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semi-axes

ellipse and circles through end points of the semi-axes

Getting the semi-axes of an ellipse by differentiation of its graph functions – a simple step for a human, but not for ChatGPT 5.x ….

Some of my readers know that I am presently writing a book about Multivariate Normal distributions and related geometric properties of their level sets (multidimensional ellipsoids). For certain topics of the book, I sometimes use the latest free edition of ChatGPT to verify some claims and to get a list of respective papers. Sometimes also for a proof … However,… Read More »Getting the semi-axes of an ellipse by differentiation of its graph functions – a simple step for a human, but not for ChatGPT 5.x ….

n-dimensional spheres and ellipsoids – III – Surface area of n-dimensional ellipsoid and its relation to MVN-statistics

In the 2nd post of this series we have derived an explicit formula for the volume of a n-dimensional ellipsoid (in an Euclidean space). One reason for the relatively simple derivation was that the determinant of the generating linear transformation could be taken in front of the volume integral. Unfortunately, an analogue sequence of steps is not possible for an… Read More »n-dimensional spheres and ellipsoids – III – Surface area of n-dimensional ellipsoid and its relation to MVN-statistics