- #1

evalover1987

- 15

- 0

## Homework Statement

Let S denote a unit circle centered at origin in xy plane, and

f is a continuous function that sends S to R (no need to be 1 to 1 or onto).

show that there's (x, y) such that f(x, y) = f(-x, -y)

## Homework Equations

have a feeling it has something to do with theorems related to topology.

## The Attempt at a Solution

by re-writing S as (cos z, sin z) for 0 <= z < 2 pi

i can reduce f to a function of one variable, f(z), such that

f(z) = - f(z + pi), but then I'm stuck what to do after that.

(or maybe I shouldn't have reduced f to a function of one variable in the first place?)