Pi approximation games

Even the integer-only cortex M3s we use take less than a microsecond for most things. On a 72MHz STM32F2:

Double Precision: 0.415us / 49.852 cycles /multiply 0.378us / 45.403 cycles /add 2.414us / 289.702 cycles /divide Single Precision: 0.194us / 23.350 cycles /multiply 0.250us / 30.052 cycles /add 0.610us / 73.202 cycles / divide

Aha, good idea, we should standardize pi to a more convenient value! :)

(Didn't they already try that?)

I suppose the american inch was bigger...

As a physicist I found the classic approximations

pi^2 = g pi x 10^7 seconds in a year

quite handy to within 1% slide rule accuracy

Dunno what it is like now, but arctan(1) was a risky choice on some old machines as the series convergence was at its worst for that argument value and the tradeoff between accuracy and speed could cause trouble. You were at the mercy of the trig library if you did it this way.

Much prettier is 98765432/8 = 12345679 (exact)

It's in the eye of the beholder, but if you like that, how about

Yes, in one of those states where evolution is "just a theory", they made pi = 3 by law.

Wikipedia is often a great starting point for these sorts of things. It typically has enough information to give you some hints - but not so much that you can't have fun finding out more:

At university I remember a project that involved calculating all the digits of pi. It was written using a functional programming language (similar to Haskell) - the result was an unending list of the digits of pi. But since the language used lazy evaluation, it didn't bother calculating the entries until you tried to print them out. I used polynomial expansions of arctan() to do the sums.

So you are saying the inch is in fact metric?

David Brown schrieb:

Hello,

it is known since centuries that calculating all the digits of pi is not possible. Pi has an infinite number of digits.

Bye

Are you thinking of the Indiana State legislature with their 1897 legal attempt to define Pi with a Bill inspired by some very dodgy maths.

AFAIK 3 was one of the very few values it did not "define" pi to be. See for example the original article by Greenblat in SciAM 1965, p427 or the reproduction in More Random Walks in Science (p126)

The least bad bit defined pi = sqrt(10) exactly and elsewhere as 3.2

The worst implicit claim in the bill had pi = 4 (exactly) Says a lot about education in Indiana.

There is a spoof version about that blames Alabama.

Boasting again? ;)

Most imperial units are defined in terms of the metric units these days. Originally they were only rough definitions (I believe an inch was variously defined as the length from a thumb joint to the end of the thumb, or alternatively as the length of three grains of barley). Then they were a bit more standardised (such as the length of a particular metal rod). But now they use specific metric definitions - so an inch is precisely 25.4 mm - and will stay that way even if the definition of a millimetre varies!

The most relevant section, "working with infinite data structures", is missing - but I hope you get the point anyway.

mvh.,

David

Which is why a 1m pendulum has a half period of ~1 second using the classic formula two pi root ell over gee or:

l g / sqrt pi * 2 *

in RPN

Cheers

That is standard fare in continued fractions. Everybody interested in these kind of approximations should take a look at this fascinating subject.

It depends. Pi has been calculated to billions of decimals. Simple floating point doesn't get you there.

Groetjes Albert

--

There was a short PDP-8 assembly program that printed the digits of e forever.

In order ?

Mel.

ng

Grin... I always just let 2*pi =3D 10, so pi =3D 5!

(and then remember there's a 1.59 floating around)

George H.

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