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.