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A spheroid is an ellipsoid having two axes of equal length, making it a surface of revolution. By convention, the two distinct axis lengths are denoted a and c, and the ...

One of the three standard tori given by the parametric equations x = (c+acosv)cosu (1) y = (c+acosv)sinu (2) z = asinv (3) with c<a. The exterior surface is called an apple ...

One of the three classes of tori illustrated above and given by the parametric equations x = (c+acosv)cosu (1) y = (c+acosv)sinu (2) z = asinv. (3) The three different ...

A plane curve given by the parametric equations x = cost (1) y = sintsin^m(1/2t). (2) The plots above show curves for values of m from 0 to 7. The teardrop curve has area ...

A trochoid is the locus of a point at a distance b from the center of a circle of radius a rolling on a fixed line. A trochoid has parametric equations x = aphi-bsinphi (1) y ...

Let a vault consist of two equal half-cylinders of radius r which intersect at right angles so that the lines of their intersections (the "groins") terminate in the ...

A surface which can be interpreted as a self-intersecting rectangle in three dimensions. The Whitney umbrella is the only stable singularity of mappings from R^2 to R^3. It ...

As a consequence of Matiyasevich's refutation of Hilbert's 10th problem, it can be proved that there does not exist a general algorithm for solving a general quartic ...

The area of a surface or lamina is the amount of material needed to "cover" it completely. The area of a surface or collection of surfaces bounding a solid is called, not ...

There are a few plane curves known as "bean curves." The bean curve identified by Cundy and Rowllet (1989, p. 72) is the quartic curve given by the implicit equation ...