Pierre De Fermat Was Born On August 20, 1601 In Southwestern France. The Son Of

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Term Paper Title	Pierre De Fermat Was Born On August 20, 1601 In Southwestern France. The Son Of
# of Words	1176
# of Pages (250 words per page double spaced)	4.7

     Pierre de Fermat was born on August 20, 1601 in southwestern France.  The son of a wealthy leather merchant he soon developed a great love for numbers and mathematics.  I chose to do this project about him because he is responsible for numerous theorems concerning probability, calculus, analytical geometry, and prime numbers.  Furthermore, he is also responsible for the creation of one of the greatest mathematical riddles of all time.

Probability, Calculus, and Analytical Geometry

     Fermat and Blaise Pascal established the probability theory still used today through their exchange of letters.  Driven by Pascal’s interest in a Parisian gambler’s problem concerning a game of chance, the two were certain to devise a set of mathematical rules that would accurately describe the laws of chance.   Together, they would begin to build a completely new aspect of mathematics, which is today known as probability.
     Fermat was also responsible for the establishment of calculus, long before Isaac Newton was even born.  Calculus, which is the ability to calculate the rate of change of two quantities respectively, as Fermat developed it helped scientists better grasp the concepts of velocity and other quantities.  It was Fermat that established the theorems that made the works of Isaac Newton, the “father of calculus”, possible.  In fact, until 1934 it was unknown that Newton had mooched Fermat’s theories to establish his law of gravity.
     Fermat was also responsible for the establishment of many basic rules of geometry.  He showed the any equation in the form xy=k^2 or in the form (a^2)+(x^2)=ky^2 can be graphed as a hyperbola.  He then showed that (a^2)+/-(x^2)=by is a parabola, that (a^2)-(x^2)=ky^2 is an ellipse, and that (x^2)+(y^2)+2ax+2by=c^2 is a circle.

Prime Numbers

     Fermat also had a unique fascination with prime numbers.  He had devised several theorems concerning the investigation of prime numbers.  A prime number is any number whose factors are only itself and one (for example: 5 is a prime number since it is only divisible by 1 and 5).  Fermat’s first theorem concerning primes was known as “Fermat’s lesser theorem”. In it, Fermat stated that integers in the form (2^2^n) +1 are always prime.  He made this assumption based on the induction of only five cases in which it worked (n=0, 1, 2, 3, 4).

Ex:   if n=1
        then (2^2^1)+1
                (2^2)+1
          4-1= 3
          3 is a prime number

This Theorem was proved wrong a century later by another mathematician,...

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