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April 27, 2024, 3:21 am UTC    
January 17, 2012 07:31PM
Hi Jammer,

Jammer Wrote:
-------------------------------------------------------
> But the Math Papyrus specifically shows a square
> that contained a circle with the circle touching
> the 4 sides @ midpoint of each and iirc the
> formula being the circle's area being 8/9ths the
> square.

No, RMP #50 shows the area of the circle is 8/9 diameter squared and when compared with the 5 1/2 seked it becomes evident the two are unrelated problems. The drawing I presented gives the relationship of the square and circle from a 5 1/2 seked perspective.

> It's been a whiule and I need relocate my notes,
> but WHY do you suggest they would deal with chords
> when their own records show they didn't?
>
> Jammer

Why not? The radius is equal to the chord of a hexagon 1/6 the circle. Radius * 6 equals the perimeter of the hexagon. i.e. example we find 36 is the perimeter of the square and circumference of the circle, 36 / 4 = 9 as the side of the square, and one quarter the circumference. 9/(11/7) = 63/11 or 5 8/11, 63/11 * 6 = 34 4/11, then 34 4/11 / 36 = 21/22 as the ratio between the length of the arc of the circle and the length of the chord of a hexagon. The chord length of a Pentagon is 98/121, which is (14/11^2 / 2) the arc 1/5 the circumference.

Regards
Jacob


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