Duncan, J.; Khavinson, D.; Shapiro, H. Rectangular parallelepipeds in ellipsoids. (English) Zbl 0865.51015 SIAM Rev. 38, No. 4, 655-657 (1996). 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) Cited in 1 Document MSC: 51N20 Euclidean analytic geometry 15A63 Quadratic and bilinear forms, inner products Keywords:rectangular parallelepipeds in ellipsoids; eigenvalues; quadric; principal axes PDFBibTeX XMLCite \textit{J. Duncan} et al., SIAM Rev. 38, No. 4, 655--657 (1996; Zbl 0865.51015) Full Text: DOI