Search Results for ""

The mean tetrahedron volume of a tetrahedron with vertices chosen at random inside another tetrahedron of unit volume is given by V^_ = (13)/(720)-(pi^2)/(15015) (1) = ...

The harmonic parameter of a polyhedron is the weighted mean of the distances d_i from a fixed interior point to the faces, where the weights are the areas A_i of the faces, ...

The study of the probabilities involved in geometric problems, e.g., the distributions of length, area, volume, etc. for geometric objects under stated conditions. The ...

Given a simplex of unit content in Euclidean d-space, pick n>=d+1 points uniformly and independently at random, and denote the expected content of their convex hull by ...

Two lines in hyperbolic geometry which diverge from each other in both directions.

A type of point at infinity in which parallel lines in the hyperbolic plane intersect at infinity in one direction, while diverging from one another in the other.

A surface possessing a saddle point.

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...

A function f(x) is said to be constructible if some algorithm F computes it, in binary, within volume O(f(x)), i.e., V_(F(x))=O(f(x)). Here, the volume V_(A(x)) is the ...

A number taken to the power 3 is said to be cubed, so x^3 is called "x cubed." This terminology derives from the fact that the volume of a cube of edge length x is given by ...