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davepamn davepamn
 

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 M¢25  Funded By Mahalo ? |  November 08, 2009 03:51 PM

How can PI be derived without a computer?

What is a simple mechanical method for deriving the measurement of PI?
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kerryk kerryk
 
 November 09, 2009 12:37 AM
Pi is the ratio of the Circumference of the circle to the Diameter because C=Pi * Diameter

You can approximate the circumference by adding up the sides of a polygon with very many sides. A decagon has 10 sides. If you notice the shape of the decagon it is more closely shaped like a circle than the 6 sided hexagon and the 8 sided octagon. As you increase the number of sides, the shape more and more approximates a circle. If you have say 20 equal sides and add them all up, which is the perimeter of that shape and divide by the length of the diameter you will notice a much closer approximation for Pi than taking the perimeter of a regular decagon (a decagon with equal sides). 1,000 sides gives a better approximation. That isn't practical to do by hand though.

Decagon (10 sides)
http://thesaurus.maths.org/mmkb/media/png/Decagon.png

Icosogan (20 sides)
http://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Icosagon.svg/600px-Icosagon.svg.png

Chiliagon (1000 sides, notice looks like a circle)
http://upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Chiliagon.svg/424px-Chiliagon.svg.png
Asker's Rating:
• Are you suggesting the Egyptians estimated 1,000 triangle areas and then summed them in their minds? It still seems like a machine is required to accurately calculate PI.


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davepamn davepamn
 
November 10, 2009 08:17 PM
How did the Egyptians calculate PI

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silverhamm... silverhamm...
 
November 08, 2009 05:05 PM
By throwing frozen hot dogs?

http://www.wikihow.com/Calculate-Pi-by-Throwing-Frozen-Hot-Dogs

Manually using PI = 4 * (4 * atan(1/5) - atan(1/239))?

http://www.cygnus-software.com/misc/pidigits.htm

With a slide ruler?

http://www.hpmuseum.org/powerlog.jpg

http://www.hpmuseum.org/srinst.htm

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opher opher
 
November 08, 2009 06:48 PM
A crude method is as follows:

a. Make a circle.
b. Find its center (that's actually not a very complex geometric construction).
c. Run a straight line through that center.
d. Measure the circumference of the circle.
e. Measure the diameter (the part of the straight line from c above contained in the circle).
f. Divide the result of d by the result of c.

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davepamn davepamn
 
November 11, 2009 05:12 PM
You need a calculator or a machine to compute PI using this process. I found the process interesting. Thanks.

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opher opher
 
November 11, 2009 09:11 PM
Not really. You can use long division with a paper and pen.

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davepamn davepamn
 
November 11, 2009 10:14 PM
Could it be that simple?

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opher opher
 
November 11, 2009 10:26 PM
Yes. Simple, but not easy to carry out with great precision.

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