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Topic: RMP # 48
Replies: 70   Last Post: Jul 23, 2010 8:57 AM

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 Franz Gnaedinger Posts: 330 Registered: 4/30/07
Re: RMP # 48
Posted: Oct 6, 2007 10:18 AM

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

Date Subject Author
9/30/07 L. Cooper
10/1/07 Franz Gnaedinger
10/1/07 L. Cooper
10/1/07 Milo Gardner
10/1/07 L. Cooper
10/2/07 Milo Gardner
10/3/07 Milo Gardner
10/3/07 L. Cooper
10/3/07 Franz Gnaedinger
10/4/07 Milo Gardner
10/4/07 Milo Gardner
10/4/07 Milo Gardner
10/4/07 Milo Gardner
10/4/07 Milo Gardner
10/4/07 Milo Gardner
10/4/07 L. Cooper
10/5/07 L. Cooper
10/5/07 Milo Gardner
10/6/07 L. Cooper
10/6/07 Franz Gnaedinger
10/6/07 Milo Gardner
10/6/07 L. Cooper
10/6/07 Franz Gnaedinger
10/6/07 Milo Gardner
10/7/07 Franz Gnaedinger
10/7/07 Milo Gardner
10/7/07 Franz Gnaedinger
10/7/07 Milo Gardner
10/8/07 Franz Gnaedinger
10/8/07 Milo Gardner
10/8/07 Franz Gnaedinger
10/8/07 Milo Gardner
10/9/07 Franz Gnaedinger
10/9/07 L. Cooper
10/10/07 Franz Gnaedinger
10/11/07 Franz Gnaedinger
10/11/07 L. Cooper
10/12/07 Franz Gnaedinger
10/12/07 Franz Gnaedinger
10/12/07 L. Cooper
10/13/07 Franz Gnaedinger
10/13/07 L. Cooper
10/13/07 Franz Gnaedinger
10/15/07 Franz Gnaedinger
10/18/07 Ed Wall
10/19/07 Franz Gnaedinger
10/20/07 Milo Gardner
12/5/07 Milo Gardner
12/14/07 Franz Gnaedinger
12/14/07 Milo Gardner
12/14/07 Milo Gardner
10/11/07 Milo Gardner
10/12/07 L. Cooper
10/12/07 Milo Gardner
10/13/07 L. Cooper
7/11/10 Dioxippus
7/12/10 Milo Gardner
7/20/10 Dioxippus
7/21/10 Milo Gardner
7/21/10 Dioxippus
7/21/10 Milo Gardner
7/23/10 Dioxippus
7/23/10 Milo Gardner
10/6/07 Hossam Aboulfotouh
10/8/07 Milo Gardner
10/11/07 Hossam Aboulfotouh
10/12/07 Milo Gardner
10/13/07 Hossam Aboulfotouh
10/13/07 Hossam Aboulfotouh
10/19/07 Hossam Aboulfotouh
10/27/07 Matt Hugh