A Favourite Theorem
Theorem:
If
f
is a continuous map from
S
^{2}
to
R
^{2}
then there exists a point
x
in
S
^{2}
so that
f(x)=f(-x)
.
Why
do I like this theorem? A proof of this theorem is
here
.
Andrew D. Lewis (andrew at mast.queensu.ca)