Pi approximation games

How is that fraction, which symbolizes a mathematical operation and not an actual number, better than a stored constant???

That's where David Brown blew it -- when he wrote "it didn't bother calculating the entries until you tried to print them out". Without that, you can fall back on the idea that logical truths exist a priori, and argue that what's impossible is to *print* all digits of pi.

There's an argument about LISP that goes: it's easy to write a LISP interpreter in LISP such that the source code can be printed on a sheet of paper; it's also easy to quine that source code so that it's applied to itself; then you have a LISP interpreter executing on a sheet of paper. I/O bandwidth is the only problem. Maybe with e-paper ..

Mel.

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

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

George H.

________________________________________

1 + 1 = 3 for extremely large values of 1!

Shoulda been a congressman.

meter (m) "The metre is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second."

kilogram (kg)

"The kilogram is equal to the mass of the international prototype of the kilogram."

second (s)

"The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom."

Note that the kilogram is now the only one defined by a physical object. ("International prototype").

Let's define pi as in Euler's identity: e^i*pi + 1 = 0

--
Virg Wall

See:

"Meanwhile, only a few Americans know that the legal definitions of the English customary units are actually based on metric units. The U. S. and British governments have agreed that a yard equals exactly 0.9144 meter and an avoirdupois pound equals exactly 0.453 592 37 kilograms. In this way, all the units of measurement Americans use every day are based on the standards of the metric system. Since 1875, in fact, the United States has subscribed to the International System of Weights and Measures, the official version of the metric system."

--
Virg Wall, P.E.

Yes, that would be one way of saying it. Inches are now defined in terms of SI units, which have replaced "metric".

Steve

Yes total nerd :)

But who want to use your PY to calculate the circle circumference, with given diameter

???

(snip)

There are at least two projects to redefine the kilogram, such that it isn't dependent on a physical object.

One involves a more accurate determination of Avogadro's number.

-- glen

You might find fun at the opposite game too, have a look:

bye,

--

piergiorgio

That's known as a 'Selleck' or a 'Magnum PI'.

Cheers

--
Syd

This is cool.

I did this by hand recently...

One could also do the set of possible voltage dividers and corresponding opamp gains.

--

John Larkin         Highland Technology, Inc

jlarkin at highlandtechnology dot com
http://www.highlandtechnology.com

Precision electronic instrumentation
Picosecond-resolution Digital Delay and Pulse generators
Custom laser drivers and controllers
Photonics and fiberoptic TTL data links
VME thermocouple, LVDT, synchro   acquisition and simulation

Err... well it will give the correct result in a sufficiently curved space-time. I can't help it if people are using it in the wrong universe!

--

John Devereux

I was lazily going off a vague memory.

See:

According to the above, they go 3/1, 22/7, 333/106, 355/113,

103993/33102, 104348/33215, the next two you note, and then 833719/265381, well, try out the site.

(snip)

The javascript code for the above site, which says no license and free to copy, uses the following to do the computation:

var maxNumerator = getMaxNumerator(d); var d2 = d; var calcD, prevCalcD = NaN; for (var i = 2; i < 1000; i++) { var L2 = Math.floor(d2); numerators[i] = L2 * numerators[i-1] + numerators[i-2]; if (Math.abs(numerators[i]) > maxNumerator) return;

denominators[i] = L2 * denominators[i-1] + denominators[i-2];

calcD = numerators[i] / denominators[i]; if (calcD == prevCalcD) return;

appendFractionsOutput(numerators[i], denominators[i]);

if (calcD == d) return; prevCalcD = calcD; d2 = 1/(d2-L2); }

I haven't gone through it in detail, but you can see that it is pretty fast. Each is generated directly from the previous one, with no loop through successive denominators.

-- glen

Avogadro's number is currently: 6.02214129*10^23 entities per mole and has an uncertainty of plus or minus 27 counts in its last two digits.

Another requires the precise definition of Planck's constant which is:

6.62606957*10^?34 and has an uncertainty of plus or minus 29 counts in its last two digits.

I wonder if either or both of these "constants" can be defined as the ratio of integers. :-)

--
Virg Wall

Any uncertainty is an artifact of measurement. It's a *count*, so ...

Avogadro's Number is a natural number - so yes.

-- Les Cargill

Chuckle... That's great...

I was thinking that most of the time I let 1/2pi =3D 1.6/10 or pi =3D 10 x 5/16 which is better than 1%.

George H.