For the sake of wrapping up the Pi argument I'm going to undertake the final situtation that is possible:
Cubit -
17 to 22 inches
Handbreadth -
2[size=-1].5[/size] to 4 inches
(All Measurements will be in inches until Pi is finally calculated)
All Cases are where the Diamter is measured from Outter brim to Outter brim and circumference is the Inner circumference:
The first thing that needs to be established is a range where Pi is close to being valid (Because under this circumstance a close value will be achieved).
There are two variables : The Converison factor used and the Handbreadth used. First lets consider the following observation:
As the conversion factor increases with a constant Handbreadth Pi very slowly decreases, Example:
CC = 17
HB = 2.5
Pi = 3.0909090909090909090909090909091
CC = 22
HB = 2.5
Pi = 3.0697674418604651162790697674419
This shows that it indeed drops, and not by much.
So what about HB?
CC = 17
HB = 4
Pi = 3.1481481481481481481481481481481
A nice increase by increasing the HB. (Pretty close value to PI)
Now this is where the problem arises. Notice the minimum CC with the Maximum HB yields a close value to PI. Therefore all CC values can yield close values with varying HB (Therefore I'll do two things):
First I'll fix the value of Pi to be exactly Pi and find out exactly the HB needed for each varying CC
CC = 17
HB = 3.83097902313
Fix HB = 4.00000
CC = 17.7500319342
CC = 18
HB = 4.05633073038 (Over the maximum HB Value)
CC = 19
HB = 4.28168243762 (Over the maximum HB Value)
CC = 20
HB = 4.50703414486 (Over the Maximum HB Value)
CC = 21
HB = Over the Value if pattern continues increasing, and it does. Check it.
CC = 22
HB = Over again. Check if you want.
After this only 17 passes the test, and maybe even 18 because it was so close.
Now I'll Vary HB and calculate the most favorable CC based on the true value of Pi:
HB = 2.5
CC = 11.0937699589 (Under the range of CC Values)
HB = 3.0
CC = 13.3125239507 (Still Under but increasing)
HB = 3.5
CC = 15.5312779425 (Still Under but closer)
(Now for alittle jump to where the CC value is exactly 17)
HB = 3.83097902313
CC = 17.000000000000
Any CC value In the range
17 - 17.7500319342 Will yield a HB within the acceptable range.
Any HB value above
3.83097902313 - 4.000 Will yield a CC within the acceptable range
Therefore without doing any further calculations it is
POSSIBLE to get the exact value of PI using these ranges in conjunction. It is only possible under the circumstance listed above.
Now one must ask : "Is this circumstance even supported by the context of the verse?"
Kings I 7:23
And he made a molten sea,
ten cubits from the one brim to the other; it was round all about, and his height was five cubits: and a
line of thirty cubits did compass it round about
and
Chronicles II 4:2
Also he made a molten sea of
ten cubits from brim to brim, round in compass ,and five cubits the height thereof; and a l
ine of thirty cubits did compass it round about.
The key words that make me question whether the inner circumference situtation could even hold true are the following : "
a line of thirty cubits did compass it round about."
When you measure "
ABOUT" something do you measure the inside? This seems to imply the circumference was measured as an
OUTSIDE CIRCUMFERNCE. If this is indeed true, which I'd be glad to hear proof otherwise, then there is one of two things possible:
The Diameter was also an outter to outter measurement meaning that the value of Pi would infact come right back to where we start : Pi = 3
OR
The diameter is an inner diameter, in which case it is
IMPOSSIBLE for Pi to be even greater than or equal to 3.
So one must consider the following : "Would the uncertainty of the converison factors of a cubit effect the Pi result even if both are measured outside?" Answer: No, they mathetical cancel out. Pi will remain exactly 3 under this circumstance.
Which brings me to the final point: "Could the uncertainty effect the Pi result under the Outer Circumference Inner Diameter situtation?" Answer: Yes and that is the final thing I'll look at.
In the first two posts I found that:
1. Lowest HB yields value nearest PI
2. Higher CC yields value nearest PI
So one can ask "Just how far outside the accepted range must we go to reach a reasonable value of PI?"
Good question lets find out:
By simple algebra and setting the PI value to an exact value of PI we find that the HB must equal exactly(Without accounting for converison factors):
HB = -.225351707243
You can't have a negative HB length.....therefore altering the HB range to satisfy the value of PI isn't a valid method.
Now doing the same for CC(Assuming HB = 2.5):
CC = -11.0937699589
Now assuming HB is 1.0
CC = -4.43750798356
Now assuming HB is 0.5
CC = =2.21875399178
Now assuming HB is .025
CC = -0.110937699589
Now assuming HB is .000000000000000000001
CC = -4.43750798356 E -21
Point? No matter how small you make HB CC will always be NEGATIVE (i.e. It is imposible for HB to work out)
So we must look to a combined effect. The closest that I got last time was:
(Cases relating to a constant value of 22 Cubits with varying Handbreathen)
HB = 2.5
Pi = 2.9333333333333333333333333333333
Therefore lets say 23 is the next factor
Pi = 2.9361702127659574468085106382979
Still very low!!!
Now lets jump to say 40
Pi = 2.962962962962962962962962962963
STILL VERY LOW!!!!!!
Lets try 150 now
Pi = 2.9900332225913621262458471760797
WE AREN'T EVEN AT 3 YET AND THE CUBIT CONVERISON HAS ALREADY SKYROCKETED TO 150!!! This is where it is pretty safe to say it isn't going to work out. The defintion of a cubit makes even 40 sound unreasonable, not to mention 150 Inches....