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fair history of civilization (logic of building and maintaining)
Posted:
Apr 8, 2011 2:57 AM
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Fair history of civilization including the one
of mathematics, logic of building and maintaining
On March 29/30 I wrote an open letter to the Swiss
minister Doris Leuthard on the topic of a fair history
of civilization. Last year, Doris Leuthard said on the
radio that Switzerland needs new projects. I wrote
her that I have one, a fair history of civilization
including the one of mathematics, logic of building
and maintaining. Our schoolbooks do as if geometry
and mathematics in general were a Greek invention,
but we owe them to Ancient Egypt and Mesopotamia.
There is a whole mathematical cosmos including
a systematic method for the calculation of the circle
below the level of Greek mathematics, worth being
explored and studied in its own right. A prospering
global society requires a fair history of civilization
that acknowledges all contributions and motivates
good people everywhere to join us in the task of
further developing our common civilization, and tackle
the big problems we are facing today, problems we
can't solve on our own.
(follows an introduction)
How long are the diagonals of a square? If the side
measures 5 paces or a multiple, the diagonal measures
7 paces or a multiple, and if the side measures 7 paces
or a multiple, the diagonal measures 10 paces or
a multiple, twice the original measurement ... This
practical formula may have done for a long time. But
then an Egyptian 'rope stretcher' would have asked:
what if the side measures 5 plus 7 units, can we expect
the diagonal to measure 7 plus 10 units? And really,
if the side measures 12 units, the diagonal measures
17 units, and if the side measures 17 units, the diagonal
measures 24 units, twice the original measurement.
The numbers 12 17 24 and their multiples are found in
the ground plan of the Djoser complex at Saqqara,
the work of the great Imhotep and his school. Going
further in the same way we obtain the line 29 41 58
and then 70 99 140, the latter numbers being present
in subsequent pyramids. Going both backward and
forward we can draw up a simple number column
whose first lines are 1 1 2 / 2 3 4 / 5 7 10 / 12 17 24 /
29 41 58 / 70 99 140 / 169 239 338 / 408 577 816 /
985 1393 ... Divide 1393 by 985 in the Babylonian
way and you obtain 1;24,51,10,3,2,... Let go the small
numbers and keep 1;24,51,10 which is the excellent
value for the square root of 2 mentioned on the
Babylonian clay tablet YBC 7289 from around 1650 BC.
You can start the number column with any line a b 2a
and even make mistakes, it will always approximate
the square root of 2. Having many values allows to
choose the one that comes handy in a given calculation.
You can operate whith entire numbers, and you can
partition a number. If the side measures for example
82 palms or 70 plus 12 palms, the diagonal measures
99 plus 17 equals 116 palms, with only a tiny mistake.
Moreover, the basic number column starting with the
line 1 1 2 (here given in linear form) has an exact
equivalent in the continued fraction for the square
root of 2, answering one more question of math history.
The simple method came first.
(to be continued)
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