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MONKEY SADDLE
Cylindrical equation: Cartesian parametrization: Cartesian equation: Cubic surface. |
Surface shaped like a saddle that allows to place a monkey's legs but also its tail (the monkey is not the mount, but the rider!).
By the point O (which is a planar
point of the surface) there pass 3 real lines of the surface, forming
between one another angles of 120° (in red above): the point O
is an Eckardt point of the surface;
by the point at infinity of Oz, which is a singular point of the
surface, there pass the 3 other lines of the surface, that are also real,
but at infinity.
O is also an umbilic.
Generalization: surface with a saddle where end n
valleys and n mountains: The case n = 2 gives the horse saddle or hyperbolic paraboloid and the case n = 3 the monkey saddle. Proposition of name by Paul Micaelli: octopus saddle... |
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Other surface with 3 valleys, 3 mountains: |
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Surface with 4 mountains, 4 valleys, flat this time : |
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Compare to the Enneper
surface.
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© Robert FERRÉOL 2017