UWEC CERCA 2025

Proven impossible by Pierre Wantzel in 1837 and Ferdinand von Lindemann in 1882, the classical problems of squaring the circle, doubling the cube, and trisecting an arbitrary angle using only a compass and straightedge have been of mathematical interest since Greek antiquity. Through advances in mathematics in the 17th-19th centuries, we discovered the set of constructible numbers in abstract algebra, which showed deep connections to our classic problems. We explore the constructible numbers, a field extension of the rational numbers, and the set of numbers discoverable using a straightedge and compass. In this talk we will present these classic geometric problems from ancient Greece, their history, and discuss how the set of constructible numbers relates back to the problems’ impossibility.