The ancient Greeks, being masters of geometric manipulation, often tried their hand at "squaring" various shapes. This involved using only the most fundamental rules of geometry to construct a square whose area equals the area of the original shape.
Can you follow in their footsteps and square a simple triangle?
The solution must hold for all types of triangles.
(In reply to re(2): Solution
by Old Original Oskar!)
All roads lead to Rome, or is it Alexandria? Your road is shorter and smoother, though. Crucial for both is "In a circle the angle in a semicircle is right" (Euclid Book III, Prop. 31). "In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle" is Book I, Prop. 47. Euclid does not treat similar triangles until Book VI, however.
Posted by Richard
on 2004-09-22 21:17:00