197/11 > 16, right?
Do this comparison for the entire sequence from 1-19, i.e. 12 to 102. What do you observe? There is no need to use a calculator btw and you don't even need to have memorized the squares. You simply add successive odd numbers starting with "1". You compute each circle as 11/14 of its corresponding square. 11/14 is the Great Pyramid's seqed.
Something odd happens at "17", ie the inscribed circle of a square of surface 81, doesn't it? A cross-over.
The surface area of a square with a base of 8 (64) virtually eclipses the odd number expansion's next square's inscribed circle's surface area, 635/8.
Which means that at 64/81 you get the best possible approximation to a circle's surface using this method. And this method is very well within the knowledge base described in the Rhind Papyrus. That's where 8/9 comes from: It's a short-cut! Drew was correct. The Rhind Papyrus is based on some information missing in it and no leap is required to draw that conclusion. In fact, the alternative, that 8/9 just came out of thin air, is much less plausible. The Law of Odd numbers is nothing more than successively adding two strips of cubits (similar to "Cubit Strips"; see Rhind 49) summing to the next higher odd number in the sequence to two sides of a square to obtain the next square in the expansion.
Yes, you guessed it: Galileo wasn't the first...
Edited 3 time(s). Last edit at 24-Jun-18 13:16 by Manu.