Rabinoz says : "I think I'll stick to = 3.14159265358979 approximately"
>> Oh yeah? One method of pi: When calculating pi by composing little angled areas, there are a lot of "tiny umbrella areas" that are abandoned. So this means, the circle area MUST be MORE than PI.
That depends entirely on the method used. Read the method used by Archimedes in
Prehistoric Calculus: Discovering PiHe used this method starting with a square and
n = 4 and doubled
n each time.
With Archimedes' method we know that
(inner polygon perimeter) < π < (outer polygon perimeter)After a lot of work for:
n = 32 then
3.136548 < π < 3.15172 or 3.14414 and
n = 128 then
3.141277 < π < 3.14222 or 3.14175 already far better than smelly
Phew!
Now Archimedes did not have a calculator or trigonometric tables but he devised a method than did not need them so read the reference.
Read that references to see how you too can toss
Phew into the
Take back those tiny umbrellas and put those into calculation, and you'll get an area of PHEW :')
Keep you silly little umbrellas and your smelly
Phew and I'll use sweetly scented
π.