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Surface-image from mathematica.

  1. Mar 21, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the parametric equations in the surface S therefore
    Z^2=1+x^2+y^2 and 2 ≤z ≤3
    and draw the image of the surface with Mathematica

    2. Relevant equations

    (below 3.)

    3. The attempt at a solution

    Use polar coordinates as parameters. The surface defined is part of a hyperboloid of two sheets. The condition 2 ≤ z ≤ 3 translates to 1 ≤ x² + y² ≤ 2 directly from the equation.

    So let x = r cosΘ and y = r sinΘ where 1 ≤ r ≤ √(2) and 0 ≤ Θ ≤ 2π. Then z = √(1 + r²). Express this as the vector valued function

    F(r, Θ) = r cosΘ i + r sinΘ j + √(1 + r²) k, 1 ≤ r ≤ √(2), 0 ≤ Θ ≤ 2π.

    I don't know how to use Mathematica to draw the surface.
    can anyone help me with it? I need a image of the surface from Mathematica.
     
  2. jcsd
  3. Mar 21, 2012 #2
    surface image
     

    Attached Files:

    • cone.pdf
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