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math.MG2019★ 2 cited
Dual quadrangles in the plane
Irina Busjatskaja, Yury Kochetkov
We consider quadrangles of perimeter in the plane with marked directed edge. To such quadrangle a two-dimensional plane with orthonormal base is correspo…
math.MG2016
Affine transformations of circle and sphere
Irina Busjatskaja, Yury Kochetkov
A non-degenerate two-dimensional linear operator transforms the unit circle into ellipse. Let be the length of its bigger axis and -- the length of smaller. We can defi…
math.MG2016
Affine transformations of the plane and their geometrical properties
Irina Busjatskaja, Yury Kochetkov
In this work, oriented for students with knowledge of basics of linear algebra, we demonstrate, how the use of polar decomposition allows one to understand metric properties of non…