Avraham (Rami) Aizenbud

אברהם (רמי) איזנבוד
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How to make a circle from a square by piecewise linear-conformal map?

 

download picture [jpg, fig]

Take a square.

download picture [jpg, fig]

Divide them into two parts.

download picture [jpg, fig]

download picture [jpg, fig]

Apply shift and homothety on each.

download picture [jpg, fig]

Combine them back...

download picture [jpg, fig]

... to obtain a circle.

This is a illustration of Cantor - Bernstein - Schroeder theorem and similar argumentation is used in Hausdorff - Banach - Tarski theorem.

Here is the Matlab code that generates those pictures.