This problem is giving me headaches for quite some time now I guess mainly because I am not a mathematician, but I would very much like to know if there is anyone here that has any deeper insight into this.
So, the Papyrus translation is given here. Additionally there is a discussion presented here on whether the translation of the object in question is correct. They say it could possibly refer to the area of a semi-cylinder.
That said, I am wondering if anyone knows how could these ancient Egyptians have derived this algorithm? There is a fraction omnipresent throughout this algorithm (1/9). What could that fraction represent? Is there any way we could explain this algorithm intuitively? I guess we can 'assume' that they didn't know calculus, so how?
P.S. I have asked this question already on Stack Exchange, but without satisfying results.
So to be more specific. The algorithm obviously works ignoring the small error compared to our current formula. They were very practical and didn't have sophisticated mathematical knowledge. So this is why I essentially want that whoever answers this forgets about our modern mathematics and thinks exclusively in the context of this algorithm and its operations to somehow make sense of this.