# Pascal, Blaise

### pressure pascalâ€™s geometry jansenist

[paskahl] (1623–62) French mathematician, physicist and philosopher: pioneer of theory of probability.

Educated by his father, Pascal showed early intellectual ability, proving one of the most important theorems of projective geometry by the age of 16. He was fervently religious, belonging to the rigorous Jansenist sect of the Roman Catholic church. He was also neurotic, dyspeptic and humourless.

Much of Pascal’s early work was on projective geometry, developed from his paper on conic sections of 1640 from which he deduced 400 propositions, deriving most of those put forward by . The most notable was Pascal’s theorem (for any hexagon inscribed in a conic, the intersections of opposite pairs of sides are collinear), also known as the problem of , which had been used by as a test case for the power of his own analytical geometry. At the age of 19 Pascal invented a calculating machine that could add and subtract, in order to help his father with his business; he built and sold about 50 and several survive. Later, his interest moved towards physics, demonstrating with the help of his brother-in-law that air pressure decreased with altitude as had predicted, by taking a mercury barometer to the summit of Puy de Dôme (a height of 1200 m, near Clermont Ferrand) in 1648. His interest in hydrostatics also led him to demonstrate that pressure exerted on a confined fluid is constant in all directions (Pascal’s Law). Together with , he also developed the mathematics of probability and combinatorial analysis, using the familiar Pascal triangle to obtain the coefficients of the successive integral powers of the binomial ( *p* + *q* ) *n* . In 1655, after a profound religious experience, Pascal entered the Jansenist retreat at Port Royal, where his sister was already a nun, and he did little further mathematical work. His philosophical work *Pensées* was published in 1670. The SI unit of pressure (or stress), the pascal (Pa), defined as a force of one newton per square metre, commemorates his work on hydrostatics, and the modern programming language Pascal marks his contribution to computing.

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