A Surface which a monkey can straddle with both his two legs and his tail. A simply Cartesian equation for such a
surface is

(1) |

(2) | |||

(3) | |||

(4) |

The coefficients of the first and second Fundamental Forms of the monkey saddle are given by

(5) | |||

(6) | |||

(7) | |||

(8) | |||

(9) | |||

(10) |

giving Riemannian Metric

(11) |

(12) |

(13) | |||

(14) |

(Gray 1993). Every point of the monkey saddle except the origin has Negative Gaussian Curvature.

**References**

Coxeter, H. S. M. *Introduction to Geometry, 2nd ed.* New York: Wiley, p. 365, 1969.

Gray, A. *Modern Differential Geometry of Curves and Surfaces.*
Boca Raton, FL: CRC Press, pp. 213-215, 262-263, and 288-289, 1993.

Hilbert, D. and Cohn-Vossen, S. *Geometry and the Imagination.* New York: Chelsea, p. 202, 1952.

© 1996-9

1999-05-26