Affine transformations of circle and sphere
Abstract
A non-degenerate two-dimensional linear operator transforms the unit circle into ellipse. Let p be the length of its bigger axis and q -- the length of smaller. We can define the deformation coefficient k() as q/p. Analogously, if is a non-degenerate three-dimensional operator, then it transforms the unit sphere into ellipsoid. If p>q>r are lengths of its axes, then deformation coefficient k() will be defined as r/p. In this work we compute the mean value of deformation coefficient in two-dimensional case and give an estimation of mean value in three-dimensional case.
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