monkey saddle meaning in French
selle de singe
Examples
- A less trivial example of a degenerate critical point is the origin of the monkey saddle.
L'un des exemples les plus simples de point critique dégénéré est la selle de singe. - The point (0,0,0) on the monkey saddle corresponds to a degenerate critical point of the function z(x,y) at (0, 0).
Le point (0,0,0) sur la selle de singe correspond au point critique dégénéré de la fonction z(x, y) en (0, 0). - The monkey saddle has an isolated umbilical point with zero Gaussian curvature at the origin, while the curvature is strictly negative at all other points.
La selle de singe a un ombilic isolé avec une courbure de Gauss nulle à l'origine alors que la courbure est strictement négative pour tous les autres points. - In mathematics, the monkey saddle is the surface defined by the equation z = x 3 − 3 x y 2 . {\displaystyle z=x^{3}-3xy^{2}.\,} It belongs to the class of saddle surfaces, and its name derives from the observation that a saddle for a monkey would require three depressions: two for the legs and one for the tail.
En mathématiques, la selle de singe est une surface définie par l’équation z = x 3 − 3 x y 2 . - To show that the monkey saddle has three depressions, one can write the equation for z using complex numbers as z ( x , y ) = Re . {\displaystyle z(x,y)=\operatorname {Re} .} It follows that z(tx,ty) = t3 z(x,y) for t ≥ 0, so the surface is determined by z on the unit circle.
Pour montrer que la selle de singe a trois creux, soit l'équation complexe z telle que z ( x , y ) = Re ( x + i y ) 3 .