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

 Messages: [ Previous | Next ]
 Franz Gnaedinger Posts: 330 Registered: 4/30/07
Re: Discussion of error/mistake in Greek texts
Posted: Dec 14, 2007 2:28 AM

Milo, unit fraction series were not rounded, but one
can round the results of multiplications. My opinion
comes from actually working with unit fraction series.
An example. Let a square measure ten by ten royal cubits.
Draw a circle around it. How long is the circumference?
10 cubits are 70 palms. The first lines of the main
number column for calculating the square and octagon
1 1 2 / 2 3 4 / 5 7 10 / 12 17 24 / 29 41 58 / 70 99 140
provide the number pair 70 and 99. If the side measures
70 palms, the diagonal measures practically 99 palms.
The diagonal serves as diameter of the circle. So let us
look out for a suiting value of pi. It is found in a

3/1 (plus 22/7) 25/8 47/15 69/22 ... 311/99

If the side of a square measures 70 palms, the circum-
ference of the circle around the square measures 311
palms. Make a formula of this. If you know the side
of a square and wish to know the circumference of the
circle around the square, multiply the side by '70 of
311 or 4 '3 '10 '105. Imagine a circle around the base
of the Great Pyramid. How long would it be? The base
measured 440 by 440 royal cubits. Multiply 440 by
4 '3 '10 '105, round all results, and sum them up:

440 x 4 '3 '10 '105 = 1760 147 44 4, sum 1955

The circumference measures practically 1,955 cubits.
Exact value 1,954.868... rc, mistake 0.1315... rc,
not even seven centimeters on more than one kilometer.
For a better result transform the 440 cubits into
3,080 palms and do the same as before:

3080 x 4 '3 '10 '105 = 1230 1027 308 29, sum 13684

The circumference measures practically 13,684 palms
or 1,954 cubits 6 palms. Exact value 1,954 cubits
6.079... palms, mistake six millimeters on more than
one kilometer. Note that we carried out a demanding
calculation involving an algebraic irrational (square
root of 2) and a transcendental number (pi) with
integers only, apart from the unit fraction series
that served as a formula.

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