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The perfect circle or sphere.

I think you could do it even with the restrictions brought about by plank's length by makeing a circle infintly large. Since an infinetly large circle would apear to have a striaght edge over a finite distance (eg the universe) a line the lenght of the universe would be a perfect circle. (why do suspect someone who understands maths is about to knock this reasoning into the midle of next week?)
 
Certain gaussian surfaces are perfectly circular or spherical.

But they don't really exist, do they?
 
Okay, so to make a perfect circle, you need to have pi, right?

and pi isn't exact. We are just 'close', right?

So, cna someone show me how close we are to pi right now? Like, can someone draw/produce for us a circle with pi expressed as 3, as 3.1, as 3.14, as 3.1416, etc???

How off would the circle look if calculated at 3, or 3.1 as the anceints did?
 
Larspeart said:
Okay, so to make a perfect circle, you need to have pi, right?

and pi isn't exact. We are just 'close', right?

So, cna someone show me how close we are to pi right now? Like, can someone draw/produce for us a circle with pi expressed as 3, as 3.1, as 3.14, as 3.1416, etc???

How off would the circle look if calculated at 3, or 3.1 as the anceints did?
Click to expand...

I've heard a relatively few decimal points will give you the circumference of the known universe within a fraction of a meter. That's probably pretty close for most applications..

I think the Bad Asronomer commented on this once, maybe he'll drop by and set me straight..
 
So dispite all the talk about 'so and so found another decimal for pi. . .' plain old 3 is pretty darn good for making a circle? Or maybe 3.1?
 
Diogenes said:


I've heard a relatively few decimal points will give you the circumference of the known universe within a fraction of a meter. That's probably pretty close for most applications..

I think the Bad Asronomer commented on this once, maybe he'll drop by and set me straight..
Click to expand...

Don't trust my numbers exactly, but I've heard 39 decimal places is enough to calculate the radius of the known universe to within the radius of a hydrogen atom.
 
Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: The perfect circle or sphere.

LuxFerum said:
Someone here understand what I'm saying or I'm really gone insane. :confused:
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You still haven't made clear what your definition of "perfect" is in this scenario.
 
geni said:
I think you could do it even with the restrictions brought about by plank's length by makeing a circle infintly large.
Click to expand...
well, thinking further, it appears that no massive object could fulfill the requirements -- at least -- not any massive object composed of atoms. We known that at atom looks approximately spherical under an electron tunnelling microscope, and we know that it's not mathematically possible to create a flat surface by packing spherical objects together. Now, the diameter of an atom is orders of magnitude greater than plank length, so we could certainly resolve it.

So, the object would have to be atomic or smaller, but now you run into all sorts of fuzziness thanks to that b*stard Werner Heisenberg, and the other quantum physicysts who'll gleefully point out that you won't be able to measure this object without changing it's shape.
 
Perhaps it may be appropriate here to put on my pedant's hat.

Larspeart: Okay, so to make a perfect circle, you need to have pi, right?
Click to expand...
No. A circle can easily be constructed without using Pi. Pi is defined in terms of a circle, not the other way around.

and pi isn't exact. We are just 'close', right?
Click to expand...
Pi is indeed exact. It's the decimal approximations of Pi that are not exact.

So, cna someone show me how close we are to pi right now?
Click to expand...
The current record is more than one trillion decimal digits (cite).

Edited to add another cite for the record trillion digit decimal expansion of Pi.
 
LuxFerum said:
Is there something in this universe that is perfectly round?
I think that the event horizon of a black hole is a perfect sphere, but I'm not sure.
Maybe some sub-atomic particle could be classified as a perfect sphere.
What do you think?
Click to expand...

I'm not sure that there is any evidence that subatomic particles have a surface at all. The 'surface' of an atom, for example, is defined by the electron(s) that 'orbit' it.
 
extra sensory potato said:

I do not have a clue what this equation means in full. Would you mind giving me a brief summary, with possibly a website with a good detailed explanation too?
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In complex analysis, e<sup>i π</sup> + 1 = 0 is a special case of the Euler formula. It is remarkable in that it relates 5 of the most fundamental numbers/constants in mathematics. The numbers 0 and 1. e is the base of the natural logarithms, approximately equal to 2.71828. i is the square root of -1 (i<sup>2</sup> = -1). π is the ratio of the circumference of a circle to its diameter, approximately equal to 3.1416.

A good explanation can be found in the book, e: The Story of a Number by Eli Maor.
 
Lux,

In string theory, there are strings joined end to end.
Perhaps these are perfect circles?
Anyone know if the theory characterizes them as perfect cirlces?

BillyJoe
(Even then, string theory could be false)
 
Brown said:
Certain gaussian surfaces are perfectly circular or spherical.
But they don't really exist, do they?
Click to expand...
Dunno, maybe. If we can detect it, or measure it it exist, or not?
But if that is true, then I can just assume that there is a sphere around point "P" with radius "R". Just because I can measure the distance "R".
that is confusing
:confused:


rockoon said:
I'm not sure that there is any evidence that subatomic particles have a surface at all. The 'surface' of an atom, for example, is defined by the electron(s) that 'orbit' it.
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If all we have in this universe is some kind of forces, then we could assume that the surface is a place where the force have the same value.

Like a gaussian surface, but they exist, or not?


And I also have think about the gravity distortion, and in the same way that it will change the shape of the object it will change the "size of the meter".
It is like relativity, when a spaceship is moving it gets shorter, but that is indetectable if you are inside the spaceship.
 
Larspeart said:
So, can someone show me a circle where 'pi' = 3?

Am I asking the question right here?
Click to expand...
If you look at a regular hexagon, and think of the distance from opposing points as the "diameter," and think of the perimeter of the hexagon as the "circumference," then the circumference divided by the diameter is 3.

Of course, a regular hexagon may look like a circle from a distance, but it is not a true circle.
 
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