Three Classical Problems of Antiquity Using only a straightedge and a compass.

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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 ( ) 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