Originally Posted by Matthew Bacorn
Not your kind of math though. Normal 8th grader math
I haven't thought of anything that spectacular since the eighth grade. It was really kind of luck that I found it anyway.
d = 1
r = 1/2
a = r
b = r
c = sqrt(a^2 + b^2)
for i, as i goes to infinity
a[i+1] = c[i] / 2
b[i+1] = r - sqrt(r^2 - a[i+1]^2)
c[i+1] = sqrt(a[i+1]^2 + b[i+1]^2)
pi approx. = c[i]*4*2^i
Basically, it gives you the length of one side of a square for the first set of statements. When you go through the loop, it gives you one side of an octogon, then one side of a 16 sided figure, then one of a 32 sided figure, then one of a 64 sided figure, then one of a 128... etc. Multiplying that number by 4, 8, 16, 32, 64, 128,... etc. respectively will give you more and more accurate approximations of the circle's circumference. In this case, that's equal to pi, since d = 1.
Originally Posted by Derek Maffett
You must be studying to become an engineer or something similar, right? Ouch.
Physicist. Really, it's the easiest thing for me. That's just how I think.
For example, the other night, I was looking for a particular house, number 318, though I couldn't read the numbers on any of the houses because of the darkness, and I wasn't sure if I had passed it or not. So, I got out of the car, walked near to one house. Saw 308. Checked the next house down the street (in the direction of my travel) and saw it was 306. Therefore, dy/dx on that side of the street in my direction was equal to -2, a constant since house numbers are linear. So, 318 = -2x + 308, x = -5, and the house I wanted was 5 places in the opposite direction. I turned around, and counted the houses, 1, 2, 3, 4, 5. Number 318, bingo.
It's easy if you have the mind for it.