THE SIMPLEST PROOF THAT PHI IS IRRATIONAL

ZEHAVA YACHAS Student, Golda’s Ganon Nursery School, Ein Kesef

For any pair of positive integers (p, q) such that ϕ = p/q, where ϕ is the positive root of ϕ = 1+1/ϕ, there is yet another pair (q, p−q) with the same property, and whose sum is smaller. Since ϕ ≠ 2/1, there can’t be such a pair.