Problem #PRU-61166

Problems Methods Examples and counterexamples Pigeonhole principle Pigeonhole principle (other) Set theory and logic Algorithm Theory Algorithm Theory

Problem

a) Using geometric considerations, prove that the base and the side of an isosceles triangle with an angle of \(36^{\circ}\) at the vertex are incommensurable.

b) Invent a geometric proof of the irrationality of \(\sqrt{2}\).