Instead of doing productive work, I just spent a few enjoyable minutes

with Scilab finding approximations to pi of the form m/n.

Because I'm posting to a couple of nerd groups, I can be confident that

most of you probably know 22/7 off the tops of your heads.

What interested me is how spotty things are -- after 22/7, the error

drops for a bit until you get down to 355/113 (which, if you're at an

equal level of nerdiness to me will ring a bell, but not have been

swimming around in your brain to be found).

But what's _really_ interesting, is that the next better fit isn't found

until you get up to 52163/16604. Then things get steadily better until

you hit 104348/33215 -- at which point the next lowest ratio which

improves anything is 208341/66317, then 312689/99532. At this point I

decided that I would post my answers for your amusement, and get back to

being productive.

Discrete math is so fun. And these newfangled chips are just destroying

the joy, by making floating point efficient and cheap enough that you

don't need to know little tricks like pi = (almost) 355/113.

--

My liberal friends think I'm a conservative kook.

My conservative friends think I'm a liberal kook.

Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software

http://www.wescottdesign.com