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Given two crossed ladders resting against two buildings, what is the distance between the buildings? Let the height at which they cross be h and the lengths of the ladders ...

In continuum theory, a dendrite is a locally connected continuum that contains no simple closed curve. A semicircle is therefore a dendrite, while a triangle is not. The term ...

A cone with elliptical cross section. The parametric equations for an elliptic cone of height h, semimajor axis a, and semiminor axis b are x = a(h-u)/hcosv (1) y = ...

An elliptic cylinder is a cylinder with an elliptical cross section. The elliptic cylinder is a quadratic ruled surface. The parametric equations for the laterals sides of an ...

A quadratic surface which has elliptical cross section. The elliptic paraboloid of height h, semimajor axis a, and semiminor axis b can be specified parametrically by x = ...

A coordinate system similar to toroidal coordinates but with fourth-degree instead of second-degree surfaces for constant mu so that the toroids of circular cross section are ...

A surface of revolution defined by Kepler. It consists of less than half of a circular arc rotated about an axis passing through the endpoints of the arc. The equations of ...

Flat polygons embedded in three-space can be transformed into a congruent planar polygon as follows. First, translate the starting vertex to (0, 0, 0) by subtracting it from ...

Prince Rupert's cube is the largest cube that can be made to pass through a given cube. In other words, the cube having a side length equal to the side length of the largest ...

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. This is the torus which is generally ...