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Re: RMP # 48
Posted:
Oct 6, 2007 10:18 AM
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Milo, the correct formulation is that math historians reading and
studying the Rhind Mathematical Papyrus found one single implicit
value of pi, namely 256/81. I discovered many more pi values in
the RMP, and they all have one thing in common: they are easily
generated with the algorithm of 'false additions' ...
Pi is less than 4 but a little bigger than 3. So begin with 4/1
and add repeatedly 3/1 in the way that was forbidden in school:
4/1 (plus 3/1) 7/2 10/3 13/4 16/5 19/6 22/7 25/8 28/9
By measuring out circles you may find that pi is slightly smaller
than 19/6. This allows another sequence starting with 3 in
the form of 9/3:
9/3 (plus 19/6) 28/9 47/15 66/21 ... 256/81
There you are with the value 256/81. In the same sequence
you find the value 66/21 that equals 22/7, and 22/7 is also
found in the first very simple sequence. Pi is more than 3
and slightly less than 22/7. If you know this you can go for
the best number sequence of false additions for pi:
3/1 (plus 22/7) 25/8 47/9 ... 333/106 355/113 377/120 ...
This sequence contains a lot of pi values for which I found
indirect evidence in the RMP. Using a lot of values around
the elusive exact value has a big advantage: you can choose
the value that comes handy in the context of a given calculation.
The accuracy achieved by this concept of irrational numbers
was sufficient for all practical and scientific purposes of the
ancient Egyptians.
Regards, Franz Gnaedinger
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