BrainMeta'   Connectomics'  

Welcome Guest ( Log In | Register )

2 Pages V  1 2 >  
Reply to this topicStart new topic
> ?PI?
kaytea111
post Aug 10, 2006, 06:40 AM
Post #1


Newbie
*

Group: Basic Member
Posts: 40
Joined: Aug 10, 2006
Member No.: 5485



Who figured out pi? are the numbers just randon, if not, what makes it so the numbers are as they are?
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
OnlyNow
post Aug 10, 2006, 07:29 AM
Post #2


Overlord
****

Group: Basic Member
Posts: 389
Joined: Feb 02, 2006
Member No.: 4822



QUOTE(kaytea111 @ Aug 10, 09:40 AM) *

Who figured out pi? are the numbers just randon, if not, what makes it so the numbers are as they are?

It's the ratio of the circumference of a circle to its diameter. Pi has been around a long time, just as soon as someone figured out that the number is always the same no matter what size the circle.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
lucid_dream
post Aug 10, 2006, 07:37 AM
Post #3


God
******

Group: Admin
Posts: 1711
Joined: Jan 20, 2004
Member No.: 956



if Pi is defined as the ratio of the circumference of a circle to its diameter, then it would vary for non-Euclidean geometries. For instance, if the circle was on the surface of a sphere.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
OnlyNow
post Aug 10, 2006, 07:40 AM
Post #4


Overlord
****

Group: Basic Member
Posts: 389
Joined: Feb 02, 2006
Member No.: 4822



QUOTE(lucid_dream @ Aug 10, 10:37 AM) *

if Pi is defined as the ratio of the circumference of a circle to its diameter, then it would vary for non-Euclidean geometries. For instance, if the circle was on the surface of a sphere.

I dunno then. that's just how I learnt it. I'm sure you'll tell me otherwise, but I think circles are so last-millennium compared with spheres and have no business hanging out on their surfaces.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
LifeMirage
post Aug 10, 2006, 09:37 AM
Post #5


Demi-God
*****

Group: Global Mod
Posts: 974
Joined: Apr 13, 2005
From: Netherlands
Member No.: 4349



QUOTE
but I think circles are so last-millennium compared with spheres and have no business hanging out on their surfaces.



Heh.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Hey Hey
post Aug 10, 2006, 10:34 AM
Post #6


Supreme God
*******

Group: Basic Member
Posts: 7766
Joined: Dec 31, 2003
Member No.: 845



QUOTE(lucid_dream @ Aug 10, 04:37 PM) *

if Pi is defined as the ratio of the circumference of a circle to its diameter, then it would vary for non-Euclidean geometries. For instance, if the circle was on the surface of a sphere.

Do you mean a circle that is drawn and then applied to the surface of a sphere, or a circle that looks to an observer like a circle when on a sphere? Pi will apply to the first, but not the second, as the second is not actually a circle. (Try drawing a circle on a deflated balloon and then inflating it).

This wouldn't apply on the Earth, as due to the Earth's rotation, it is not a perfect sphere. It is a little flatter at the poles, and there is a bulge at the equator. So don't bother looking for proof with circles on the surface of the Earth (hee, hee).
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Hey Hey
post Aug 10, 2006, 10:35 AM
Post #7


Supreme God
*******

Group: Basic Member
Posts: 7766
Joined: Dec 31, 2003
Member No.: 845



QUOTE(OnlyNow @ Aug 10, 04:40 PM) *

I think circles are so last-millennium compared with spheres and have no business hanging out on their surfaces.

biggrin.gif
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Rick
post Aug 10, 2006, 10:41 AM
Post #8


Supreme God
*******

Group: Basic Member
Posts: 5916
Joined: Jul 23, 2004
From: Sunny Southern California
Member No.: 3068



I think the question being asked is how the digits of pi are computed. It's an infinite series, a sum of fractions.

http://www.faqs.org/faqs/sci-math-faq/spec...bers/computePi/
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Hey Hey
post Aug 10, 2006, 10:46 AM
Post #9


Supreme God
*******

Group: Basic Member
Posts: 7766
Joined: Dec 31, 2003
Member No.: 845



QUOTE(Rick @ Aug 10, 07:41 PM) *

I think the question being asked is how the digits of pi are computed. It's an infinite series, a sum of fractions.

http://www.faqs.org/faqs/sci-math-faq/spec...bers/computePi/

don't twenty-two sevenths of a circle make more than a circle ...... ( wink.gif )
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
trojan_libido
post Sep 28, 2006, 07:32 AM
Post #10


God
******

Group: Basic Member
Posts: 1351
Joined: Sep 19, 2006
From: UK
Member No.: 5681



A circle is a 2D shape, projecting it onto a 3D sphere means the circle has to take on a 3D form and so I don't think that applies.

I understand what your saying about non-Euclidean geometries though Lucid, if a person on the surface of a planet made what they percieve as a 2D triangle, if it was large enough the angles could add up to more than 180 degrees. It is even possible to have 3 90 degree angles in a triangle projected on a sphere.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
HiddenVariable
post Jan 13, 2007, 06:13 PM
Post #11


Newbie
*

Group: Basic Member
Posts: 26
Joined: Jan 13, 2007
Member No.: 7000



Once it was realized that the ratio of circumference to diameter was constant, this could be represented. Today it is represented by the greek letter pi.

There are many ways to compute the successive digits. But it has an infinite number of digits, so no one 'knows' all of it. Whether the digits are 'random' or not depends on your conceptualization of 'random.'
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Chip
post Mar 02, 2007, 02:12 PM
Post #12


Unregistered









Hey, thanks for the link, Rick. That was what I was hoping to see when I came into this subject. I'm studying Python and wondered about some computational means to estimate PI. Wasn't it Archimedes who came to a process to estimate PI? I understand PI to be an irrational number and some how or other that has been proved so there will be no consistently repeating pattern to its endless digits. Irrational numbers have been used to simulate random number generators, I understand, though I am unaware as to whether or not the non-repeating, non-terminal decimal digits are really random. If some game or gambling method used such a process, if you knew the irrational number, you could "win" all the time. Other irrationals that come to mind are Euler's number and the golden mean (Phi). I once wrote a program that figured out Phi to as many decimal places as you wanted to stipulate and that your computer and alotted time could handle. I wonder about non-Euclidean geometry and PI. For a triangle on a sphere the angles always sum to greater than 180 degrees and on a hyperbola, to always less than 180. What about PI on a hyperbola?
Go to the top of the page
+Quote Post
Chip
post Mar 13, 2007, 03:52 PM
Post #13


Unregistered









Read an article recently that PI ranges in spherical geometry, greater than or equal to 2 and less than PI of Euclidean geometry. Just thinking about it I suspect PI ranges in hyperbolic geometry as greater than PI up to infinity?
Go to the top of the page
+Quote Post
Rick
post Mar 14, 2007, 02:15 PM
Post #14


Supreme God
*******

Group: Basic Member
Posts: 5916
Joined: Jul 23, 2004
From: Sunny Southern California
Member No.: 3068



That would seem to be the case.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Hey Hey
post Mar 20, 2007, 10:33 AM
Post #15


Supreme God
*******

Group: Basic Member
Posts: 7766
Joined: Dec 31, 2003
Member No.: 845



The geometry of the Universe is flat. This means the geometry you learned in high school applies over the largest distances in the universe. Hey, I'm back to knowing some useful math again!
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Rick
post Mar 20, 2007, 11:28 AM
Post #16


Supreme God
*******

Group: Basic Member
Posts: 5916
Joined: Jul 23, 2004
From: Sunny Southern California
Member No.: 3068



QUOTE(Hey Hey @ Mar 20, 2007, 11:33 AM) *

The geometry of the Universe is flat. ...

That's really convenient. Of the infinitely varied geometries available, we get the plain old boring one. At least it makes visualizing stuff somewhat easier that would be the case otherwise.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
simon
post Mar 21, 2007, 03:01 AM
Post #17


Aspiring
**

Group: Basic Member
Posts: 79
Joined: Jan 08, 2007
Member No.: 6876



Is the exact volume of a sphere measurable ?
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Hey Hey
post Mar 21, 2007, 03:50 AM
Post #18


Supreme God
*******

Group: Basic Member
Posts: 7766
Joined: Dec 31, 2003
Member No.: 845



QUOTE(simon @ Mar 21, 2007, 11:01 AM) *
Is the exact volume of a sphere measurable ?
Exact - now come on Simon, get a grip!
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Rick
post Mar 21, 2007, 07:56 AM
Post #19


Supreme God
*******

Group: Basic Member
Posts: 5916
Joined: Jul 23, 2004
From: Sunny Southern California
Member No.: 3068



There is no such thing as an exact measurement (if we exclude countable things), but the exact volume of an abstract sphere is computable.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Hey Hey
post Mar 21, 2007, 11:27 AM
Post #20


Supreme God
*******

Group: Basic Member
Posts: 7766
Joined: Dec 31, 2003
Member No.: 845



Fair enough. Just for interest:

Regardless of the choice of convention for indexing the number of dimensions of a sphere, the term "sphere" refers to the surface only, so the usual sphere is a two-dimensional surface. The colloquial practice of using the term "sphere" to refer to the interior of a sphere is therefore discouraged, with the interior of the sphere (i.e., the "solid sphere") being more properly termed a "ball." Wolfram MathWorld
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
simon
post Mar 22, 2007, 01:59 PM
Post #21


Aspiring
**

Group: Basic Member
Posts: 79
Joined: Jan 08, 2007
Member No.: 6876



Balls then the exact(ish) volume occuPIed by a spherical ball thingy. That is what I'm am trying to get a grip of. The answer I feel is close at hand. Gaffaw!!
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
simon
post Mar 22, 2007, 02:02 PM
Post #22


Aspiring
**

Group: Basic Member
Posts: 79
Joined: Jan 08, 2007
Member No.: 6876



Why isn't there an exact measurement ?
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
simon
post Mar 22, 2007, 02:18 PM
Post #23


Aspiring
**

Group: Basic Member
Posts: 79
Joined: Jan 08, 2007
Member No.: 6876



OK I just figured it, organically. So how abstract is measurement to start with then ? I detect an infinite regress, I may have to eat some porridge !
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Rick
post Mar 22, 2007, 07:01 PM
Post #24


Supreme God
*******

Group: Basic Member
Posts: 5916
Joined: Jul 23, 2004
From: Sunny Southern California
Member No.: 3068



I have to disagree with Wolfram. My computational geometry text (Springer-Verlag) defines a sphere as the solid interior plus the boundary (surface).
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
mu6
post Apr 05, 2007, 01:07 PM
Post #25


Newbie
*

Group: Basic Member
Posts: 10
Joined: Oct 26, 2005
Member No.: 4586



QUOTE(Rick @ Mar 22, 2007, 07:01 PM) *

I have to disagree with Wolfram. My computational geometry text (Springer-Verlag) defines a sphere as the solid interior plus the boundary (surface).

:-)
No sphere without the boudary!
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
mu6
post Apr 05, 2007, 01:16 PM
Post #26


Newbie
*

Group: Basic Member
Posts: 10
Joined: Oct 26, 2005
Member No.: 4586



IMO, Pi has some "cyclic numbers" involved. You know numbers like 0.142857142857 ... from divisions by 7.
A never ending story.
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
mu6
post Apr 05, 2007, 01:26 PM
Post #27


Newbie
*

Group: Basic Member
Posts: 10
Joined: Oct 26, 2005
Member No.: 4586



Since a circle is only described by the radius and Pi their relationship is the only way to analyze.
IMO Pi is a composed number, where several cyclic numbers are combined (which emanate from parts of the circles when arcs are projected).
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
trojan_libido
post Apr 15, 2007, 07:34 AM
Post #28


God
******

Group: Basic Member
Posts: 1351
Joined: Sep 19, 2006
From: UK
Member No.: 5681



spiralling?
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
Rick
post Oct 10, 2007, 02:14 PM
Post #29


Supreme God
*******

Group: Basic Member
Posts: 5916
Joined: Jul 23, 2004
From: Sunny Southern California
Member No.: 3068



QUOTE(mu6 @ Apr 05, 2007, 02:16 PM) *

IMO, Pi has some "cyclic numbers" involved. You know numbers like 0.142857142857 ... from divisions by 7.
A never ending story.

Because pi is an irrational number, it will never repeat. Like any random sequence, there may be some sections of repetition within the sequence, but the sequence can never be predictable. If it should repeat continuously, that would be predictable, and by definition of an irrational number, be impossible.

For a proof that pi is indeed irrational, see:

http://www.lrz-muenchen.de/~hr/numb/pi-irr.html
User is offlineProfile CardPM
Go to the top of the page
+Quote Post
P.j.S
post Jun 14, 2009, 04:30 PM
Post #30


Overlord
****

Group: Basic Member
Posts: 358
Joined: Jun 12, 2009
Member No.: 32189



Hi Rick!

"For a proof that pi is indeed irrational, see:

http://www.lrz-muenchen.de/~hr/numb/pi-irr.html"

The proof works out correct when the symbol for pi is used in the calculus.
But if I'm not mistaken pi is a ratio a/b. Exchange a/b for the pi symbol in the work
and see that the proof that pi is irrational will whither away.

In other words also a/b proves to be a bigger value than the symbol of pi.

It does in other proofs of irrational pi that I have encountered anyway from Group members on MSN.

Pete
User is offlineProfile CardPM
Go to the top of the page
+Quote Post

2 Pages V  1 2 >
Reply to this topicStart new topic
1 User(s) are reading this topic (1 Guests and 0 Anonymous Users)
0 Members:

 



Lo-Fi Version Time is now: 19th November 2017 - 09:44 AM


Home     |     About     |    Research     |    Forum     |    Feedback  


Copyright BrainMeta. All rights reserved.
Terms of Use  |  Last Modified Tue Jan 17 2006 12:39 am

Consciousness Expansion · Brain Mapping · Neural Circuits · Connectomics  ·  Neuroscience Forum  ·  Brain Maps Blog
 · Connectomics · Connectomics  ·  shawn mikula  ·  shawn mikula  ·  articles