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General Chat / Pi
« on: March 24, 2003, 09:17:54 PM »
"what are you on?? you made the brilliand deduction that sin(Pi/x)x approaches Pi?? Holy sh!t you're a genius. how long did you play with your graphing calculator to figure that one out? and you should really signify where it approaches Pi. is it at 0, or 2, or Pi, or infinity?? What's the derivative of that function smart guy?"
Eh, was that sarcasm? I did figure that out, regardless of whether I was the first or not (I never saw an equation like that anywhere else). I'm not sure what you're trying to say here.
Anyway.. woo, math!
the formula is actually a simplified version of f(x) = sin(360/x/2)2x/2. It gives the perimeter of a regular polygon with x sides. I imagined triangles reaching out to each side from a central point, so that there are x triangles. Then, you divide 360 by x to get the angle of each of those congruent triangles nearest to the center... find the sine of that and double it to get the length of each side, multiply that by x to get the perimeter, and divide by 2 to get pi (2 is the diameter - for simplicity's sake, I have assumed a radius of 1)
Eh, was that sarcasm? I did figure that out, regardless of whether I was the first or not (I never saw an equation like that anywhere else). I'm not sure what you're trying to say here.
Anyway.. woo, math!
the formula is actually a simplified version of f(x) = sin(360/x/2)2x/2. It gives the perimeter of a regular polygon with x sides. I imagined triangles reaching out to each side from a central point, so that there are x triangles. Then, you divide 360 by x to get the angle of each of those congruent triangles nearest to the center... find the sine of that and double it to get the length of each side, multiply that by x to get the perimeter, and divide by 2 to get pi (2 is the diameter - for simplicity's sake, I have assumed a radius of 1)