MathDB

Affine transformation with rectangles in the plane

Source: MIPT Undergraduate Competition 2019 2.3

August 17, 2020

geometryrectangletopologymappingsfunctions

Problem Statement

Let

A

and

B

be rectangles in the plane and

f : A \rightarrow B

be a mapping which is uniform on the interior of

A

, maps the boundary of

A

homeomorphically to the boundary of

B

by mapping the sides of

A

to corresponding sides in

B

. Prove that

f

is an affine transformation.