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pascal triangle The Pascal triangle actually known long before Pascal is a table of the binomial coefficients where the n kth entry is Each entry is the sum of the pair immediately above it binomial coefficient The binomial coefficients are the coefficients of powers of x in the expansion of 1 xn We have where the binomial coefficient is the number of ways of choosing an unordered subset of size k from a set of size n The binomial coefficients are the entries in the Pascal triangle binomial theorem The Binomial Theorem is the result which allows one to expand a binomial x yn xn an-1xn-1y an-2xn-2y2 yn where the coefficients ai are called binomial coefficients probability theory Probability theory studies the possible outcomes of given events together with their relative likelihoods and distributions In fact there is considerable debate about exactly what probability means in practice Some mathematicians regard it as simply a component of an abstract theory while others give it an interpretation based on the frequencies of certain outcomes infinitesimal An infinitesimal is an arbitrarily small quantity which early mathematicians found it necessary to incorporate into their theories in the absence of a proper theory of limits Infinitesimal calculus is the Differential and Integral Calculus projective geometry Projective geometry is the branch of geometry dealing with the properties and invariants of geometric figures under projection from a point So for example a circle may be projected into an ellipse or a hyperbola and so these curves may all be regarded as equivalent in projective geomet Born 19 June 1623 in Clermont now Clermont-Ferrand Auvergne France Died 19 Aug 1662 in Paris France Blaise Pascal was the third of Etienne Pascals children and his only son Blaises mother died when he was only three years old In 1632 the Pascal family Etienne and his four
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