Problem #PRU-61166

Problems Algorithm Theory Methods Examples and counterexamples. Constructive proofs Theory of algorithms (other) Pigeonhole principle Pigeonhole principle (other) Discrete Mathematics

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 \(\sqrt{2}\).