How is this physically possible?

>>8751430
What are you even trying to say? There is space between atoms dumb shit.

>>8751452
If you were to find a structure resembling a right triangle in nature for which you knew the legs in len(atoms) or len(molecules) such as pic related, and you solved for c, the length of the hypotheses would be irrational. How is this possible for a physical object?

>>8751520
You would need to look for an atom thats slighty bigger than the other ones

>>8751520
Pi is an irrational number. But we know that the circumference of a basketball is Pi times the diameter of the ball.

Irrational != Not Real

>>8751520
wow

>>8751520
Why would it be impossible?

>>8751530
This. Irrational numbers aren't unnatural. They just can't be expressed as the ratio of two integers. Everything's gonna be fine, senpai.

>>8751525
So why can't you do the same for literally anything in math?
>my proof is bullshit, but if I substitute this slightly bigger number, it works
And what if the structure is composed of singular atoms/molecules
>>8751530
>But we know that the circumference of a basketball
And in that instance, the circumference is irrational. The basketball circumference != ratio circumference, it only nears an arbitrary or real-world(read: measurable) value of the ratio. And if you can measure the basketball circumference, then it's the diameter that's irrational, ergo the same problem I'm asking.
>>8751541
Maybe it isn't. Which begs the question: what does an irrational physical object look like?

>>8751590
>then it's the diameter that's irrational

I can wrap a string around the ball, and measure the circumference, then pierce the ball with a measurement rod of some sort and meaasure the diameter. Neither of those numbers are irrational. Pi is. But they're all real measurements.

>>8751609
>But they're all real measurements
Wrong. Given that Pi is irrational, either the circumference or the diameter is irrational. You can only measure to arbitrary precision using arbitrary values, and will never get the actual measurement. E.g. wrap a 1 unit long string into a circle, and measure the diameter: you cannot, because d = 1/Pi is irrational.

>>8751590
By >>8751661, it should be the case that you physically can't measure sqrt(2) atoms, then, yes? It'll always be to arbitrary precision, just like the ball in the example.

>>8751761
I feel like starting out with "suppose I observe a perfect right triangle nature" dooms the thought experiment since perfectly straight lines and perfectly right angles don't occur in nature, at least to my knowledge.

>>8751430
huh?

>>8751520
OP you're retarded

>>8751520
how is it not possible

>>8751430
Unlike ideal mathematical objects, things in real life are never perfect squares, spheres etc. The hypotenuse would be approximately root 2

>>8751430
I think it's due to an atom being expressed in three dimensions, and a triangle only being expressed in two.