# Blasé Pascal

Life History

I, Blasé Pascal was born on June 19, 1623, in Clermont-Ferrand, France. I was a child prodigy who was educated by my father, a civil servant. My earliest work was in the natural and applied sciences where I made important contributions to the construction of mechanical calculators, the study of fluids, and clarified the concepts of pressure and vacuum by generalizing the work of Evangelista Torricelli. I myself also wrote in defense of the scientific method. I helped create two major new areas of research, wrote a significant treatise on the subject of projective geometry at the age of sixteen, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. In 1646, my sister and I Jacqueline converted to Jansenism. My father died in 1651. Following a mystical experience in late 1654, he had his "second conversion", abandoned his scientific work, and devoted himself to philosophy and theology. In this year, I wrote an important essay on the arithmetic of triangles. I died on August 19, 1662 thank to stomach cncer.

Anecdotes

In 1654, prompted by a friend interested in gambling problems, I corresponded with Fermat on the subject, and from that collaboration was born the mathematical theory of probabilities. The friend was the Chevalier de Méré, and the specific problem was that of two players who want to finish a game early and, given the current circumstances of the game, want to divide the stakes fairly, based on the chance each has of winning the game from that point. From this discussion, the notion of expected value was introduced The work done by Fermat and Pascal into the calculus of probabilities laid important groundwork for Leibniz' formulation of the infinitesimal calculus.

Mathmatical Contributions

I have contributed much to math. My Treatise on the Arithmetical Triangle (Traité du triangle arithmétique) described a convenient table presentation for binomial coefficients, now called Pascal's triangle. It is a geometric arrangement of the binomial coefficients in a triangle.

This construction is related to the binomial coefficients by my rule, which states that if

$(x+y)^n=\sum_{k=0}^n{n \choose k}x^{n-k}y^{k}$

then

${n \choose k} = {n-1 \choose k-1} + {n-1 \choose k}$

for any nonnegative integer n and any integer k between 0 and n.

In mathematics, my rule or more commonly known as Pascal's rule is a combinatorial identity about binomial coefficients. It states that for any natural number n we have

${n-1\choose k} + {n-1\choose k-1} = {n\choose k}$

where $1 \leq k < n$ and ${n\choose k}$ is a binomial coefficient.

I began work on my calculator in 1642, when I was only 19 years old. I had been assisting his father, who worked as a tax commissioner, and sought to produce a device which could reduce some of his workload. I received a Royal Privilege in 1649 that granted me exclusive rights to make and sell calculating machines in France. By 1652 I had produced some fifty prototypes and sold just over a dozen machines, but the cost and complexity of the Pascaline, as i called it, combined with the fact that it could only add and subtract, and the latter with difficulty—was a barrier to further sales, and production ceased in that year.

Pascalines came in both the decimal and non-decimal varieties, both of which exist in museums today. The contemporary French currency system was similar to the Imperial pounds ("livres"), shillings ("sols") and pence ("deniers") in use in Britain until the 1970s.The initial prototype of the Pascaline had only a few dials, whilst later production variants had eight dials, the latter being able to deal with numbers up to 9,999,999.