Thread: value of pi

Originally Posted by JDoolin

This is off by only .04% so it's a pretty good estimate.

When I first saw this estimate (22/7), I thought it was pretty hokey, but I have a newfound respect for it after looking for a better one

I can find a few with base of less than 100, which give slightly better approximations, but the massive improvement takes place with 355/113. This one is almost 5,000 times more accurate than 22/7.

Originally Posted by Clinton

The value of pi isn't necessarily 22/7 that's just a fractional expression that is relatively close and doesn't repeat just like pi.

Actually, rational numbers (fractions) do repeat when expressed as decimals or in any other base.

Originally Posted by Stu B

The real question is why would the ratio of the circumference of a circle to its diameter be irrational and not exact. Why couldn't the circumference of a circle be 1/3 of its diameter?

Why, indeed? And why not another ratio? Almost, as if it was designed that way.

And the version I remember is 3.1415926535 that was from the back of my old sliderule which took it out to about 35 places but I figured I'd never need more accuracy than 10 places that's also truncated not rounded.

Originally Posted by Homo bibiens

When I first saw this estimate (22/7), I thought it was pretty hokey, but I have a newfound respect for it after looking for a better one

I can find a few with base of less than 100, which give slightly better approximations,

You can't get any better than 311/99, 3 and 14/99, which is 3.14141414... of course

However, a nice bump comes at 333/106, which is 3.141509...

I also like the "binary" 201/64, which is a terminating decimal as well: 3.140625 exactly

but the massive improvement takes place with 355/113. This one is almost 5,000 times more accurate than 22/7.

The good ones come from the continued fraction for pi: 3;7,15,1,292,1,1,1,...etc.

22/7 = 3 + 1/7
333/106 = 3 + 1/(7+1/15)
355/113 = 3 + 1/(7+1/(15+1/1))

The next one is just not that pretty, because of that huge 292 bump.

There are many exact representations of pi available for computation.