Double Hearts Ratio Puzzle - Solution

Using the illustration below, we can calculate the following areas:

The red area is two circles, one of radius 3, the other of radius 2
Area of big red circle = π×3² = 28.27 (to 2 decimals)
Area of small red circle = π×2² = 12.57 (to 2 decimals)

So we have:

A(square) = 9 x 9 = 81
A(red) = 28.27 + 12.57 = 40.84
A(orange) = 81 - 40.84 = 40.16
Thus, A(red) > A(orange)

Author: Peter Grabarchuk
This Puzzle © 2008 Peter Grabarchuk. All Rights Reserved.