Egyptisk matematik

Jeg sidder og roder med noget egyptisk matematik... og faldt over denne gennemgang af et gammelt egyptisk regne-eksempel, ud fra eksemplet kan konkluderes at egypterne havde en nærmere tilnærmelse af pi. Dette har jeg dog svært ved lige at overskue, og ville høre om der var nogen smarte hoveder der kunne hjælpe mig på vej.. :)

Find the volume of a cylindrical granary of diameter 9 and height 10.
Take away 1/9 of 9, namely, 1; the remainder is 8. Multiply 8 times 8; it makes 64. Multiply 64 times 10; it makes 640 cubed cubits. Add 1/2 of it to it; it makes 960, its contents in khar. Take 1/20 of 960, namely 48. 4800 hekat of grain will go into it.

Method of working out:

1 12
1 8
2 16
4 32
\8 64
\10 640
\1/2 320
TOTAL 960
1/10 96
\1/20 48

This is an example of estimating volume of cylinder of given diameter and height, and changing units from cubic cubits to measures of grain.

In order to obtain the volume of the cylinder, the scribe subtracts from the diameter its 1/9, squares the remainder, and multiplies by the altitude. In this way he finds that 640 is the contents of the granary, in cubed cubits. As a khar is is 2/3 of a cubed cubit he adds to 640 its 1/2, which gives him 960 as the number of khar in the granary. Finally, dividing by 20, he obtains 48 as the number of hundreds of quadruple hekat. Formula used is equivalent to V = (8/9)2 d2 x h = 64/81 d2 h

which gives the estimate p = 3.1605