Platonic Constructions
Plato's Rules
Plato’s rules for (straightedge and compass) construction
• Given two points, you can construct the line passing through them
• Given two points, you can construct the circle centered at one point and passing
through the other point [the “Circle with Center" tool].
• You can construct points of intersection of lines and circles [the Point tool]
Triangle Construction
Triangle Construction Proof
Consider an arbitrary segment labeled AB. Construct two circles centered at each point A and B with radii the distance between A and B. The radii of both circles is equal to the distance of the segment AB. One circle is centered at A with a radius of AB and the other circle is centered at B with the same radius. Point C is the point of intersection of the two circles. Point C is the same distance(AB) from both A and B because it is on the circle of both circles centered at A and B. All sides AB, BC, and BC are equal with the same distance between point A and B.