I can't find anything in the literature explaining the formula for the volume of a truncated pyramid in relation to Horus-eye fractions.

There is a relationship which appears to have been overlooked which provides an insight into how the formula was understood, though not necessarily how the formula was discovered which I think could have been determined empirically.

The formula in the MMP is simply a quick method of determining the volume of a truncated pyramid. The formula can be 'proved' to be correct by selecting any random example of a truncated pyramid because the answer can be verified by long calculations. This is not the same as a geometric proof or a mathematical proof.

The Horus-eye fractions have hieroglyphs which can be assembled to form a pictogram that resemble parts of the eye of the falcon god Horus, as noted by Robins and Shute in their publication on the Rhind Mathematical Papyrus for the British Museum.

Is this a modern interpretation?

Did the ancient Egyptians ever put together the fractions in this way?

If the fractions explain the formula from a plan view then could it be that the hieroglyphs were chosen because the Egyptians believed that the falcon god Horus saw the plan view of a truncated pyramid (from directly above) as the plan of mean cross-sectional area?

Could it be that the formula for the volume of a truncated pyramid was regarded as the peak of ancient Egyptian mathematics so that the hieroglyphs had to be invented to celebrate the discovery?

The volume of a truncated pyramid is simply mean cross-sectional area multiplied by height, as is the formula for the volume of a pyramid.

The mean cross-sectional area of a complete pyramid is the same for every pyramid whereas that of a truncated pyramid has a variable ratio less than 1 but greater than 1/3 so the task was simply find a formula expressing the variable ratio which can then be shown to be the case from the erudite model of peculiar dimensions in MMP.

Why is the Egyptological literature silent on an ancient numerical solution based on mathematical tools known to be in the skill set of the ancient Egyptians?

The numerical solutions begs the question 'Why would it ever be wrong?' which is not quite the same as a mathematical proof which can never be disproved.

Mark



Edited 5 time(s). Last edit at 10/29/2020 03:11AM by Mark Heaton.