MathDB

A segment

d

is said to divide a segment

s

if there is a natural number

n

such that

s = nd = d+d+ ...+d

(

n

times). (a) Prove that if a segment

d

divides segments

s

and

s'

with

s < s'

, then it also divides their difference

s'-s

. (b) Prove that no segment divides the side

s

and the diagonal

s'

of a regular pentagon (consider the pentagon formed by the diagonals of the given pentagon without explicitly computing the ratios).

Problem Statement