Two Unusual Ways of Estimating PiDate: 03/24/97 at 21:55:10 From: Phydeaux Subject: Two Unusual Ways of Estimating Pi Hello, Dr. Math, I have to write a detailed five page report on the history of Pi and two ways to calculate it. The history of pi is no big deal to me. It's the ways to estimate pi that is bugging me. I have found the information on Buffon's needle problem but I'm looking for something VERY unusual. I've also discovered (through Buffon's needle problem) that pi is associated with things that don't have anything to do with circles or spheres. Help me out, please. As I said, I'm looking for two unusual ways to estimate pi. Muchas gracias, Tim Dwyer Date: 03/25/97 at 14:49:12 From: Doctor Steven Subject: Re: Two Unusual Ways of Estimating Pi Pi is defined as the ratio of the area of a circle to its radius squared. If you inscribe polygons with the same radius as the circle, then their area is smaller than the circle. Find the ratio of their area to the radius and you have an estimate that is too small for Pi. If you circumscribe polygons with the same radius as the circle then they have an area that is larger than the circle. Find the ratio of their area to the radius squared and you get an estimate that is too high for Pi. You've now squeezed Pi between two values. The more sides you add to your polygons the better the approximations, and the tighter the interval where you know Pi to be. (Hint: if you let the radius equal one then the area of the polygons should approximate Pi). The probability that an integer picked at random will have repeated prime factors is 6/PI^2. Using the 100 million decimal place expansion of Pi, take every 100 digits as an integer, find whether it has repeated prime factors. The proportion of integers that do should equal 6/Pi^2. Using this method "researchers" have found the value of Pi to about 20 decimal places. (Not a very useful approximation method for Pi, but a very neat one.) Hope this helps. -Doctor Steven, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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