MathDB

Mapping of interior points of spehere and circle

Source: Romanian TST 2000

November 9, 2009

geometry3D geometryspherefunctioncalculustopologyanalytic geometry

Problem Statement

Let

S

be the set of interior points of a sphere and

C

be the set of interior points of a circle. Find, with proof, whether there exists a function

f:S\rightarrow C

such that

d(A,B)\le d(f(A),f(B))

for any two points

A,B\in S

where

d(X,Y)

denotes the distance between the points

X

and

Y

.
Marius Cavachi