## Pascal, Blaise (1623–1662)Pascal's studies of the cycloid inspired others to develop the calculus. His experiments (performed by his brother-in-law) observing the heights of a column of a barometer at different altitudes on the mountain Puy-de-Dôme (1646) confirmed that the atmospheric air had weight. He also pioneered hydrodynamics and hydrostatics, in doing so discovering Pascal's law In 1654, he and Pierre de Fermat, in an exchange of correspondence, laid the foundation for the theory of probability. They considered the dice problem, already studied by Girolamo Cardano, and the problem of points also considered by Cardano and, around the same time, by Luca Pacioli and Niccoló Tartaglia. The dice problem asks how many times one can expect to throw a pair of dice before getting a double six; the problem of points asks how to divide the stakes if a game of dice is incomplete. Pascal and Fermat solved the problem of points for a two-player game but didn't develop powerful enough methods to solve it for three or more players. In the same year, Pascal was almost killed in an incident in which the horses pulling his carriage bolted and the carriage was left hanging over a bridge above the river Seine. Though rescued unharmed, he shortly after converted to the rigorous Jansenist sect of the Catholic Church. His philosophical work Pensées, written between 1656 and 1658 contains his famous argument,
often called Pascal's Wager, for belief in God.
Having suffered poor health for most of his adult life, he died in great
pain of cancer at the age of 39. ## Pascal and his calculating machineTo follow the method of using the Pascaline, suppose that the operator wishes to add together the numbers 2, 5, and 3. With a stylus or peg he turns the right hand dial anticlockwise from where the figure 2 is marked round to 0. The dial moves in the opposite direction to the dial on a telephone and it does not spring back to its starting position when the peg is removed. This action turns the pinwheel and hence the cylinder 2/10 of a revolution from 0 to 2. The operator now repeats the process, this time "dialing" 5. The pinwheel turns the cylinder a further 5/10 of a revolution, so that the total registered there is 7. One again he dials a number, in this example number 3. The pinwheel moves through 3/10 of a turn, as does the cylinder. Because the cylinder is marked in tenths, however, and ten units have been added (2 + 5 + 3), this brings it round to 0 again. A trip mechanism within the calculator, however, "carries" the figure 1 to the cylinder immediately to the left, i.e., it turns the next wheel 1/10 of a revolution, from 0 to 1. There are six cylinders altogether, which represent (from left to right) single figures, tens, hundreds, thousands, ten thousands and hundreds of thousands, respectively. The adding of the single figures 2, 5, and 3 gives 0 in the single figure cylinder and 1 on the tens cylinder, thus producing the answer total 10. With the six cylinders, sums can be added up to a total of 999,999. In fact some Pascalines have two sets of numbers on the dials and the cylinders, the second set running in the reverse direction (i.e., from 9–0 instead of 0–9). The latter can be used for subtraction, and are covered up on the cylinders by a sliding strip of metal when not in use. Some of Pascal's machines were designed for adding livres, sous, and deniers (the contemporary French currency), and may be regarded as the forerunners of modern cash registers. ## Related category• MATHEMATICIANS | |||||||

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