How many different ways are there to determine Pi

How many different ways are there to determine Pi or a good an aproximation at least
Everybody know how to take a circles diameter and rap that around the circle


and you get
3.141592653589793238..........
But how about some other creative means medium or mode to add to the list of ways to solve

This thread had Pi and subtract Phi squared you'll get one cubit (Pi - Phi^2 = cubit).
which has to do with the Great Pyramid and its construction
www.abovetopsecret.com...

When i think of solving Pi in a rational way i came up with this




Pi (3.14159265...) can only be rational if you make 2 circles one inside the other put 2 on both sides of the inside one which is truthfully the same as the outer circle their both 0s right
The inside one just has a circle +1 and a -1 or -1, +1 or circle ( A ) and ( B ) the center one we will call ( O ) and the outer ( o ) So ( O ) = (o) but ( A ) and ( B ) do not equal ( o )
but each one A or B does equal ( O ) the center circle But ( A ) and ( B ) are polarities to the other

And inversely




You see Infinity is both within and without the ( O ) center circle and ( o ) outer circle making them 2 the same But one different the ones ( A ) and ( B ) are only different from ether ones + or - perspective if you use all the 3 inside circles radius ( A ) ( O ) ( B ) and across the big circle ( o ) and rap the central ( O ) with that you get 9.1428571428571428571428571428571... much more rational
Since its like triangulating the circle on a simple line graph

There must be more ways to break down a problem such as this so please throw them out there


And I'm not trying to say one is better then another or this is the right way and that's the wrong
Im just trying to gain some knowledge about one of the foundations of worlds

Meaning sometimes one way maybe better then the other but next problem it might be another because that depends on your situation and the venerable involved that are always changing

Like l know how averages work and finding a range it would be foolish to say the mode is the best way over the medium and mean to find your solution
Thats stupid because its always best to use all available means mediums and modes to help you out
and show the world that there is more then one way to slice a Pi



I'm a fan of ending with inspiring quotes

"Suddenly you’re awake. But where are you? Everywhere you look there’s white. White walls hug and confine you, stretching deeper and deeper, marking the boundaries of a straight, narrow, featureless hallway. You’re bewildered, but who wouldn’t be? Finally you stand and look behind you. All white, everything, going back to where it vanishes. You push against the hard white floor, swaying and almost losing your balance because you’ve been asleep so long. Looking ahead, you realize the hallway is not exactly like it was behind you. Almost the same, but not quite. Way, way in the distance you can see some specks. And, reasoning that specks are better than nothing, you begin walking toward them. It takes a long time, but then the specks grow and define themselves. They have become signs, gold in color and arrow-shaped. They hang at the end of the hallway, and you can see lettering on them. Closer and closer you walk, until you can see that there’s a second hallway perpendicular to this one. One arrow points left and reads: “Casino.” The other points right and reads: “Life.” Choose Life.-- "America's Mad Genius" Mike Caro

infosthetics.com...
pi in music

avoision.com...
pi10k

Your very own PI MUSIC MAKER!~

pi in colors
infosthetics.com...

have fun with the Pi music maker, it's awesome LOL!

The maybe oldest method to calculate pi by Archimedes(287-212 BC).

From geometrical considerations you can derive the following equations for the perimeters of circumscribed and inscribed regular polygons of a circle:

pci(n+1) = 2 * pin(n) * pci(n) / (pin(n) + pci(n))
pin(n+1) = sqrt(pin(n) * pci(n+1))

Use inscribed/circumscribed squares perimeters as start values:

pci(0) = 4
pin(0) = 2 * sqrt(2)

For faster convergence start with the perimeters of hexagons(Archimedes):

pci(0) = 2 * sqrt(3)
pin(0) = 3

Here is a statistical method, from memory...

Draw a square. Inside the square draw a semi circle with radius equal to the side of the square.

Throw darts at the square recording whether they are inside or outside the semi circle. The more darts the better.

Work out the ratio of darts inside or outside the semi circle and multiply by 4 to get PI.

Inspired by EasyPleaseMe:

Submerge a sphere with known radius into a container with a fluid and measure the displacement, calculate pi from it. It would work with a cylinder too. The limiting factor here would be the symmetry of the shape and the measurement.

Archimedes btw figured out that the volume of a sphere is 2/3 that of a circumscribed cylinder.

reply to post by IblisLucifer


There's always the simplest of the integration methods:

pi = 2*[int_0, inf](1/((x^2)+1))dx

You can approximate that with summation by taking it to as many terms as you like.

And, of course, there's the Gregory-Leibniz series:

pi = 4 - (4/3) + (4/5) - (4/7) + (4/9) - (4/11) + (4/13) - (4/15) + (4/17) - (4/19) + (4/21) - ...

reply to post by MESSAGEFROMTHESTARS


pi music rocks now we know where pop stars get their music

There is another method I can't quite remember using Fibonacci numbers and Phi. I'm sure google knows though...

reply to post by IblisLucifer


The appearance of Pi in the Giza pyramids design is most likely just an unintentional outcome of the way they made their measurements during the construction IE using a measuring wheel on a stick with Pi being the relationship of the wheel's circumference to its diameter (very simple). If a number of measurements are made using exact numbers of turns of the wheel, Pi will be evident all over the place even if you had no idea of its value or significance at the time.

In my early years in electrical engineering (pre calculators) I used a slide-rule extensively (Faber-Castel 2/83N engineering rule) and that was sufficiently accurate for the purpose back then when calculating resonant circuits, polar/cartesian conversion, machine characteristics etc. Graduating to early calculators that didn't have the constant built in required a little manipulation and the old school 22/7 was not quite up to the task for me precision-wise so I came up with 355/113 which is good to about 6 decimal places - sufficient accuracy for just about any computational task. Of course every scientific calculator now has Pi built in but, at first, there were no scientific calculators.

Pi = 3.141592654
22/7 = 3.142857143 good enough for elementary maths +0.04025% error
355/113 = 3.14159292 much better for more serious stuff +0.0000085% error

The nature of the Pi ratio means you can never have a precise value so must always settle for what's 'accurate enough' for the job at hand. There'd be very few applications requiring accuracy beyond 6 or 7 decimals unless you're into astrophysics or something similar.

The most beautiful thing about the golden number is after all the conjecture, arguments and toil there is simply one. The number is what it is, it is unchanging and the only way to "determine" it differently is to change other quantifiers, the number itself will always be constant.

reply to post by Pilgrum


If you really want to go nuts with double precision and long integers there's always:
312689 / 99532 = 3.141592653618936 (for 9.28e-10% error)

The best integer pair under a million is:
833719 / 265381 = 3.141592653581078 (for 2.77e-10% error)

The question is how accurate an 'estimation' is really needed for real-world applications?

Look up Count Buffon's Problem.

You can determine an estimate of pi with toothpicks. Recall doing this in high school physics.

reply to post by Pilgrum


Last one I promise

Wrote a little prog and streamlined it for fast results to the limits of IEEE 64 bit double precision maths on my PC and the results for the winners are:
Under 10 000 000: 5419351 / 1725033 = 3.14159265358982
Under 100 000 000: 80143857 / 25510582 = 3.14159265358979

Both of these are more accurate than my 12 digit calculator (matches the built-in Pi constant which has 1 or 2 digits beyond what can be displayed).