Wendel's theorem
Encyclopedia
In geometric probability
theory, Wendel's theorem, named after James G. Wendel, gives the probability that N points distributed uniformly at random on an n-dimensional hypersphere all lie on the same "half" of the hypersphere. In other words, one seeks the probability that there is some hyperplane
intersecting the center of the hypersphere such that all the points lie on the same side of the hyperplane. Wendel's theorem says that the probability is
Geometric probability
Problems of the following type, and their solution techniques, were firststudied in the 19th century, and the general topic became known as geometric probability....
theory, Wendel's theorem, named after James G. Wendel, gives the probability that N points distributed uniformly at random on an n-dimensional hypersphere all lie on the same "half" of the hypersphere. In other words, one seeks the probability that there is some hyperplane
Hyperplane
A hyperplane is a concept in geometry. It is a generalization of the plane into a different number of dimensions.A hyperplane of an n-dimensional space is a flat subset with dimension n − 1...
intersecting the center of the hypersphere such that all the points lie on the same side of the hyperplane. Wendel's theorem says that the probability is
