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geometry > algebraic geometry > Diophantine geometry > Diophantine equation > Fermat's right triangle theorem
number > number theory > Diophantine geometry > Diophantine equation > Fermat's right triangle theorem
... > mathematical analysis > function > elementary function > polynomial > polynomial equation > Diophantine equation > Fermat's right triangle theorem
algebra > polynomial > polynomial equation > Diophantine equation > Fermat's right triangle theorem
mathematical analysis > equation > polynomial equation > Diophantine equation > Fermat's right triangle theorem

Terme préférentiel

Fermat's right triangle theorem  

Définition(s)

  • Fermat's right triangle theorem is a non-existence proof in number theory, published in 1670 among the works of Pierre de Fermat, soon after his death. It is the only complete proof given by Fermat. It has several equivalent formulations, one of which was stated (but not proved) in 1225 by Fibonacci. In its geometric forms, it states :
    - A right triangle in the Euclidean plane for which all three side lengths are rational numbers cannot have an area that is the square of a rational number. The area of a rational-sided right triangle is called a congruent number, so no congruent number can be square.
    - A right triangle and a square with equal areas cannot have all sides commensurate with each other.
    - There do not exist two integer-sided right triangles in which the two legs of one triangle are the leg and hypotenuse of the other triangle.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Fermat%27s_right_triangle_theorem)

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http://data.loterre.fr/ark:/67375/PSR-ZGKLC0BW-C

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RDF/XML TURTLE JSON-LD Date de création 28/08/2023, dernière modif. 28/08/2023