All posts by cclabtech

Sophie Germain

Sophie GermainSophie Germain2Sophie Germain was a French mathematician physicist and philosopher.

She was born on the 1 April 1776 at Paris and she died when she was 55 years old on the 27 June 1831 at Paris too .

Sophie Germain was the first and only woman who demonstrated Fermat’s Last Theorem or number theory.


There aren’t invalid integers x , and z such as :  xn + yn = zn  as soon as n is an integer strictly upper to 2.

In case n = 1, the equation xn + yn = zn corresponds to the usual addition.

In case n = 2, this equation has another infinity of not invalid solutions, the smallest of which is (3, 4, 5)  :   32 + 42 = 52

See also  Fermat’s Last Theorem


Pierre de Fermat

Pierrre de FermatPierre de Fermat was a great French mathematician who is given credit for early developments that led to infinitesimal calculus (the mathematical study of change).

He is best known for Fermat’s Last Theorem, which he described in a note at the margin of a copy of Diophantus’ Arithmetica.

Pierre de Fermat theorem

In number theoryFermat’s Last Theorem states that no three positive integers a, b, and c satisfy the equation :

an + bn = cn

for any integer value of n greater than 2.

The cases n = 1 and n = 2 are known to have infinitely many solutions since antiquity.

See also Sophie Germain


FibonacciLeonardo Fibonacci was born in Italy in 1175 and he died in 1250.

He lived in Algeria where he began his education with the mathematics. He popularized the Arabic numerals and algebraic notation.

The Fibonacci numbers sequence is a sequence of integers, in which every number is the sum of the previous two. Fibonacci numbers are intimely connected with the golden ratio φ.

Fibonacci sequence

Binet’s formula allows to calculate the terms of Fibonacci’s sequence without using the recursion.Fibonacci binet

We recognize the golden ratio φ and the other root of the equation occurring in this formula :Fibonacci golden ratio

With these notations, the Binet’s formula becomes :

Fibonacci binet2

A short video to learn more (in french) :