MathDB
Problems
Contests
National and Regional Contests
Iran Contests
Iran MO (3rd Round)
2004 Iran MO (3rd Round)
10
10
Part of
2004 Iran MO (3rd Round)
Problems
(1)
Easy [contraction on the euclidean plane]
Source: Iran 2004
9/14/2004
f
:
R
2
→
R
2
f:\mathbb{R}^2 \to \mathbb{R}^2
f
:
R
2
→
R
2
is injective and surjective. Distance of
X
X
X
and
Y
Y
Y
is not less than distance of
f
(
X
)
f(X)
f
(
X
)
and
f
(
Y
)
f(Y)
f
(
Y
)
. Prove for
A
A
A
in plane:
S
(
A
)
≥
S
(
f
(
A
)
)
S(A) \geq S(f(A))
S
(
A
)
≥
S
(
f
(
A
))
where
S
(
A
)
S(A)
S
(
A
)
is area of
A
A
A
geometry
function
perimeter
geometry proposed