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.

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.

Heh.

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).

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 ...... ( )

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.

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.'

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?

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?

That would seem to be the case.

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!

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.

Is the exact volume of a sphere measurable ?

Exact - now come on Simon, get a grip!

There is no such thing as an exact measurement (if we exclude countable things), but the exact volume of an abstract sphere is computable.

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

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!!

Why isn't there an exact measurement ?

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 !

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!

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

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).

spiralling?

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