The quadrature of the circle is a traditional problem of Mathématiques appearing in Géométrie. It belongs to the Three major problems of Antiquity, with the Trisection of the angle and the Duplication of the cube. In the oldest found mathematical text, the Papyrus Rhind (~ 1650 av. J. - C.), the Ahmès scribe proposed already an approximate solution of the problem. The Scientific first Greek to be been interested in the question was Anaxagore de Clazomènes.

The problem is to build a of the same square surface than a circle given using a rule and of a compass (see constructible Nombre). It goes back to the invention of the geometry and occupied of many mathematicians during the centuries. Gregoire of Saint-Vincent was impassioned by the problem: he wrote a work of: 1000 pages estimating - incorrectly - to have solved. It is in 1837 that Pierre-Laurent Wantzel shows a theorem which allows exhiber the form of the equations of the problems impossible to solve with the rule and the compass. But it will be necessary to await until in 1882 so that the German mathematician Ferdinand von Lindemann shows the transcendence π to apply the theorem of Wantzel to the problem of the quadrature of the circle and thus to show that it was impossible to realize. The Academy of Science, which had already had a presentiment of this result one century before, did not accept any more a “proof” of this squaring since 1775.

A solution of squaring requires the construction of the square Racine of $\ pi$, $\ sqrt \left\{\ pi\right\}$, which is impossible because of the transcendence of $\ pi$: indeed only certain algebraic numbers (whose rational ones and the irrational quadratic ones) can be built using a rule and of a compass.

This problem remained popular and of many quadrateurs amateurs send still today false evidence to the scientific academies.

## Metaphor

To seek the quadrature of the circle is an expression indicating an insoluble problem.

## See too

Simple: Squaring the circle

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