What happens if you have a right triangle with a plank length side?

[Beamin]

Imagine a= 1 plank length and b= 1 plank length. What does c=? You can't have a plank length between 1 and 2. Does the universe break when you try to measure it? What happens if you tried to shoot a photon down the length of c? When would it get to the other vertex? You can't have 1.XX plank times. Would the universe round down to one? That would mean faster then light travel if it rounds up to two the photon has extra time and would violate it's "quantum energyness".

[Ampera]

Imagine a computer monitor, and the pixels that exist within it. Now imagine you attempt to do the same thing in this instance. You try to make a right triangle where the hypotenuse = C, and the two legs A and B measure 1 pixel each.

Well, you start off with one leg which is one pixel in length, and then another leg 90 degrees adjacent to that one, forming a single pixel. Then try to make a right triangle out of that. Keep in mind, you can't divide a pixel into two smaller ones on a computer screen unless you have some alien technology. You just can't do it.

As far as I am aware, an plank length is the smallest length that would physically make sense in our 3D space. It is the "pixel" of the world. You can treat the plank length as if it were something that could be divided and get root2 plank lengths and make one, but it wouldn't work in our 3D space. You just can't do it, just like you can't divide a pixel in a monitor.

EDIT: Dave, I found a bug in SMF, or possibly an unpleasant feature. When editing, and using the alt code 251 to get a square root symbol, (?) I can see it while editing

http://prntscr.com/g4este

but when I post it, I just get a question mark.

[alm]

Yes, the forum does not support unicode properly. Same with some international characters. You can use Mathjax: \$\sqrt{a^2+b^2}\$. Quote my post to see the source. Does not work with preview, unfortunately.

BTW, the guy's name is Max Planck.

[Ampera]

Yes, the forum does not support unicode properly. Same with some international characters. You can use Mathjax: \$\sqrt{a^2+b^2}\$. Quote my post to see the source. Does not work with preview, unfortunately.

BTW, the guy's name is Max Planck.

Apologies, didn't bother to look up if the spelling is correct.

[Beamin]

So the universe is digital. So would a black hole look choppy if you zoomed in? Like this:
0
000
0000
00000
000000
000000
000000
00000
0000
000
0

[Cerebus]

Imagine a= 1 plank length and b= 1 plank length. What does c=? You can't have a plank length between 1 and 2. Does the universe break when you try to measure it? What happens if you tried to shoot a photon down the length of c? When would it get to the other vertex? You can't have 1.XX plank times. Would the universe round down to one? That would mean faster then light travel if it rounds up to two the photon has extra time and would violate it's "quantum energyness".

The idea of a "right triangle" is an idea from Euclidean geometry. When you're dealing with objects of Planck length you're not in Kansas the Euclidean world any more, you're in the wibbly wobbly quantum world where everyday common sense doesn't work. Heck, Euclidean geometry breaks down if you start drawing triangles on the surface of a sphere instead of on a plane, and you're trying to take it with you into a world where particles can tunnel through impenetrable barriers or be in two places at once.

[m98]

There is this huge misconception that Planck units somehow state anything about the fundamental properties of space. They don't. They are simply a series of units derived by some fundamental constants, simplifying some calculations. A Planck length just defines a rough scale where quantum effects begin dominating. Not more, not less.

[Beamin]

There is this huge misconception that Planck units somehow state anything about the fundamental properties of space. They don't. They are simply a series of units derived by some fundamental constants, simplifying some calculations. A Planck length just defines a rough scale where quantum effects begin dominating. Not more, not less.

So how does it apply or not apply to our triangle? Also on the quantum scale are we using "lobochvikien (spelling!) space? You know the space that kalry-yakawa(spelling again but you know what I'm trying to say)
 manifolds fit into?

We might be able to make our right triangle work in one of those coordinate systems. Been a while since  read elegant universe by brian greene.