Surprising Cavalieri congruence between a sphere and a tetrahedron
We have seen that the areas of the sections in one sphere are:
The corresponding areas of the sections in the Howard Eves's tetrahedron are equal
Therefore, Howard Eves claims that
"Theorem 2. There exist a tetrahedrom to witch a give sphere is Cavalieri congruent."
The vertical cursor allows us to change the height of the section.
If we click and drag on the figure we can rotate it.
Howard Eves, mathematician and historian of Mathematics, received the George Polya Award for the article Two Surprising Theorems on Cavalieri Congruence.