MathDB

9. Lep

p

be a connected non-closed broken line without self-intersection in the plane

\varphi

. Prove that if

v

is a non-zero vector in

\varphi

and

p

has a commom point with the broken line

p+v

, then

p

has a common point with the broken line

p+\alpha v

too, where

\alpha =\frac{1}{n}

and

n

is a positive integer. Does a similar statemente hold for other positive values of

\alpha

? (

p+v

denotes the broken line obtained from

p

through displacemente by the vector

v

.) (G. 1)

Problem Statement