### Pierre de Fermat - Wikipedia

Presentation on theme: "Pierre de Fermat."— Presentation transcript: He developed a close relationship with Blaise Pascal. Anders Hald writes that, "The . The Frenchman Blaise Pascal was a prominent 17th Century scientist, and correspondence with his French contemporary Pierre de Fermat and the Dutchman. Blaise Pascal was 17th century genius who invented the mechanical calculator. Pierre de Fermat is famous for a theorem that took three.

## Pierre de Fermat.

Logic and Memory I hate to admit it, but it was taxes that got it all started. Elder Pascal was constantly busy calculating and tabulating his potential tax haul. InKing Louis XIV granted Pascal a patent for his odd device but it failed to effect much change over the next 45 years. Pascal, by the way, would contribute more than a mechanical calculator to this tale. He proved that vacuums exist; that one could measure pressure by inverting a tube of mercury; and in figuring out how others could beat the house at gambling, ended up inventing probability theory.

Leibniz used something called a stepped drum, a cylinder with a number of cogs carved into it, and gears that would engage a different number of cogs depending on their position.

### Pascal - 17th Century Mathematics - The Story of Mathematics

It was incredibly complex, which is why very few were ever built. Inside a Pascaline or a Leibniz box were two simple elements needed to create the modern computer: Project Expressif you build it, they will comeinvention of the telegraphIsaac NewtonJohn Nash: He had been puzzled by the following dice problem.

Which is more likely: Gombaud believed the two events would occur equally often but could not prove it. He wrote to his mathematician friend Blaise Pascal, asking if this was indeed the case. To tackle the dice problem, Pascal enlisted the help of Pierre de Fermat, a wealthy lawyer and fellow mathematician.

Many of the new concepts would become central to mathematical theory. Other options, such as predicting which half of the table the ball lands in, were less sensitive to initial conditions. The co-efficients produced when a binomial is expanded form a symmetrical triangle see image at right.

Pascal was far from the first to study this triangle.

### Chevalier de Mere's Problem

But Pascal did contribute an elegant proof by defining the numbers by recursion, and he also discovered many useful and interesting patterns among the rows, columns and diagonals of the array of numbers. For instance, looking at the diagonals alone, after the outside "skin" of 1's, the next diagonal 1, 2, 3, 4, 5, The next diagonal within that 1, 3, 6, 10, 15, The next 1, 4, 10, 20, 35, It is also possible to find prime numbers, Fibonacci numbers, Catalan numbers, and many other series, and even to find fractal patterns within it.

Pascal also made the conceptual leap to use the Triangle to help solve problems in probability theory. In fact, it was through his collaboration and correspondence with his French contemporary Pierre de Fermat and the Dutchman Christiaan Huygens on the subject that the mathematical theory of probability was born.

## Chevalier de Méré's Problem

Some apparently quite elementary problems in probability had eluded some of the best mathematicians, or given rise to incorrect solutions. It fell to Pascal with Fermat 's help to bring together the separate threads of prior knowledge including Cardano 's early work and to introduce entirely new mathematical techniques for the solution of problems that had hitherto resisted solution.

His work on the Problem of Points in particular, although unpublished at the time, was highly influential in the unfolding new field.