# The quest for True Pi

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Tue 21 Oct, 2008 04:42 pm
Calculating Pi, Philosophy of Mathematics
Using the polygon method, mathematicians have been able to calculate Pi up to an ever increasing amount of decimal places. Last I looked it was measured correct to over a trillion decimal places. wikipedia.org/wiki/Pi

3.14159 26535 89793 is correct to 15 decimal places using the polygon method

Zu Chongzhi came up with this easy to remember rational ratio for Pi :
355/113 (correct to 6 decimal places) wikipedia.org/wiki/Zu_Chongzhi
which is 10 000 times more accurate than the well known :
22/7 (correct to 2 decimal places)

Wikipedia claims that the next best rational ratio for Pi is :
52163/16604 = 3.14159 23874
(correct to 6 decimal places) wikipedia.org/wiki/Zu_Chongzhi

With the aid of microsoft visual basic and my old 2003 entry level PC,
these ratios were discovered:

16 500 / 5 252 correct to 3 decimal places
8 800 000 / 2 801 127 correct to 8 decimal places
522 450 / 166 301 correct to 8 decimal places
208 341 / 66 317 correct to 8 decimal places
1 038 510 / 330 568 correct to 8 decimal places
30 750 000 / 9 788 029 correct to 9 decimal places
7 293 000 / 2 321 434 correct to 10 decimal places
24 491 250 / 7 795 807 correct to 12 decimal places

They have not been tested for all prime numbers, they may be simplified further. Its seems clear to me, that there are many more such ratios. And, with God's grace, you may even find the holy grail of mathematics : The perfect rational ratio for Pi.

I would just like to point out that the polygon method has two flaws. Firstly, with each iteration in the sequence, there is a rounding error. Secondly, true Pi would always be slightly bigger than a polygon with countless zillions of sides.

So how could we know if true Pi actually has been calculated? The only way to test it would be to build precision machinery that requires true Pi in order to function perfectly. We would then use any of the ratios that are higher than the best polygon calculation, and just see which one functions best.

from
Pi : Rational Ratios, Calculating Pi :shocked:

withawhy

Wed 22 Oct, 2008 02:38 am
@Poseidon,
A circle is an impossible shape. Pi is infinite.

:shifty:

Poseidon

Wed 22 Oct, 2008 04:11 am
@withawhy,
withawhy wrote:
A circle is an impossible shape. Pi is infinite.

:shifty:

I fear you may be right, but can you prove this?

withawhy

Wed 22 Oct, 2008 05:00 am
@Poseidon,
Pi is the explanation to why we have consciousness.

Unknown is why & how Pi entered the equation..

I've been thinking about pi recently, ill try to get you a more clear answer. I think more visually than mathematically, so youll probably find my answer unsatisfying

Khethil

Wed 22 Oct, 2008 06:37 am
@withawhy,
withawhy wrote:
Pi is the explanation to why we have consciousness.

Would you mind explaining, when you're able? I've simply got to hear this one.:popcorn:

Poseidon

Wed 22 Oct, 2008 11:43 am
@withawhy,
withawhy wrote:
Pi is the explanation to why we have consciousness.

Unknown is why & how Pi entered the equation..

I've been thinking about pi recently, ill try to get you a more clear answer. I think more visually than mathematically, so youll probably find my answer unsatisfying

Not at all! :phone:
I prefer visual thought to mathematical thought.
Its far more useful, creative and productive.
Math is mere mechanism.

Pi gives consciousness! :eek:
hmm.... now you got me going off on a real tangent ... well done! :bigsmile:

Resha Caner

Wed 22 Oct, 2008 02:49 pm
@Poseidon,
I can give you a rational ratio that is better than any you listed (accurate to 15 places) without even using a computer. It is:
3 141 592 653 589 793 / 1 000 000 000 000 000

Poseidon wrote:
And, with God's grace, you may even find the holy grail of mathematics : The perfect rational ratio for Pi.

It's a fun puzzle. I've played with it myself. But this is far from being the Holy Grail. Rather, it falls into the same category as proving Euclid's Parallel Postulate, trisecting an angle, finding a system that is both consistent and complete, and building a perpetual motion machine.

Poseidon

Thu 23 Oct, 2008 11:49 am
@Poseidon,
I was waiting for that one. :rolleyes:
Missed the point of it all a bit, methinks? :whistling:

The essence is simplicity : your example moves us no closer to true pi.

1043 / 332 (4 decimal places)

3173 / 1010 (4 decimal places)

Not that these are great examples.

But my computer program is getting more and more advanced, searching for sequences of numbers that have the ratios of prime dividers, next I'll try square roots.

Of course this is probably a wild goose chase, but as the saying goes : 'thats what wild geese are for'.

I'm still anticipating how pi gives us consciousness.

Perhaps it has to do with how the invention of the wheel must have boosted the idea of philosophy back in ancient Iraq?

I'm pretty sure that all the great thinkers have tried to find True Pi from time to time. In cricket terms its kind of like practising in the nets. It may not boost your average, but it keeps the mind sharp and focussed.

withawhy

Thu 23 Oct, 2008 02:30 pm
@Poseidon,
You are the beginning of God. your birth was your beginning. to get to the next level, all you have to do is believe. i dont know where you dont go, but i know you need to believe to move onto the next level. you want to know.. we all want to know. what happens to us after we die. pi equals infinite, infinite is impossible, nothing in our reality is impossible, therefore the knowledge of death is that. its pi. its impossible. impossible knowledge is impossible to ever learn. no matter how far down we go into our cells, how far out we go in space or how long we take pi. the circle is an impossible shape.

we can use drugs, meditation, conversations to reach the expanding wall, but we can never reach the next shelf until we die. the fun part, the reason we are all on this message board, its fun to try. its fun to reach closer down the numerical ever growing path of pi.

You are the beginning of god. your birth was your beginning. If the next doesnt exist yet, what does? consciousness before. billions of humans have died. what you enter is their mind. the mind of all conscious beings that have existed in our planet. the ever pressing push to keep expanding "IT"s consciousness. why does love feel good. why does an orgasm feel good. Consciousness is pushing to expand itself and those things are rewards for doing so. Philosophy, discovery, feel good to do. If PI ended, there would be no excitement left to see what was next. you can count up and try to reach infinite, we can even count down, but we will continue to get better and bigger numbers. there isnt a name for the end number because there isnt one. we can visually see something that doesnt exist. the circle doesnt exist anywhere in the universe. it is an impossible shape. everything to a certain extent is 3d. we live in a 3 dimensional world. as long as we dont have an answer to pi, there will be something impossible to find. the fact there is something impossible in a mathematically perfect world explains consciousness. there is something outside of our reality, something beyond this. mathematically there needs to be, because nothing is impossible, nothing is forever. we may never find pi, but the fact that we can try though, that is beautiful.

Poseidon

Thu 23 Oct, 2008 03:51 pm
@Poseidon,
That was well written.

But I think you describe a spiral,
which actually is a circle where the ratio between diameter and circumference is NOT equal to Pi.

!
But as for Pi,
and these Pi in the sky Ideas

damn it!

I am going to try and try and try !!!

(with a little help from my freind - visual basic)

withawhy

Fri 24 Oct, 2008 05:37 pm
@Poseidon,
a spiral is impossible to draw and impossible to find an end, so to me its less exciting.

from what ive read, pi is infinite. do you know if its infinite or just long?

Poseidon

Sun 26 Oct, 2008 08:53 am
@Poseidon,
well the claim is that Pi is infinite.
there has been no repitition of numbers down to the trillionth decimal !

but they are only looking from this angle, which seems to be presumptuous,
my algorithm is trying all the variations I can think of from
sin(pi) to square root of pi, with various divisors and whatever else I can shovel into the pc!

it probably is infinite, but how can we be so sure?

The intuition which leads me: is the perfect nature of pythagorus' triangle. Its just astounding that such perfection is in the universe, so it seems plausable that pi is also a perfect number.

its a wild goose chase, if ever there was one!

Poseidon

Sun 26 Oct, 2008 06:59 pm
@Poseidon,
Pi = Asin(sqr(.5))*4
(visual basic)

or

Pi = sin^-1(sqr(.5))*4

I calculated it this way.
I cannot seem to find any other reference to doing it this way.
At least wiki don't have it this way.

Resha Caner

Mon 27 Oct, 2008 10:41 am
@Poseidon,
Poseidon wrote:
I was waiting for that one. :rolleyes:
Missed the point of it all a bit, methinks? :whistling:

The essence is simplicity : your example moves us no closer to true pi.

No, I got the point. I think you missed the sarcasm of my reply. I understand the search for "simplicity". I would call it the search for "elegance".

So, in that regard, how many digits must one memorize with these fractions you are generating vs. the number of digits of pi that they produce? If an elegant fraction existed for pi, I expect it would have already been found. The number of digits in some of your examples goes beyond what I would consider elegant.

At one point it sounded as if you think the current calculation of pi may have an error in it. Maybe I interpret wrongly, but, regardless, that amused me.

Poseidon wrote:
Of course this is probably a wild goose chase, but as the saying goes : 'thats what wild geese are for'.

I like that. I'll add it to my list of handy quotes.

Poseidon wrote:
I'm pretty sure that all the great thinkers have tried to find True Pi from time to time. In cricket terms its kind of like practising in the nets. It may not boost your average, but it keeps the mind sharp and focussed.

Exactly. It's the challenge of solving the puzzle that has value: how do I calculate the digits of pi? If you think you're going to actually find a rational number ... well ... hmm ... I've got some magic beans that calculate pi. Would you like to buy them?

Poseidon wrote:
I'm still anticipating how pi gives us consciousness.

I took that as a joke, but if there's anything behind it, it might be a fun discussion.

Resha Caner

Mon 27 Oct, 2008 10:43 am
@Poseidon,
Poseidon wrote:
Pi = Asin(sqr(.5))*4
(visual basic)

or

Pi = sin^-1(sqr(.5))*4

I calculated it this way.
I cannot seem to find any other reference to doing it this way.
At least wiki don't have it this way.

Please tell me you're not using intrinsic functions in your "method". That's the computational equivalent of circular logic.

Poseidon

Tue 28 Oct, 2008 02:29 pm
@Poseidon,
Yes it is circular.
sin^-1 requires that we already know pi.

its a process, a quest, not an answer, but a mode for moving towards one.

Like I said its a wild goose chase.

I'll leave the sarcasm to the sarcastic.

withawhy

Tue 28 Oct, 2008 06:41 pm
@Poseidon,
Infinite and Perfection. Two words I sometimes feel are synonymous. Poseidon, good luck on your quest. I admire the way your mind works.

Poseidon

Wed 29 Oct, 2008 12:24 pm
@Poseidon,
Just a point on the circular 'logic' of maths.

Surely all math theory is circular?

eg 1+1=2 because
2=1+1

In fact, if the math your doing is not circular (reversible),
then it is by definition :

wrong.

Resha Caner

Wed 29 Oct, 2008 02:34 pm
@Poseidon,
Maybe I was too negative. Like I said, it's a fun puzzle.

But I don't think all math is circular. Circularity involves a proof in which you define what you're going to prove.

Circular and reversible are not the same.

So, have you played with the other natural irrational numbers? e? The Fibonacchi number? If you want to get philosophical, natural irrationals have some interesting implications akin to those of Godel's incompleteness theorum.

balhallah

Thu 18 Dec, 2008 03:53 pm
@Poseidon,
Why do you epxress Pi as a fraction? If it is to save on digits to remember, it seems a bit comical that some fractions listed contain more digits than the version of Pi they result in.

Is this a method used to search for more decimal places?

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