Skip to content

n-ellipsoid

3-dim projections of 4-dim MVN

n-dimensional spheres and ellipsoids – IV – numerical check of Rivin’s formula for the surface areas of ellipsoids in 3 dimensions and the perimeters of ellipses

In the third post of this series we have discussed an idea of I. Rivin (see [1], [2]). Rivin has shown that the surface area of a general (n-1)-dimensional ellipsoid in a n-dimensional Euclidean space can be expressed in terms of an expectation value of a specific function weighted by a multivariate Gaussian probability density [pdf]. In contrast to (n-1)-spheres… Read More »n-dimensional spheres and ellipsoids – IV – numerical check of Rivin’s formula for the surface areas of ellipsoids in 3 dimensions and the perimeters of ellipses

Concentric surfaces of ellipsoids

n-dimensional spheres and ellipsoids – II – volume of n-ellipsoids

This post series provides some insights into the nature of n-dimensional spheres and ellipsoids and the derivation of some special integrals over their volumes. In this 2nd post we look at the volume of a “(n-1)–ellipsoid“. This term refers to a closed ellipsoidal surface in a n-dimensional Euclidean space. Such a surface is a (n-1)-dimensional manifold. See the 1st post… Read More »n-dimensional spheres and ellipsoids – II – volume of n-ellipsoids

n-dimensional spheres and ellipsoids – I – Gamma-function, volume and surface of n-spheres

This post series summarizes some properties of spheres and ellipsoids in a n-dimensional Euclidean space. In addition we are going to study some special integrals over the volume of so called n-spheres and their surfaces. As a preparatory step we look at some useful properties of the so called Gamma-function, which almost automatically appears when one works with integrals in… Read More »n-dimensional spheres and ellipsoids – I – Gamma-function, volume and surface of n-spheres