Archimedes' proposal is based on covering all the parabolic segment by triangles, but how are this figures? Manipulate this applet and discover characteristics about the first triangle.[br][br][br]-   What is the height of the pink triangle? [br][br]- Is it possible to find a triangle with an AC base that has a bigger height than the pink triangle (this triangle has to remain inside the parabolic segment)? [br][br]- What is the area of the pink triangle? [br][br]- Is it possible to find a triangle with an AC base that has a bigger area than the pink triangle (this triangle has to remain inside the parabolic segment)? 

Well! You have discovered that Archimedes made the biggest triangle inside the surface. He used the same method to cover empty places and finally he got this construction.