论文标题
直观，有用的有用，并且历史上可能的证据证明了两个埃及金字塔体积公式（公元前1850年）。关于历史和数学教学学之间边界的想法
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
论文作者
论文摘要
1930年左右的埃及学家和数学历史学家在表明新发现的莫斯科纸莎草纸的问题14左右在公元前1850年左右做出了令人钦佩的工作。他们在暂时解释了使埃及人正确性的暂时解释方面取得了较少的成功。特别是，他们从未研究过剖析三种相同副本的可能性，并将它们重新组合成三盒不同尺寸的盒子，它们的体积很容易被计算。这是令人惊讶的，因为历史学家到达的公式似乎暗示了此程序。埃及人大约在2000年后，中国学者刘·惠（Liu Hui）完全解决了九个章节几乎相同的问题。如果1930年左右的数学历史学家知道刘hui的算法，他们也可以为埃及案例得出暂定的结论。本文表明，正是他们对严格的欧几里得几何形状和相对现代的代数的了解使这些历史学家的判断扭曲了，这对Liu Hui来说并非如此。他们的失败似乎劝阻后来埃及学家寻找解释，甚至在他的作品变得众所周知时都指向刘海。因此，没有机会利用埃及数学的巨大直观和教学潜力。本文不是对埃及数学史学的贡献，作者不是专家，而是使用次要历史来源在方法论层面上争论。该论文的一部分是受Paul Shutler（2009）的最新出版物的启发，该出版物提出了与第二个公式的特殊和数学上关键案例的直观且历史上可能的证据，这与完整的金字塔有关。
Egyptologists and historians of mathematics around 1930 did an admirable job in showing that problem 14 of the newly discovered Moscow Papyrus from around 1850 BCE amounts to a general and exact calculation of the volume of a truncated pyramid (frustum). They were less successful in giving tentative explanations of what convinced the Egyptians of its correctness. In particular, they never looked into the possibility of dissecting three identical copies of the frustum and recomposing them into three boxes of differing sizes whose volumes can be easily calculated. This is surprising because the formula at which the historians arrived seems to suggest this procedure. About 2000 years after the Egyptians, the Chinese scholar Liu Hui did exactly this for the almost identical problem from the Nine Chapters. If those historians of mathematics around 1930 had known Liu Hui's algorithm they could have easily drawn tentative conclusions also for the Egyptian case. The present paper suggests that it was their knowledge of rigorous Euclidean geometry and of relatively modern algebra which distorted the judgment of those historians, something which could not have been the case for Liu Hui. Their failure seems to have discouraged later Egyptologists to look for explanations or to even point to Liu Hui when his work had become known. Thus a chance was missed to use the great intuitive and pedagogic potential of a remarkable piece of Egyptian mathematics. This paper is not a contribution to the historiography of Egyptian mathematics for which the author is no specialist but argues primarily on a methodological level using secondary historical sources. The paper is partly inspired by a more recent publication of Paul Shutler (2009) who suggests an intuitive and historically possible proof also for the special, and mathematically crucial case of the second formula, which is related to the full pyramid.
