MathDB

Easy [contraction on the euclidean plane]

Source: Iran 2004

September 14, 2004

geometryfunctionperimetergeometry proposed

Problem Statement

f:\mathbb{R}^2 \to \mathbb{R}^2

is injective and surjective. Distance of

X

and

Y

is not less than distance of

f(X)

and

f(Y)

. Prove for

A

in plane:

S(A) \geq S(f(A))

where

S(A)

is area of

A

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