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). combinatoricscombinatorial geometry