A Twist-Hinged Dissection of Triangles
This Demonstration shows a twist-hinged dissection of triangles showing that . The three main triangles pictured are equilateral. An equilateral triangle with side length has area , and the lengths of the sides of the three main triangles (check "show points" to see this) have side lengths 3, 4, and 5. The dissection shows that the sum of the areas of the two smaller triangles is equal to the area of the larger triangle. When you eliminate the factor from the equation, you obtain .
 G. N. Frederickson, Hinged Dissections: Swinging & Twisting, New York: Cambridge University Press, 2002 p. 240.