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Pi: Pythagoras be Tripping

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posted on Feb, 23 2012 @ 08:24 AM
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"Of what use is your (Lindemann's proof of transcendental of pi) beautiful investigation regarding pi? Why study such problems when irrational numbers do not exist?" -Leopold Kronecker

And that right there is the problem: perfect circles do not exist, except in the human mind. There are some who think Pythagoras was snacking on Soma when he, uh, invented (sorry, I won't say discovered) Pi. A great many mathematicians throughout the centuries have been trying to find a way around using it. Bucky Fuller was able to cut Pi out of geometry altogether.


If you inscribe one triangle on a spherical system, you inevitably describe four triangles. There is a concave small triangle and a concave big triangle, as viewed from inside, and a convex small triangle and a convex big triangle, as viewed from outside. Concave and convex are not the same, so at minimum there always are inherently four triangles.

Background Nothingness: One spherical triangle ABC drawn on the Earth's surface inadvertently produces four triangles as the corners of the surface triangle are inherently related to the center of the Earth D, and their lines of interrelatedness together with the three edge lines of the surface triangle describe a tetrahedron. (See Fig. 812.03.) Drawing a triangle on the surface of the Earth (as described at Sec. 810) also divides the surface of the Earth into two areas__one large, one small__both of which are bound by a closed line with three edges and three angles. The large triangle and the small triangle have both concave and convex aspects__ergo, four triangles in all. Euler did not recognize the background nothingness of the outside triangles. (See Sec. 505.81.)

Under the most primitive pre-time-size conditions the surface of a sphere may be exactly subdivided into the four spherical triangles of the spherical tetrahedron, each of whose surface corners are 120-degree angles, and whose "edges" have central angles of 109 28'. The area of a surface of a sphere is also exactly equal to the area of four great circles of the sphere. Ergo, the area of a sphere's great circle equals the area of a spherical triangle of that sphere's spherical tetrahedron: wherefore we have a circular area exactly equaling a triangular area, and we have avoided use of pi .


There are many mathematicians who are advocating the replacement of pi with tau (another irrational number, but one that allows one to work more easily with real-world geometries). Here's an excellent, if dense article:www.math.utah.edu...

And this one's pretty great, too.

www.wired.co.uk...

And then there's these folks who attempt to prove that Pi is, indeed, rational:

webonastick.com...

Here's what I wonder: does basing your entire system of mathematics on a figmentary number some Greek genius pulled out of thin air while loopy on (maybe) amanita strike you as a little odd? Especially when there are ways to calculate real-world geometries without resorting to Pi?



edit on 23-2-2012 by Eidolon23 because: tidy that up some.




posted on Feb, 23 2012 @ 08:27 AM
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reply to post by Eidolon23
 


Thanks you for posting this, I find this totally interesting but way over my comfort level and skills set! Always good to try and learn new things.........even if it may take a while!

Will watch the video and properly read the articles later.
edit on 23-2-2012 by Flavian because: (no reason given)
edit on 23-2-2012 by Flavian because: (no reason given)



posted on Feb, 23 2012 @ 08:43 AM
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ok, so what about phi - the golden ratio? was davinci stoned too?
poussin? the architects of gothic cathedrals?!
perhaps the builders of the ancient pyramids didn't recognize pi the way we do today but the pyramids are right in front of us to proove the theory!
pi is the first letter in the greek for periphery
vitruvian man by da vinci is a good example of phi



posted on Feb, 23 2012 @ 08:45 AM
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a2 + b2 = c2




posted on Feb, 23 2012 @ 08:49 AM
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Originally posted by reficul
ok, so what about phi - the golden ratio? was davinci stoned too?
poussin? the architects of gothic cathedrals?!


Maybe.
No, I kid. I know, Pi works. Sort of. Well enough, anyway. Until it gets booted by Tau, which gives a greater degree of real-world accuracy.


perhaps the builders of the ancient pyramids didn't recognize pi the way we do today but the pyramids are right in front of us to proove the theory!


Or, like Bucky Fuller, they had other means of calculating dimensions.



posted on Feb, 23 2012 @ 08:49 AM
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To say that calculating algebra/physics becomes simpler by defining Tau = 2*pi is like comparing one apple to two apples - the crate is just as full, but the number you use to describe it is just half as large..

Tau is useless for everyone accustomed to calculators, working with formulas etc.
What would I win if I wouldn't calculate omega=2*pi*f but use omega=tau*f? Yeah, I didn't have to write a "2"! Naah, thats simply irrelevant.

The only positive point in exchanging 2*pi against tau: the publishing companies could print every engineering book again by substituting 2*pi.. Which is mentioned in those books A LOT...



posted on Feb, 23 2012 @ 08:53 AM
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So we're just supposed to dismiss a tried-and-proven idea that has not only existed for centuries, but has been, and is still being, used for thousands of jobs involving geometry?

Good luck with this.


Personally, I value phi more than pi, because phi has all sort of mysterious and universal occurrences. Pi is just a tool for calculation. Phi is math in nature, which is SUPPOSEDLY random. Hence, it introduces order in chaos and refutes arguments against divinity...

All in all, it's a very interesting number. What's not to like?
edit on CThursdayam343453f53America/Chicago23 by Starchild23 because: (no reason given)



posted on Feb, 23 2012 @ 08:59 AM
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Oh, I'm not anti-Pi. Sure, if it ain't broke, don't fix it. But can we obtain a reliable measurement of an object that exists by way of a number that doesn't?


I just had an interesting thought (that Pi is inherently broken), which I don't put any weight on; and though I suspected it would make for a highly inflammable topic, I thought it was worth discussing.

To the poster above you re: selling books. That is hilarious, and likely the case.
edit on 23-2-2012 by Eidolon23 because: Pi is a figment of your imagination.



posted on Feb, 23 2012 @ 09:36 AM
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reply to post by daaskapital
 



a2 + b2 = c2


1^2 +1^2 = Here we go again.



posted on Feb, 23 2012 @ 09:50 AM
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reply to post by Eidolon23
 


i love bucky balls!!!



posted on Feb, 23 2012 @ 09:52 AM
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reply to post by Eidolon23
 


Inherently broken.. Yes, pi is strange. But, as the impossibility to square the circle shows, it is no problem with our numbers in itself, that our way to count is incoherent.

It is a problem with the circle. Natures favorite form is not built for calculations.. Make from this what you want.. Even maybe (remember, we are on ATS: any thought is allowed) that the ability to calculate was never intended in this universe.



posted on Feb, 23 2012 @ 09:52 AM
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reply to post by Eidolon23
 


www.getbuckyballs.com



posted on Feb, 23 2012 @ 01:44 PM
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reply to post by Eidolon23
 


I don't know if this helps or lends insight or is even in the same ball park but...

I knew something was up when my math teacher started talking about getting 'pretty' numbers. Pretty numbers? Yeah, he said, the ones that aren't irrational or have an ugly decimal.

I have to stop there as I am currently struggling with math and this guy is a genius (my math prof.) and I will just make an ass of myself but...

It was food for thought. Because, for instance, I thought that if we tried to build a house using a calculator the thing would never get built. I believe that one would get their head so far up the butt of the minutiae, that just getting the first pieces fabricated would take lifetimes...

...and that made me think of a beloved teacher of mine. I study Chinese Cultural Arts with him. he said one day that all art, in order to be beautiful, had to be at least "a little bit not perfect, a little off".

I never forgot that, and it makes me think now of human beings making pretty numbers.

Thanks for another stimulating thread, Eidolon, you rock.

X.



posted on Feb, 23 2012 @ 02:35 PM
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Yo, empiricists and mathematicians. You are not going to like this, and I am fully expecting to get flayed, but...

Using infinity as a constant when obtaining finite measurements is just fubared. Further, having an imaginary number at the core of your discipline is no more valid than having an imaginary deity at the core of your theology. They have plenty of proofs for God too, you know.

Okay, spank those sturdy chargers, I'm ready to be drawn and quartered.
edit on 23-2-2012 by Eidolon23 because:




posted on Feb, 23 2012 @ 11:03 PM
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reply to post by Eidolon23
 

Leopold Kronecker was expressing a rather extreme opinion, much beloved of conspiracy theorists nowadays, but far from universally accepted among mathematicians. Kronecker famously believed that only integers exist, and 'all else is the work of man'.

This is one small facet of the larger question of whether mathematical quantities have an independent existence in nature, or whether they are human inventions.

Wherever you may stand on that, it is undeniable that the ratio of a circle's radius to its circumference is a fixed quantity and that quantity has the value 2π. You may be right that there are no perfect circles in nature (but are you sure? What about the wavefront from a point electromagnetic source in interstellar space, far from a gravity well?) Still, mathematics is about generalization, not about particular cases. Generally speaking, c/r –> 2π for any circle, and the formula may be relied upon for all practical purposes.



posted on Feb, 23 2012 @ 11:21 PM
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reply to post by Eidolon23
 


Using infinity as a constant when obtaining finite measurements is just fubared.

Of course it is. But π is not infinity. It is a finite number with a value of between 3.1415926535 and 3.1415926536. That's not infinity, that's just slightly more than three. The fact that the value cannot be absolutely stated in numerical calculations does not mean it is not fixed. A lot of people get the infinite and the indefinite mixed up.

Back in the day, a popular British teatime spread sported on its label the words 'Marmite keeps indefinitely'. The manufacturers weren't claiming the stuff would still be around long after the stars grow cold. They meant it didn't have a fixed period beyond which it would be unfit for consumption.


Further, having an imaginary number at the core of your discipline is no more valid than having an imaginary deity at the core of your theology.

π is not an imaginary number. Imaginary numbers contain some multiple of the square root of -1. π is an irrational number. It does not lie at the core of mathematics or even geometry – that core consists of the concept of number and basic arithmetical operations.



posted on Feb, 23 2012 @ 11:30 PM
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Originally posted by Eidolon23
And that right there is the problem: perfect circles do not exist, except in the human mind.


So? It doesn't have to be perfect to need a good value of pi:
www.guinnessworldrecords.com...

The most perfect manmade spheres constructed to date are the fused solid quartz gyroscopic rotors built for NASA's Gravity Probe B spacecraft. There are four spheres onboard, each measuring 3.81 cm (1.5 in) across. Their average departure from mathematically perfect sphericity is 1.8 X10-7 of the diameter. This means that, if scaled up to the size of the Earth, the maximum height/depth of topographic features would be 1.5 m (4.92 ft).
How many triangles do you think you need to not use pi and get that accuracy?

For simple calculations I do truncate a lot of digits of Pi and that's usually close enough...but in some cases more accuracy may be needed.



Originally posted by Eidolon23
There are many mathematicians who are advocating the replacement of pi with tau (another irrational number, but one that allows one to work more easily with real-world geometries). Here's an excellent, if dense article:www.math.utah.edu...
Oh it's dense alright, in this meaning of the word:

dense:

a : slow to understand : stupid, thickheaded


Not very compatible with "excellent". Make it simple:

Yes the circumference of a circle is 2*pi*r, so what?

The formula is also pi*d and there's no 2 in that formula.

So if we used tau, the formula would be tau/2 * d

You've still got a 2 in there. Using tau doesn't eliminate that, in fact it creates it, there was no 2 there before.

Pretty silly idea.



posted on Feb, 23 2012 @ 11:42 PM
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Thanks, guys. I am grateful to you for dropping by and throwing down. That wasn't nearly as bad as I expected, and I particularly appreciated Astyanax drawing the distinction between the infinite and indefinite.


Say, did anyone actually visit the "Pi is a rational number" page? Because it is wicked funny.



posted on Feb, 24 2012 @ 01:41 AM
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reply to post by Eidolon23
 


Its all make believe none of it exists outside there paradigms, or even in there paradigms it does not exactly exist if you just keep digging and asking those dreaded questions of why and how. It's all in there heads really, like everything else.

Nothing is perfect, if it was perfect it would not be in this fragmented existence.

And that's why nothing is the only thing that is questioned in its existence, fragment by fragment nothing is eventually found to be something. Does nothing exist? Nothing must exist, or else everything would be something. And if everything is something.... Well that's just crazy talk, because it's obvious nothing really exists.

Math is evilz, boooo, I would throw some tomatoes at it and this thread. But I ate them... No flag from me, only a star, and only because for some reason my trigger finger moved by itself, without my expressed permission, before I had a chance to stop it, like it was possessed or had a mind of its own.

But now that I have snapped back to my senses! I go to say that I much prefer pie to either pi or phi.



posted on Feb, 24 2012 @ 04:03 PM
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reply to post by Eidolon23
 


Huh, well its based on a 10 digit number system. You can choose and create any number system you like.

en.wikipedia.org... en.wikipedia.org... is a scream.

So let me ask this rhetorical question, "In a 14 digit number system would 7 be considered rational? 7 would be simply moved to the 5 value in place in the 10 digit number system within a 14 digit number system, but how about a 21 digit number system? library.thinkquest.org... Both seem to be trapped within a constant, but use a decimal system in your number system. Use a rate of increase in spreading out your number system. Yes there is an escape velocity for this numbers conundrum.

However there is a much less complicated route to escape this constant gravity.

The ratio between a circumference of a circle to its diameter can be used to construct a number system where the ratio constant could be deemed rational. www.mathsisfun.com... Simply square root the ratio where a rational number appears by assigning values accordingly to find a starting point for you invented number system, and work out from there in constructing your number system to complete the entire frame work. The Babylonians had a 12 digit number system, "Where does pi appear on your watch?" Hint convert 12 O clock to 10 O clock.

You will find when you load your number system into something like this www.algebra.com... you will find irrational numbers really do not have an impact on any outcomes. Because the definition of irrational numbers is only relative to the 10 digit number system not the methodology of the thrums themselves.

This concludes that the argument that pi is either irrational or rational is pointless regarding the ratio between a circle's circumference and its diameter.

edit on 24-2-2012 by LilDudeissocool because: It's moot.





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