In mathematics, the Legendre forms of elliptic integrals, F(φ,k), E(φ,k) and Π(φ,k,n) are defined by Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse and were first studied by Giulio Fagnano and Leonhard Euler. ...
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The Legendre form of an elliptic curve is given by In mathematics, an elliptic curve is a plane curve defined by an equation of the form y2 = x3 + a x + b, which is non-singular; that is, its graph has no cusps or self-intersections. ...
Legendre's researches connected with the gamma function are of importance, and are well known; the subject was also treated by Carl Friedrich Gauss in his memoir Disquisitiones Generales Circa Series Infinitas (1816), but in a very different manner.
Legendre's theorem is a fundamental one in geodesy, and his contributions to the subject are of the greatest importance.
Legendre's name is most widely known on account of his Eléments de Géométrie, the most successful of the numerous attempts that have been made to supersede Euclid as a text-book on geometry.
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