It seems that plenty of people think that Cavalieri’s theorem is being applied when doing a Cavalieri estimator. It’s not. Cavalieri’s theorem uses a comparison between 2 objects of the same height.

Think about it. When does anyone measure the height of the object that they are studying? There is no need to do that. There is of course an estimate of the height of the object, but no measurement. Cavalieri’s theorem requires two objects to be the same height. Not close to the same height or roughly the same height, but the exact same height.

Back in the 1950s it was well known that the 1902 paper describing the application of Cavalieri’s theorem had been incorrect. That’s long before the term stereology was coined.

Despite it being rather clear that the Cavalieri theorem does not apply (remember that no height measurements are taken or required) there are still those that incorrectly claim a link.