(March 7, 2022 at 2:39 am)Anomalocaris Wrote: The geometric demonstration of 6 identical square based pyramids with height equal to half of the sides fitting into a cube does not seem generalizable to pyramid with non-square bases or other height to base ratios.
For that, we need more general facts about what happens under expansion or contraction along different directions.
Or, you could compare corresponding rectangular figures approximating the two pyramids and compare the volumes of the approximations. This is close to what Archimedes would have done. It is *close* to calculus, but not there yet.
