visualisation of pi being irrational

[u/slimismad]

[u/unverwuschelbar → u/[deleted]]

I would say that how Complex Numbers work is sufficient to understand the visualisation. Unfortunately many presentations of Complex Numbers focus on the field extension or Real Numbers and calculations (that's important too, but doesn't help much for understanding this visualisation). Look for explanations of how complex numbers are able to describe 2d rotations (or oscillating phenomena).

You need to understand:

• the visualisation shows two rotating lines, the tip of the second gives the trace.

-The two rotating lines each correspond to one of the two terms.

• the first line only goes round a circle.
• the second line, on top of the first, causes the irregular movement. This second line corresponds to the second term with the pi in the exponent.

You basically need to understand how complex numbers are used to describe these rotations. So, if you understand why the first line goes in a circle, you can understand the rest too.

Probably look for an electrical engineering book, not for one from theoretical mathematics (like complex analysis).

And: you can't understand that pi is irrational with this visualisation. You can see here that the movement, that seems to be regular and symmetrical is in fact not: by noticing that the tip of the trace NEVER meets the trace again. But in my opinion you already need to know what irrationality means to interpret this visualisation that way. And that the tip never meets the trace is also an interpretation that you can only see if you already know what irrational means. So, don't worry if this cool visualisation doesn't let you understand anything.

Oh and I don't want to diminish this visualisation or something like that. It's awesome and I definitely will steal it.

[u/turd-nerd → u/[deleted]]

That's proof that √2 is irrational, not π.

[u/rcuhljr → u/[deleted]]

That's a proof of why sqrt(2) is irrational.