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Let us say theoretically you have a perfect sphere and you are using it as a dice, would it be a D1 or a D∞?
Ie:
If you were to use a sphere as a dice would you consider it a one sided dice (always rolls the number 1) or an infinite sided dice (can roll any positive integer)
Suggested arguements:
A D∞ is impossible
A D1 is useless
Assuming it was actually, by some magic, a perfect sphere, it would be an infinity sided die, imo.
Yes
Both.
It would be infinite, and infinitely useless.
I'd roll a one with the infinite dice.
I would just throw it at people.
A theoretically perfect sphere would have theoretically one side as there would be no minute flat areas which would constitute a seperate side
I say infinity but what do I know, I'm a moron. :p
Yeah. A sphere by definition contains infinite points.Quote:
Originally Posted by Shoeberto
And the probability of getting a specific side is 1/∞ which is 0 :p
You can't write infinity numbers on a dice :colbert: Not if you want to use it anyway.
Can you have a 1 sided die? Wouldn’t that just be a lotto ball?
It depends on how tiny numbers you can paint.
Well they would have to be infinitely small and you would have to believe a sphere is made up of infinite flat surfaces with infinitesimal areas rather than having no flat surfaces at all
http://imgs.xkcd.com/comics/random_number.pngQuote:
Originally Posted by AntRid
technically, for layman's purposes, Manus is right. It only has 1 side. There is nothing separating the sides from anything else. Technically, dice have infinite points on them, but nothing defies where on "side" begins and ends - there's just the external layer that is perfectly smooth and would be 1 side.
From a physic's perspective, the sphere has as many sides as it has atoms composing the outmost layer - and because that amount is dependent upon the sphere, if it is remotely capable of being seen with the naked eye, then we can, for clarity's sake, say it is infinite. But still, it's just ONE side. Those are just individual points upon that side.
The debate of the century is why everyone labels their debate the debate of the century.
Fine I lied, this is really just filler while im waiting for the next "does 0.999... = 1" thread
I thought we already proved that a million times. And by we, I mean all of the smart people which doesn't include me.
No because to prove something as true in math, you must disprove it is false. :doublecolbert:
Going way back to geometry, when you compare the shapes of the various regular polygons, the higher and higher the number of sides, the more and more it looks like a circle. A circle is a regular polygon with an infinite number of sides, no?
Oh man I love those threads.Quote:
Originally Posted by blackmage_nuke
Pretty much. (I came up with this conclusion in 3rd grade, and I attribute to it whatever success I've had in calculus)Quote:
Originally Posted by NorthernChaosGod
As for having one side, it's trivial to divide the circle into hemispheres, and subdivide it from there. It will eventually come to a stop even if it has no sharp corners, and from there will behave like a typical die.