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Math Help - Monkey Saddle

  1. #1
    Junior Member
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    Monkey Saddle

    By examining the behavior of x^3 - 3xy^2 on straight lines through the origin, show that the surface z = x^3 - 3xy^2 qualifies as a monkey saddle?

    Can someone explain how I would go about doing this problem? I'm very confused
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  2. #2
    MHF Contributor

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    Quote Originally Posted by messianic View Post
    By examining the behavior of x^3 - 3xy^2 on straight lines through the origin, show that the surface z = x^3 - 3xy^2 qualifies as a monkey saddle?

    Can someone explain how I would go about doing this problem? I'm very confused
    You should read this page, it is very inspiring as to what the surface looks like and why; the discussion after z(x,y)={\rm Re}(x+iy)^3 answers exactly your question, in slightly different terms.
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