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math.CO2013
On Crosspatch Knight's Tours
Nikolai Beluhov
A knight's tour is often represented as a broken line connecting the centers of successively visited squares. We say that two knight moves form a cross if the midpoints of their re…
math.MG2013
The Mixed Poncelet-Steiner Closure Theorem
Nikolai Beluhov
We state and prove a new closure theorem closely related to the classical closure theorems of Poncelet and Steiner. Along the way, we establish a number of theorems concerning coni…