Pierre de Fermat - Wikipedia
Pascal turned for help to Pierre de Fermat, a lawyer who was also a brilliant Nothing in relation to the infinite, everything in relation to nothing, a mean between .. “speculation” — literally, probability theory as applied to market speculation. Pierre de Fermat's Last Theorem celebrated in a cheeky Google doodle Through his close relationship with Blaise Pascal, a mathematician. Blaise Pascal ( – ) and Pierre De Fermat ( – ) also led to the development of what is known today as Efficient Market Hypothesis and related . There is, however, one great difference between the beauty of mathematical.
It is also possible to find prime numbers, Fibonacci numbers, Catalan numbers, and many other series, and even to find fractal patterns within it.
Pierre de Fermat
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. 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 His work on the Problem of Points in particular, although unpublished at the time, was highly influential in the unfolding new field.
The first of the two players say, Fermat and Pascal to achieve ten points or wins is to receive a pot of francs. But, if the game is interrupted at the point where Fermatsay, is winning 8 points to 7, how is the franc pot to divided? Fermat claimed that, as he needed only two more points to win the game, and Pascal needed three, the game would have been over after four more tosses of the coin because, if Pascal did not get the necessary 3 points for your victory over the four tosses, then Fermat must have gained the necessary 2 points for his victory, and vice versa.
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Pascal then looked for a way of generalizing the problem that would avoid the tedious listing of possibilities, and realized that he could use rows from his triangle of coefficients to generate the numbers, no matter how many tosses of the coin remained. Pascal and Fermat had grasped through their correspondence a very important concept that, though perhaps intuitive to us today, was all but revolutionary in This was the idea of equally probable outcomes, that the probability of something occurring could be computed by enumerating the number of equally likely ways it could occur, and dividing this by the total number of possible outcomes of the given situation.
Fermat was a trained lawyer making mathematics more of a hobby than a profession. Nevertheless, he made important contributions to analytical geometry, probability, number theory and calculus.
This naturally led to priority disputes with contemporaries such as Descartes and Wallis. Pierre de Fermat Fermat was the first person known to have evaluated the integral of general power functions. With his method, he was able to reduce this evaluation to the sum of geometric series. It was while researching perfect numbers that he discovered Fermat's little theorem. Fermat developed the two-square theoremand the polygonal number theoremwhich states that each number is a sum of three triangular numbersfour square numbersfive pentagonal numbersand so on.
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Although Fermat claimed to have proven all his arithmetic theorems, few records of his proofs have survived.
Many mathematicians, including Gaussdoubted several of his claims, especially given the difficulty of some of the problems and the limited mathematical methods available to Fermat.
His famous Last Theorem was first discovered by his son in the margin in his father's copy of an edition of Diophantusand included the statement that the margin was too small to include the proof. It seems that he had not written to Marin Mersenne about it. It was first proven inby Sir Andrew Wilesusing techniques unavailable to Fermat. Although he carefully studied and drew inspiration from Diophantus, Fermat began a different tradition.
Diophantus was content to find a single solution to his equations, even if it were an undesired fractional one. Fermat was interested only in integer solutions to his Diophantine equationsand he looked for all possible general solutions. He often proved that certain equations had no solutionwhich usually baffled his contemporaries. From this brief but productive collaboration on the problem of pointsthey are now regarded as joint founders of probability theory.
In it, he was asked by a professional gambler why if he bet on rolling at least one six in four throws of a die he won in the long term, whereas betting on throwing at least one double-six in 24 throws of two dice resulted in his losing. Fermat showed mathematically why this was the case.