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# Calculus surfaces (small)

With transparent film used to support the hyperboloid of two sheets.

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Not a Photo

Not a Photo

###### Digital Preview

Not a Photo

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.

#### Dimensions

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

Designer

henryseg says:
@natalia Awesome thanks!
natalia says:
@henryseg You're featured on our blog today http://www.shapeways.com/blog/archives/1903-Friday-Finds-Curate-our-Homepage.html

• ##### White Strong & Flexible

White nylon plastic with a matte finish and slight grainy feel.

##### henryseg

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