Equable Polygons and the Area of a Circle
Date: 10/30/2001 at 14:00:55 From: suzi-mary Subject: Area of circle and pi I have been researching equable regular polygons and have found a general formula to work out the length of side the polygon (of any shape) must have to be equable. Apparently this is closely linked to finding an equation for the area of a circle without using pi (and therefore proving pi). If you could help me in any way, I would be eternally greatful. Thanks.
Date: 11/01/2001 at 11:25:09 From: Doctor Roy Subject: Re: Area of circle and pi Hello, Thanks for writing to Dr. Math. The method is quite simple. Find the distance from the center of a regular polygon to any of the vertices. Call this distance r. Then calculate the area of the polygon. Find a relation between the area and r^2, and you will get an approximation for pi. I hope this helps. - Doctor Roy, The Math Forum http://mathforum.org/dr.math/
Date: 11/01/2001 at 12:49:32 From: Doctor Peterson Subject: Re: Area of circle and pi Hi, Suzi-Mary. I think what you have in mind may be the idea hinted at here: Finding a Circle's Area Without Pi http://mathforum.org/dr.math/problems/anna.2.24.01.html The formula for an area that doesn't use pi is A = Cr/2 where C is the circumference and r is the radius. This is also true for polygons, if you use the right "radius"; see this answer for more details on doing this with polygons, and also on what it proves about pi: Why Pi? http://mathforum.org/dr.math/problems/crystal.01.25.01.html Using this formula makes it easy to find the size of an "equable" polygon or circle! I hadn't thought of this approach myself. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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