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Egyptologists and historians of mathematics around 1930 did an admirable jobin showing that problem 14 of the newly discovered Moscow Papyrus from around1850 BCE amounts to a general and exact calculation of the volume of atruncated pyramid (frustum). They were less successful in giving tentativeexplanations of what convinced the Egyptians of its correctness. In particular,they never looked into the possibility of dissecting three identical copies ofthe frustum and recomposing them into three boxes of differing sizes whosevolumes can be easily calculated. This is surprising because the formula atwhich the historians arrived seems to suggest this procedure. About 2000 yearsafter the Egyptians, the Chinese scholar Liu Hui did exactly this for thealmost identical problem from the Nine Chapters. If those historians ofmathematics around 1930 had known Liu Hui's algorithm they could have easilydrawn tentative conclusions also for the Egyptian case. The present papersuggests that it was their knowledge of rigorous Euclidean geometry and ofrelatively modern algebra which distorted the judgment of those historians,something which could not have been the case for Liu Hui. Their failure seemsto have discouraged later Egyptologists to look for explanations or to evenpoint to Liu Hui when his work had become known. Thus a chance was missed touse the great intuitive and pedagogic potential of a remarkable piece ofEgyptian mathematics. This paper is not a contribution to the historiography ofEgyptian mathematics for which the author is no specialist but argues primarilyon a methodological level using secondary historical sources. The paper ispartly inspired by a more recent publication of Paul Shutler (2009) whosuggests an intuitive and historically possible proof also for the special, andmathematically crucial case of the second formula, which is related to the fullpyramid.

Intuitive, didactically useful, and historically possible proofs for the  two Egyptian pyramid volume formulas (1850 BCE). Thoughts on the border  between history and didactics of mathematics