This site contains an online textbook as well as other mathematical content. Created and run by Peter Saveliev.

Peter Saveliev

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Dr. Saveliev is a professor of mathematics at Marshall University, Huntington WV, USA. He has been involved in research in algebraic topology and several other fields.

Prior to his mathematics Ph.D. from the University of Illinois at Urbana-Champaign, he worked as an applied mathematician and software engineer at a large R&D institute in Moscow, Russia, on numerical methods of image matching for missile navigation/guidance systems. He also worked at a start-up company on an automated fingerprint identification system.

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Earlier this year I took a better look at the poster of Drawing Hands by Escher hanging in my office. What is depicted isn't symmetric! I decided to fix the problem and I call the result Painting Hands.

Correcting Drawing Hands by Escher

This illustrates how the antipodal map (aka the central symmetry) reverses orientation in the odd dimensions and preserves it in the even dimensions. That's why to be symmetric the original would have to have two right hands!

Note: I am frequently asked, what should "Saveliev" sound like? I used to care about that but got over that years ago. So, one can just read it as is; "Sav-leeeeeev" seems the most popular. Or, call me Peter.