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Topic: Calculating Pi using polygon sides sum / radius
Replies: 40   Last Post: Aug 2, 2013 5:27 PM

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 William Elliot Posts: 2,637 Registered: 1/8/12
Re: Calculating Pi using polygon sides sum / radius
Posted: Jul 31, 2013 3:30 AM
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On Tue, 30 Jul 2013, jonas.thornvall@gmail.com wrote:

> If you create a hexagon with the radius of one, and recursively double the
> number of vertices of the hexagon(have same radius as side length)
> Maybe this is a valid way to calculate Pi?

Given a regular n sided polygon, with distance from center to the vertices
of r, the length of one side is 2r.sin pi/n and the total length of all the
sides is 2rn.sin pi/n =

Now lim(n->oo) 2r.pi.(sin pi/n)/(pi/n)
= lim(n->oo) 2r.pi.(sin pi/n)/(pi/n) = 2pi.r

For n = 6, sin pi/6 = 1/2, so 2*6r(1/2) = 6r is a crude first approximation
for the circumference of a circle of radius r, giving approximately 3 for pi.

Date Subject Author
7/30/13 JT
7/30/13 JT
7/30/13 Peter Percival
7/30/13 JT
7/30/13 Richard Tobin
7/30/13 JT
7/30/13 Peter Percival
7/30/13 JT
7/30/13 JT
7/30/13 JT
7/30/13 JT
7/31/13 William Elliot
7/31/13 JT
7/31/13 Peter Percival
7/31/13 William Elliot
8/1/13 JT
8/1/13 JT
8/1/13 Virgil
8/1/13 Virgil
8/1/13 JT
8/1/13 JT
8/1/13 Virgil
8/1/13 JT
8/1/13 Virgil
8/1/13 Virgil
8/1/13 Shmuel (Seymour J.) Metz
8/1/13 Virgil
8/2/13 JT
8/2/13 JT
8/2/13 Virgil
8/2/13 JT
8/2/13 Virgil
8/2/13 Brian Q. Hutchings
8/2/13 Brian Q. Hutchings
8/2/13 Virgil
8/2/13 JT
8/2/13 Shmuel (Seymour J.) Metz
8/1/13 JT
8/1/13 Virgil
8/1/13 JT
8/1/13 Virgil

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