converting parametric equation to a single equation is this possible? tia sal2

Discussion in 'Maple' started by temp, Dec 9, 2007.

  1. temp

    temp Guest

    Greets All

    I'm trying to find out how to convert the hopf Clifford parametric
    equation to a single equation. Do you know if this is possible?

    Clifford hopf torus
    x(u,v) cos(u+v)/(sqrt(2.)+cos(v-u))
    y(u,v) sin(u+v)/(sqrt(2.)+cos(v-u))
    z(u,v) sin(v-u)/(sqrt(2.)+cos(v-u))

    I found this doing some searching "Cartesian coordinates for a torus azimuthally symmetric about the z-axis"

    does this equation apply also?
    tia sal2
    temp, Dec 9, 2007
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  2. temp

    G. A. Edgar Guest

    eliminate u and v ... I get (using Maple)
    y^2+1-2*2^(1/2)*(x^2+y^2)^(1/2)+x^2+z^2 = 0 or
    y^2+1+2*2^(1/2)*(x^2+y^2)^(1/2)+x^2+z^2 = 0 a single equation
    y^4-6*y^2+2*x^2*y^2+2*z^2*y^2+1-6*x^2+2*z^2+x^4+2*z^2*x^2+z^4 = 0
    G. A. Edgar, Dec 9, 2007
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