Three Classical Problems of Antiquity

Using only a straightedge and a compass

Three Classical Problems of Antiquity(using only straightedge and compass)

• Delian Problem (Doubling the Cube)• Squaring the Circle• Trisecting a Given Angle

Delian Problem: Delos

Delos’ Highest Hill

Terrace of the Lions

Rene Descartes (1596-1650)

Constructible Numbers: a is constructible if and only if there exist two points on a number line a units apart: (a,0) or (0,a).

Lemma: If a and b are constructible numbers, then a+b, a-b, ab, a/b are also constructible.

Lemma: Square roots are constructible numbers.

Pascal’s Triangle