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Rectangular parallelepipeds in ellipsoids. (English) Zbl 0865.51015

The authors give short elementary proofs for some geometric facts. We give an example: Let \(A\) be a real \(n\times n\) symmetric matrix with distinct eigenvalues. A general quadric is given by \(\langle Ax, x\rangle=1\). Then any rectangular parallelepiped inscribed in the quadric has its sides parallel to the principal axes of the quadric.
Reviewer: E.Ellers (Toronto)

MSC:

51N20 Euclidean analytic geometry
15A63 Quadratic and bilinear forms, inner products
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