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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 (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