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Working paper

Affine transformations of circle and sphere

arxiv.org. math. Cornell University, 2016. No. 1607.05325.
A non-degenerate two-dimentional linear operator Ф  transforms the unit circle into ellipse.We define the coefficient of deformation k(Ф), as the relation of the lendth of the smaller ellipses axis to its bigger one. In this work we compute the mean value of k(Ф).Analogously, we define the deformation coefficient  k(Ф) in three-dimensional case and give an estimation of its mean value.