N-sphere chord length distribution
share
This work studies the chord length distribution, in the case where both ends lie on a N-dimensional hypersphere (N ≥ 2). Actually, after connecting this distribution to the recently estimated surface of a hyperspherical cap SLi11, closed-form expressions of both the probability density function and the cumulative distribution function are straightforwardly extracted, which are followed by a discussion on its basic properties, among which its dependence from the hypersphere dimension. Additionally, the distribution of the dot product of unitary vectors is estimated, a problem that is related to the chord length.
READ FULL TEXT