Pascal's calculator

Pascal's calculator is a the mechanical calculator that Blaise Pascal invented in the early 17th century. Pascal's invention was called the arithmetic machine, Pascal's calculator, and later the Pascaline. Pascal was led to develop a calculator by the laborious arithmetical calculations required by his father's work as supervisor of taxes in Rouen. He designed the machine to add and subtract two numbers directly and to perform multiplication and division through repeated addition or subtraction.

Pascal designed the machine in 1642. After 50 prototypes, Pascal presented his first machine to the public in 1645. He dedicated it to Pierre Séguier, then chancellor of France. Pascal built around twenty more machines during the next decade, many of which improved on his original design. In 1649, King Louis XIV of France gave Pascal a royal privilege (similar to a patent), which gave him the exclusivity of the design and manufacturing of calculating machines in France.

Nine Pascal calculators, including the first surviving mechanical calculator to from the 17th century. See Competing designs below. Most of them are on display in European museums.

Blaise Pascal

Blaise Pascal (/pæˈskæl, pɑːˈskɑːl/;French: [blɛz paskal]; 19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, writer and Christian philosopher. He was a child prodigy who was educated by his father, a tax collector in Rouen. Pascal's earliest work was in the natural and applied sciences where he made important contributions to the study of fluids, and clarified the concepts of pressure and vacuum by generalizing the work of Evangelista Torricelli. Pascal also wrote in defense of the scientific method.

In 1642, while still a teenager, he started some pioneering work on calculating machines. After three years of effort and fifty prototypes, he built 20 finished machines (called Pascal's calculators and later Pascalines) over the following ten years, establishing him as one of the first two inventors of the mechanical calculator.

Pascal was an important mathematician, helping create two major new areas of research: he wrote a significant treatise on the subject of projective geometry at the age of 16, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. Following Galileo and Torricelli, in 1646, he refuted Aristotle's followers who insisted that nature abhors a vacuum. Pascal's results caused many disputes before being accepted.

Pascal's triangle

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients. In much of the Western world, it is named after French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in India,Persia (Iran), China, Germany, and Italy.

The rows of Pascal's triangle (sequence A007318 in OEIS) are conventionally enumerated starting with row n = 0 at the top (the 0th row). The entries in each row are numbered from the left beginning with k = 0 and are usually staggered relative to the numbers in the adjacent rows. Having the indices of both rows and columns start at zero makes it possible to state that the binomial coefficient appears in the nth row and kth column of Pascal's triangle. A simple construction of the triangle proceeds in the following manner: In row 0, the topmost row, the entry is (the entry is in the zeroth row and zeroth column). Then, to construct the elements of the following rows, add the number above and to the left with the number above and to the right of a given position to find the new value to place in that position. If either the number to the right or left is not present, substitute a zero in its place. For example, the initial number in the first (or any other) row is 1 (the sum of 0 and 1), whereas the numbers 1 and 3 in the third row are added to produce the number 4 in the fourth row.

Pascal

Pascal or PASCAL may refer to:

People

Places

In science and technology

Other uses