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• Monkey_saddle abstract "In mathematics, the monkey saddle is the surface defined by the equation It belongs to the class of saddle surfaces and its name derives from the observation that a saddle for a monkey requires three depressions: two for the legs, and one for the tail. The point (0,0,0) on the monkey saddle corresponds to a degenerate critical point of the function z(x,y) at (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.To show that the monkey saddle has three depressions, one can write the equation for z using complex numbers asIt follows that z(tx,ty) = t3 z(x,y) for t ≥ 0, so the surface is determined by z on the unit circle. Parametrizing this by eiφ, with φ ∈ [0, 2π), one can see that on the unit circle, z(φ) = cos 3φ, so z has three depressions. By replacing 3 with any integer k ≥ 1, one can create a saddle with k depressions.".
• Monkey_saddle thumbnail Monkey_Saddle_Surface_(Shaded).png?width=300.
• Monkey_saddle wikiPageID "812032".
• Monkey_saddle wikiPageRevisionID "605855562".
• Monkey_saddle hasPhotoCollection Monkey_saddle.
• Monkey_saddle title "Monkey Saddle".
• Monkey_saddle urlname "MonkeySaddle".
• Monkey_saddle subject Category:Multivariable_calculus.
• Monkey_saddle subject Category:Surfaces.
• Monkey_saddle type Artifact100021939.
• Monkey_saddle type Object100002684.
• Monkey_saddle type PhysicalEntity100001930.
• Monkey_saddle type Surface104362025.
• Monkey_saddle type Surfaces.
• Monkey_saddle type Whole100003553.
• Monkey_saddle comment "In mathematics, the monkey saddle is the surface defined by the equation It belongs to the class of saddle surfaces and its name derives from the observation that a saddle for a monkey requires three depressions: two for the legs, and one for the tail. The point (0,0,0) on the monkey saddle corresponds to a degenerate critical point of the function z(x,y) at (0, 0).".
• Monkey_saddle label "Affensattel".
• Monkey_saddle label "Apenzadel".
• Monkey_saddle label "Monkey saddle".
• Monkey_saddle label "Selle de singe".
• Monkey_saddle label "Обезьянье седло".
• Monkey_saddle sameAs Affensattel.
• Monkey_saddle sameAs Selle_de_singe.
• Monkey_saddle sameAs Apenzadel.
• Monkey_saddle sameAs m.03dqcq.
• Monkey_saddle sameAs Q382375.
• Monkey_saddle sameAs Q382375.
• Monkey_saddle sameAs Monkey_saddle.
• Monkey_saddle wasDerivedFrom Monkey_saddle?oldid=605855562.
• Monkey_saddle depiction Monkey_Saddle_Surface_(Shaded).png.
• Monkey_saddle isPrimaryTopicOf Monkey_saddle.