Calculus surfaces (small)

by henryseg
Calculus surfaces (small) 3d printed Mathematical Art With transparent film used to support the hyperboloid of two sheets.
With transparent film used to support the hyperboloid of two sheets.

This is a collection of common example surfaces from classes in multivariable calculus. Much larger versions of these surfaces are available here.

Contour lines, together with 8 radial curves make up the surfaces. All surfaces are plotted in such a way to show values of z in [-2,2]. The hyperbolic paraboloid is further cut along a cylinder of radius sqrt(2). The equations of the surfaces are:

  • Elliptical cone: z = +- sqrt(2x^2 + y^2)
  • Hyperboloid of one sheet: z = +- sqrt(x^2 + y^2 - 1)
  • Hyperboloid of two sheets: z = +- sqrt(x^2 + y^2 + 1)
  • Circular paraboloid: z = x^2 + y^2
  • Elliptical paraboloid: z = 2x^2 + y^2
  • Hyperbolic paraboloid: z = x^2 - y^2
  • Sphere: z = +- sqrt(1 - x^2 - y^2)
  • Ellipsoid: z = +- sqrt(1 - (x^2)/2 - y^2)

Note that the hyperboloid of two sheets is not connected. In the photo here I have propped them apart using a piece of overhead projector transparency sheet, rolled into a tube and secured with sticky tape.


IN: 4.471 w x 5.177 d x 2.07 h
CM: 11.356 w x 13.15 d x 5.258 h


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@natalia Awesome thanks!
February 1, 2013, 11:24 pm
@henryseg You're featured on our blog today
February 1, 2013, 10:26 pm


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