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To pick a random point on the surface of a unit sphere, it is incorrect to select spherical coordinates theta and phi from uniform distributions theta in [0,2pi) and phi in ...

Let a cone of opening parameter c and vertex at (0,0,0) intersect a sphere of radius r centered at (x_0,y_0,z_0), with the cone oriented such that its axis does not pass ...

The curve formed by the intersection of a cylinder and a sphere is known as Viviani's curve. The problem of finding the lateral surface area of a cylinder of radius r ...

Let two spheres of radii R and r be located along the x-axis centered at (0,0,0) and (d,0,0), respectively. Not surprisingly, the analysis is very similar to the case of the ...

A planar embedding, also called a "plane graph" (Harary 1994, p. 103; Harborth and Möller 1994), "planar drawing," or "plane drawing," of a planar graph is an embedding in ...

An integral embedding of a graph, not to be confused with an integral graph, is a graph drawn such that vertices are distinct points and all graph edges have integer lengths. ...

A circular embedding is a graph embedding in which all graph vertices lie on a common circle, usually arranged so they are equally spaced around the circumference. Specific ...

An xyz embedding, also called an "xyz drawing," is a three-dimensional embedding such that every axis-parallel line contains either zero or two vertices. Such an embedding is ...

A lattice embedding is a one-to-one lattice homomorphism.

A graph embedding, sometimes also called a graph drawing, is a particular drawing of a graph. Graph embeddings are most commonly drawn in the plane, but may also be ...