/sci/ - Science & Math

Pic related is a pretty-good detail of 56 (top) through 60 (bottom). 59 (right) and 59B share the same row. You can blow it up bigger at page 14 of

http://www.f.waseda.jp/sidoli/MI314_02_Egypt_Babylon.pdf

Basically, these problems give us a hint of legit trig, and inverse trig at that!

A ROYAL CUBIT is a length unit, equal to 7 PALMS, another length unit. Fingers are involved later, but I'm going to look at the context of the other problems before I pronounce on the latter - wiki has been wrong with respect to units as they are used in Rhind more than once.

P.56: A (four-sided) pyramid is 250 (royal) cubits high, and the side of its base is 360 (royal) cubits long. What is its /seked/?

Ans: 360 is halved, to give 180. We then consider the right triangle in the interior of the pyramid, with (adjacent) leg 180 (royal cubits), running from the middle of a base to the bottom center of the pyramid, and (opposite) leg 250 (royal cubits), running from that point to its peak. The hypotenuse, immaterial to the problem, bisects a face of the Pyramid, but the angle theta that it forms with the adjacent leg, which is just the inverse cotangent of 18/25, is what we want.

There is a little dimensional analysis to express the seked first as "so many (royal) cubits", and later as "so many" palms, which I need to think about a bit more.