From: L' Ermit (lhermit@hotmail.com)
Date: Mon Jan 07 2002 - 13:00:43 MST
[Mermaid]People were religious. People prayed in Sanskrit. People who built
sacrificial altars need to know the value of Pi, even if it was handed down
from the Sulbasutras which were earlier handed down from Babylonian sources.
To remember a value, they had to remember it and what easier way for
priests-mathematicians-creators of sacrificial altars to Gods to remember a
numerical value than a prayer to a diety? I have laid my reasoning, logic
and sources bare and naked on the table. You havent. Neither has
Hermit...despite his screeching, he hasnt.
====
[Hermit] Ok. The PsychoBitch is advancing another mathematically inept
(ludicrous even) argument. Here's why. Let's build a <em>huge</em> "altar."
Say 100m in radius.
Now lets calculate the differences between PI to 18 digits (just because
this is the limit of precision for Excel) and the actual circumference as
calculated to various degrees of precision.
Precision PI Radius Delta Calculated Circumference to PI to 18 digits
0 3.00000000000000 600 28.31853072 28.31853072 metres
1 3.10000000000000 620 8.318530718 8.318530718 metres
2 3.14000000000000 628 0.318530718 318.530718 millimetres
3 3.14200000000000 628.4 -0.081469282 -81.46928204 millimetres
Below here, a 1 degree C thermal difference causes a greater difference
(20mm) in the circumference than the rounding of PI*
4 3.14160000000000 628.32 -0.001469282 -1.469282042 millimetres
5 3.14159000000000 628.318 0.000530718 530.717958 micrometres
6 3.14159300000000 628.3186 -6.9282E-05 -69.28204198 micrometres
7 3.14159270000000 628.31854 -9.28204E-06 -9.282042015 micrometres
Limits of physical measurement (using a micrometer)
8 3.14159265000000 628.31853 7.17958E-07 717.9579598 nanometres
9 3.14159265400000 628.3185308 -8.2042E-08 -82.04199275 nanometres
Limits of physical measurement (using laser inferometry)
10 3.14159265360000 628.3185307 -2.04204E-09 -2.042042979 nanometres
11 3.14159265359000 628.3185307 -4.20641E-11 -42.06412996 picometres
12 3.14159265359000 628.3185307 -4.20641E-11 -42.06412996 picometres
13 3.14159265358980 628.3185307 -2.04636E-12 -2.046363079 picometres
14 3.14159265358979 628.3185307 NA NA femtometres
15 3.14159265358979 628.3185307 NA NA femtometres
16 3.14159265358979 628.3185307 NA NA femtometres
Below the size of the nucleus of an atom
17 3.14159265358979 628.3185307 NA NA attometres
18 3.14159265358979 628.3185307 NA NA attometres
19 Limit of precision for Excel
*The coefficient of expansion for granite (which is a higly stable material)
between 30 and 300 C is 5.0-15.0 micrometers per degree C. So, taking the
median at 10 um.C^-1, by the time that we are using 3 digits of PI, on a
100m diameter theoretical alter, the 20mm difference in circumference caused
by a 1 C temperature change will dominate any differences caused by rounding
errors. Which is why suggesting that working to anything more than 2 digits
is ridiculous (real life does see temperature changes in excess of 10 C). It
is also why measuring PI to more than 3 digits would not yield a useful
result - it can only be calculated unless temperatures are also taken into
account - and the thermometer was only invented some two or three thousand
years after the Harrapans were around).
PS 100m radius altars were not common. Even a 10m altar would have been
unusual. Not even mythical giant Indian priests had arms long enough to
cover more than about 1.5 m in from the edge. <grin>
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This archive was generated by hypermail 2.1.5 : Wed Sep 25 2002 - 13:28:38 MDT