How to calculate pi

22nd July in UK speak is better = 22/7 = 3.1428...

Later DEC VAX hardware implemented 128-bit floats in hardware.

Mathematica handles arbitrary precision quite well. See the N[] operator.

Joe Gwinn

There's always a long line at Mission Pie on that day.

I'm baking a pi right now. I promised the neighbors some of the last one, but Certain Parties ate all of it. So I have a moral obligation to do another one.

Do you still say "four and twenty" ?

How about "fortnight" ?

Only when baking blackbirds into a pi.

Well, you did ask... ;-)

And there are FOSS multiple precision libraries if you want an unencumbered solution.

I opted to use BigRationals in the "calculator" interface that I export to users as it frees them from having to think about the math, significant digits, cancellation, etc. (but it is rather slow)

Pub food? At least it's a break from shepherd's pi.

I generally use REXX for that sort of thing--NUMERIC DIGITS can be anything you like (or don't mind waiting for). ;)

No arbitrary-precision built-in math functions though.

bc works too.

Cheers

Phil Hobbs

Am 11.07.21 um 22:33 schrieb snipped-for-privacy@highlandsniptechnology.com:

Shepherd's Pie? Found it only once on Island. There is no need to repeat the experience.

< >

Gerhard

Am 11.07.21 um 23:08 schrieb Gerhard Hoffmann:

In England and its colonies s/Is/Ice/

I only skimmed it, but didn't see any direct reference to Machin's formula, which I once used in a program to calculate Pi:

The expansion of arctan uses odd powers of 1/x, and Machin's formula has x=5 (as well as 239) so you get more than one extra digit of Pi for every extra term you evaluate.

There are many even faster-converging identities, but you can read about them all at the above page. The fastest ones (e.g. Jörg Uwe Arndt's) give you ten digits of pi for each additional term.

Clifford Heath.

The constant "pi" is defined as the smallest positive real number x such that e^(ix) = -1

Oh yes, but at that level it is allowable. Physics undergraduates by that stage know perfectly well that it is a coincidence. Not a good idea to use that crude an approximation in a practical exam though!

We were also allowed seconds in a year = pi x 10^7 in theory papers.

Which isn't in your teacher trolling table and is good to 0.5% or so.

That seems more than a bit overkill - no wonder they got into trouble.

I can count on the fingers of one hand the times when I have actually

*needed* to use quad precision (mostly for checking a double precision algorithm) and most physics problems can be solved in single precision. You seldom have 6 meaningful significant digits in real experimental data (although mass spectrometry is one place where you sometimes do).

I prefer Maxima through the wxMaxima GUI since it is free.

It isn't quite as powerful as Mathematica but it can still do the job if used carefully. It is easy to end up with mismatched brackets but apart from that it is fine and you really can't beat the price!

Only in dodgy antiquated blackbird pie recipes.

Fortnight is still in common usage.

I always had a slight admiration for IBM date/time formats:

20210722

Sorting by date becomes trivial if you do it their way. PITA with either UK or US formalisms.

One of the nastier requirements specifications tests we used to use for software quality improvement had US style dates in it (in the UK). It was astonishing how few people noticed they were MM/DD/YYYY format.

Ancestry is a bit of a PITA for this as they translate the month number into a name and a select few entries are MM/DD DD/MM transposes!

I've been wanting to switch from my current 20-year-old copy of Mathcad to something like Maxima running in a Jupyter notebook, but there's no supported way to do that at the moment.

Cheers

Phil Hobbs

And 22/7 takes care of almost all the rest.

Dan

We need double floats to do some numeric-ratio frequency synthesizer math.

Number theory, primes and relative primes and common divisor sorts of stuff, pop up now and then. The people who make frequency synth chips obviously have code to drive them (as in eval kits) but won't reveal it. PITA.

We have a new PLL that does hop-skip-jump sampling of one waveform from another clock. Sort of anti-equivalent-time sampling.