Pi approximation games

I like the idea that both 22 and 7 each fit into a byte whereas 355 does not. And, 22/7 is hi by only .04%. Beautiful!

John S

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:-)

Jack Crenshaw's book, "Math Toolkit for Real-Time Programming"

Suppose you do the same thing with the fine structure constant -- let me know what you discover.

Steve

I once knew pi to 100 places, but now I've forgotten everything past

My old HP35 calculators have a key for pi. The newer ones hide it, a tiny pastel shift key thing. So I just key in 3.14. Rob down the hall uses 3.

We are increasingly using floats in embedded stuff. Our ARM LPC3250 has SIMD hardware FP operations.

I learned to twin the first 3 odd digits - 113355. Then divide the first 3 into the last 3. Easily remembered. Art

but highly mnenomic - it's 2345678 with the 3 dropped and the 6 turned into a divide sign...

-- Les Cargill

Now you mention it :-)

You can always declare a constant or use pi=4*arctan(1) although I seldomly see the latter.

Here's something totally useless:

Off the subject, but this one is really funny...

That's mean - at the end "not all these are wrong" - several looked close (at least in my head).

Yes. It was the first problem in the book for the HP 25C calculator that I got many years ago.

There is an algorithm that some calculators use for converting a decimal result to a fraction. If I remember, that one easily finds successively better fractions approximating any given value.

I don't remember the details, but I do remember how funny it is, in that at one point it takes two fractions, and adds their numerators and denominators, before goint to the next step.

I believe it is described in the manual for one of the HP calculators that does that conversion.

Otherwise, I have the TI-92, which will generate fraction (rational) results, then you ask for an approximate result. Some calculations will give a symbolic pi result.

-- glen

I like this one

...

not quite m/n but

alpha = cos(pi*137)/137 * tan(pi*(29*137))/(pi*(29*137))

actually i think that sqrt(4*pi*alpha) = 0.30282212 is the more fundamental number than the fine-structure constant. the fine-structure constant should be thought of as a consequence of this number.

i've sent him some series that were simpler and better than his (at least those that were published at the time). i have no idea what rules of optimization he was using.

he wrote back. didn't see anything happen about it since.

We had a teacher that insisted it was exactly equal!