced as a symbol for multiplication by G. W. Leibniz. On July 29, 1698, he wrote in a letter to John Bernoulli: “I do not like X as a symbol for multiplication, as it is easily confounded with x; … often I simply relate two quantities by an interposed dot and indicate multiplication by ZC · LM. Hence, in designating ratio I use not one point but two points, which I use at the same time for division.”

**1739** D’Alembert, age 21, submitted his ﬁrst mathematical paper to the Academy of Sciences. *VFR As his knowledge of mathematics was mainly due to self-study, he often found that others had already established his mathematical discoveries by more elegant and more direct means. In 1739 d’Alembert submitted his first paper to the French Académie Royale des Sciences, in which he described the errors found in the standard textbook, Analyse démontrée, written by Charles Reyneau. *webpage of Robert Nowland

**1773** First schoolhouse West of the Alleghenies.*VFR (built in Schoenbrunn, OH.)

**1867** Thomas Hill, president of Harvard College, who was also somewhat of a mathematician, wrote Benjamin Peirce, who was a professor there: “I have the honor of informing you that the University, on Commencement Day, conferred on you the Degree of Doctor of Laws in recognition of the transcendent ability with which you have pursued mathematical physical investigations, and in particular for the luster which she has herself for so many years borrowed from your genius.” [P. 10 of Benjamin Peirce, AMM offprint, 1925] *VFR

**1878** This was the height of search for the intra-Mercurial planet Vulcan using eclipses to block the Sun. (*Vulcan was a small planet proposed to exist in an orbit between Mercury and the Sun. In an attempt to explain peculiarities of Mercury's orbit, in the 19th-century French mathematician Urbain Jean Joseph Le Verrier hypothesized that they were the result of another planet, which he named Vulcan*.) Several observers claim sightings, but they are never confirmed. The problem is finally resolved by Albert Einstein (1879-1955) in his general theory of relativity in 1916. *NSEC

**1958** President Eisenhower signed the National Aeronautics and Space Act. NASA opened for business on 1 October 1958, and within a week launched Project Mercury—the start of the U.S. manned space program. *VFR

**2005,** another candidate for tenth planet was announced by Mike Brown of California Institute of Technology. Its diameter is estimated at 2,100 miles - about 1-1/2 times that of Pluto. Its orbit is eccentric and inclined at about 45 degrees to the main plane of the solar system. It was named 2003 UB313 on a photograph made 31 Oct 2003. Later, its motion was recognized, on 8 Jan 2005. With orbits significantly inclined to the others, the status as a planet of either or even Pluto, is a subject for debate. They are in a region of numerous frozen comet-like objects beyond Neptune - the Kuiper Belt. The object Sedna - somewhat smaller than Pluto - was also found there in 2004. NASA also in an official statement referred to 2003 UB313 as a tenth planet*TIS

2015 On July 29, 2015, a 15th type of pentagon that would tile the plane was announced by Casey Mann, Jennifer McLoud, and David Von Derau of the University of Washington Bothell. In 1918, K. Reinhardt discovered five different families of convex pentagons that could tile the plane. This was the complete list until 1968, when Richard Kershner wrote about three more families of tiling pentagons. Martin Gardner wrote about the complete list of eight tiling pentagons in 1975, and then got a message from Richard James III about another type. Martin updated the readers of Mathematical Games, but then got a message from a housewife with no mathematical training, Marjorie Rice, who found four more families of tiling pentagons. In 1985, Rolf Stein found a convex pentagon that can tile the plane. Now, there is one more. *Wolfram

*guardian.com |

**1858 Francesco Gerbaldi** (29 July 1858, La Spezia, Italy to 29 June 1934, Pavia, Italy) was an Italian geometer, who proved Gerbaldi's theorem. In geometry, Gerbaldi's theorem, proved by Gerbaldi (1882), states that one can find six pairwise apolar linearly independent nondegenerate ternary quadratic forms. These are permuted by the Valentiner group. (*say that three times real fast*) *Wik

**1862 Eduard Brückner** (July 29, 1862–May 20, 1927) pioneer climate researcher. He also studied the glaciers of the Alps and particularly the effect of the ice ages on the Earth's surface features. By analyzing direct and indirect observations of climatic fluctuations, he discovered the 35-year Brückner climatic cycle (1887) of swings between damp-cold and warm-dry conditions. He initiated scientific debate on whether climate change should be interpreted as a natural function of the Earth system, or whether it was influenced by man's activities, such as deforestation. He considered the impact of climate change on the balance of power between nations and its economic significance in agricultural productivity, emigration, river transportation and the spreading of diseases.*TIS

**1898 Isidor Isaac Rabi** (29 July 1898 – 11 January 1988) was an American physicist who was awarded the Nobel Prize for Physics in 1944 for his invention (in 1937) of the atomic and molecular beam magnetic resonance method of measuring magnetic properties of atoms, molecules, and atomic nuclei. He spent most of his life at Columbia University (1929-67), where he performed most of his pioneering research in radar and the magnetic moment associated with electron spin in the 1930s and 1940s. His Nobel-winning work led to the invention of the laser, the atomic clock, and diagnostic uses of nuclear magnetic resonance. He originated the idea for the CERN nuclear research center in Geneva (founded 1954). *TIS

**1912 Noel Bryan Slater,** often cited NB Slater, (1912 in Blackburn , January 31 1973) was a British mathematician and physicist who worked on including statistical mechanics and physical chemistry, and probability theory.*Wik

**1781 Johann Kies** (September 14, 1713—July 29, 1781) a German astronomer and mathematician. Born in Tübingen, Kies worked in Berlin in 1751 alongside Jérôme Lalande in order to make observations on the lunar parallax in concert with those of Nicolas Louis de Lacaille at the Cape of Good Hope.

From 1742 to 1754, at the recommendation of the mathematician Leonhard Euler, he was made professor of mathematics at Berlin's Academy of Sciences and astronomer at its observatory.

He subsequently taught also at the Collegium of Tübingen. From 1754 to 1755, Kies served as director of the Astronomisches Rechen-Institut in Heidelberg.

Kies was one of the first to propagate Newton's discoveries in Germany, and dedicated two of his works to the Englishman: De viribus centralibus (Tübingen, 1758) and De lege gravitatis (Tübingen, 1773). Kies is also the author of a work on lunar influences: De influxu lunae in partes terrae mobiles (Tübingen, 1769). He wrote many other works, both in French and in Latin, on astronomy.

Kies corresponded with Euler from 1747 to 1767. Their correspondence consists of 8 letters, all of which were written by Kies.

The crater Kies on the Moon is named in his honor. *TIA

**1839 Gaspard de Prony**. (July 22, 1755 - July 29, 1839) Cauchy was elected his successor at the Bureau des Longitudes but was not admitted as he refused to take the oath of allegiance. *VFR

In 1793, de Prony began a major task of producing logarithmic and trigonometric tables for the French Cadastre. The effort was begun at the request of the French National Assembly, which, after the French Revolution wanted to bring uniformity to the multiple measurements and standards used throughout the nation. The tables and their production were vast, with values calculated to between fourteen and twenty-nine decimal places. Inspired by Adam Smith's Wealth of Nations, de Prony divided up the labor, bragging that he "could manufacture logarithms as easily as one manufactures pins." At the top of the organizational hierarchy were scientists and mathematicians who devised the formulas. Next were workers who created the instructions for doing the calculations. At the bottom were about ninety "computers" (as they were called) who were not trained in mathematics, but who followed the instructions."

One of de Prony's important scientific inventions was the 'de Prony brake' which he invented in 1821 to measure the performance of machines and engines. He also was first to propose using a reversible pendulum to measure gravity, which was independently invented in 1817 by Henry Kater and became known as the Kater's pendulum. He also created a method of converting sinusoidal and exponential curves into a systems of linear equations. Prony estimation is used extensively in signal processing and finite element modelling of non linear materials. Prony was a member, and eventually president, of the French Academy of Science. He was also elected a foreign member of the Royal Swedish Academy of Sciences in 1810. His name is one of the 72 names inscribed on the Eiffel Tower. *Wik

**1898 John Alexander Reina Newlands**, (July 22, 1755 - July 29, 1839) was a British chemist who first established an order of elements by the atomic weights, and observed a periodicity in the properties. Every eighth element has similar properties, hence he named the Law of Octaves (7 Feb 1863). It took another quarter century, and the work of others, such as Mendeleev, for the significance of his discovery to be recognized. He died in London.*TIS

**1944 David Eugene Smith** (January 21, 1860 in Cortland, New York – July 29, 1944 in New York) died in New York City at the age of eighty-four.*VFR Smith attended Syracuse University, graduating in 1881 (Ph. D., 1887; LL.D., 1905). He studied to be a lawyer concentrating in arts and humanities, but accepted an instructorship in mathematics at the Cortland Normal School in 1884. He also knew Latin, Greek, and Hebrew. He became a professor at the Michigan State Normal College in 1891, the principal at the State Normal School in Brockport, New York (1898), and a professor of mathematics at Teachers College, Columbia University (1901).

Smith became president of the Mathematical Association of America in 1920. He also wrote a large number of publications of various types. He was editor of the Bulletin of the American Mathematical Society; contributed to other mathematical journals; published a series of textbooks; translated Klein's Famous Problems of Geometry, Fink's History of Mathematics, and the Treviso Arithmetic. He edited Augustus De Morgan's Budget of Paradoxes (1915) and wrote many books on Mathematics. *Wik

**1962 Ronald Aylmer Fisher** FRS (17 February 1890 – 29 July 1962) was an English statistician, evolutionary biologist, eugenicist and geneticist. Among other things, Fisher is well known for his contributions to statistics by creating Fisher's exact test and Fisher's equation. Anders Hald called him "a genius who almost single-handedly created the foundations for modern statistical science" while Richard Dawkins called him "the greatest of Darwin's successors". In 2010 Dawkins named him "the greatest biologist since Darwin". Fisher was opposed to the conclusions of Richard Doll and A.B. Hill that smoking caused lung cancer. He compared the correlations in their papers to a correlation between the import of apples and the rise of divorce in order to show that correlation does not imply causation.

To quote Yates and Mather, "It has been suggested that the fact that Fisher was employed as consultant by the tobacco firms in this controversy casts doubt on the value of his arguments. This is to misjudge the man. He was not above accepting financial reward for his labours, but the reason for his interest was undoubtedly his dislike and mistrust of puritanical tendencies of all kinds; and perhaps also the personal solace he had always found in tobacco."

After retiring from Cambridge University in 1957 he spent some time as a senior research fellow at the CSIRO in Adelaide, Australia. He died of colon cancer there in 1962.

He was awarded the Linnean Society of London's prestigious Darwin–Wallace Medal in 1958.

Fisher's important contributions to both genetics and statistics are emphasized by the remark of L.J. Savage, "I occasionally meet geneticists who ask me whether it is true that the great geneticist R.A. Fisher was also an important statistician"*Wik The stained glass window is from the Greatroom at Caius College.

**1994 Dorothy Mary Hodgkin** OM FRS (12 May 1910 – 29 July 1994), known professionally as Dorothy Crowfoot Hodgkin or simply Dorothy Hodgkin, was a British biochemist who developed protein crystallography, for which she won the Nobel Prize in Chemistry in 1964.

She advanced the technique of X-ray crystallography, a method used to determine the three-dimensional structures of biomolecules. Among her most influential discoveries are the confirmation of the structure of penicillin that Ernst Boris Chain and Edward Abraham had previously surmised, and then the structure of vitamin B12, for which she became the third woman to win the Nobel Prize in Chemistry.

In 1969, after 35 years of work and five years after winning the Nobel Prize, Hodgkin was able to decipher the structure of insulin. X-ray crystallography became a widely used tool and was critical in later determining the structures of many biological molecules where knowledge of structure is critical to an understanding of function. She is regarded as one of the pioneer scientists in the field of X-ray crystallography studies of biomolecules. *Wik

**1996 Marcel-Paul "Marco" Schützenberger** (October 24, 1920 – July 29, 1996) was a French mathematician and Doctor of Medicine. His work had impact across the fields of formal language, combinatorics, and information theory.[1] In addition to his formal results in mathematics, he was "deeply involved in [a] struggle against the votaries of Darwinism,"[2] a stance which has resulted in some mixed reactions from his peers and from critics of his stance on evolution. Several notable theorems and objects in mathematics bear his name (for example Schutzenberger group).*Wik

**2004 Walter Feit **(October 26, 1930 – July 29, 2004)was an Austrian mathematician who (with John Thompson) proved one of the most important theorems about finite simple groups.*SAU

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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