Don Barone Wrote:
-------------------------------------------------------
> Hi Graham ...
>
> Interesting that you mention 1/2 and 2/3rds which
> when added to gether gives us 7/6ths or 1.1666 and
> interestingly enough the square root of 10 is
> 3.1623 and the value of Pi in Ancient Egypt is
> said by some to be:
>
> ... Rhind papyrus Problem 50. A circular field
> has diameter 9 khet. What is its area.
>
> The written solution says, subtract 1/9 of of the
> diameter which leaves 8 khet. The area is 8
> multiplied by 8, or 64 setat. Now it would seem
> something is missing unless we make use of modern
> data:

Nothing was missing as they used a square grid to find the area by using a formula they had at hand, the area of a square formula. Since using the "area of a square" formula they had no need for a Pi value in solving the problem so nothing is missing.


> The area of a circle of diameter d is
> (d/2)2 =d2/4.

Say what? Now something is missing.

>Now assume 64 = 92/4 = 81/4, then
> = 3 + 1/9 + 1/27 + 1/81 ~ 3.1605.

81/4 = 20.25 so neither one of these equals 64.


But 3 + 1/9 +
> 1/27 + 1/81 is a number, presumably, intrinsically
> more pleasing to the egyptians than
> 3 + 1/13 + 1/17 + 1/160.

Well X + 1/X^2 + 1/X^3 + 1/X^4 does seem to flow easier into memory then the other value.

> So 2 + 1/2 + 2/3rds = ~ Pi
>
> So 2 + 1/2 + 2/3rds = ~ square root 10
>
> So ~ Pi = ~ square root 10

Close but not accurate enough for the AEs using the "couple inches over hundreds of RC" comparision argument. A better fit would be Pi equals the cube root of January(insert any month preferred with 31 days in it).


> However the best is still ... 355/113 = Pi !

Yeah it is a pretty accurate fraction though I don't remember seeing unit fractions with numerator other then 1 except 2/3rds and possibly 3/4ths.

Regards,
Lobo-hotei
lobo

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