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Summer Session 12
August 10

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Construct a surface which appears as a triangle along the x-axis, appears as a triangle along the y-axis, apprears as an astroid along the z-axis and whose z-cross section are formed by ellipses. vrml

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Construct a solid which appears as an equilateral triangle along the x-axis, appears as a half-ellipse along the y-axis, appears as a circle along the z-axis.
vrml

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Construct the Klein bottle with parametric equations x = (a+cos(u/2) sin(v) - sin(u/2) sin(2v)) cos(u)
y = (a+cos(u/2) sin(v) - sin(u/2) sin(2v)) sin(u)
z = sin(u/2) sin(v) + cos(u/2) sin(2v)

vrml

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Construct the hyperboloid of two sheets given by the equation x² - y² - z² = 1.

vrml

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Construct the smallest sphere that contains the six circles each of which is inscribed in a face of a cube.
vrml

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Construct the part of the sphere x² + y² + z² =1 lying outside the cylinder (x - 0.5)² + y² = 0.25.

vrml

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Construct three tori of the same size each enclosing the other two.
vrml

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Show that a certain section of a cube consists of a hexagon.
vrml                         vrml

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Construct the surface given by the equation (x² + y² + z²)² = 2z(x²+ y²)

vrml                                     vrml

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Construct the surface given by the equation over the square [-2, 2] x [-2,2]. vrml Construct the same surface located above the disc
vrml

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Construct the graph of the function as (x,y) ranges over the unit disc.
 vrml

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Construct the solid enclosed by the paraboloids z = 5x² + 5y² and z = 6 - 7x² -y².

 vrml

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