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3 Axis Number System

Anonymous Sat 01 Aug 05:15:54 2020 No.11959103 View Reply Original Report

Quoted By: >>11959117 >>11959133 >>11959153 >>11961487 >>11962540

Amateur math anon, I've been working on a 3 axial number system a lil and I think it's pretty dope, no idea what the fuck it could be used for though. Still interesting nonetheless

Anonymous

Anonymous Sat 01 Aug 2020 05:19:20 No.11959117 Report

Quoted By: >>11959146

>>11959103
Have any non-trivial theorems about it? This just looks like you're using roots of unity on the complex plane.

Anonymous

Anonymous Sat 01 Aug 2020 05:25:18 No.11959133 Report

Quoted By: >>11959154

>>11959103
you mean like quaternions?

Anonymous

Anonymous Sat 01 Aug 2020 05:31:18 No.11959146 Report

Quoted By: >>11962451

>>11959117
Not yet, im still trying to figure out how you'd "access" this plane to begin with, in a similar way one gets to the complex plane. And just looked into roots of unity, it definitely does resemble the behavior of those systems by a lot. The only thing that sets it apart is the additive properties as far as i can tell but that can probably be brought back to roots of unity, ill test that after posting this.

When originally creating the diagram I envisioned the complex plane as running perpendicular to all other planes, but even then that could just be roots of unity inside of a 3 dimensional complex space using r,i, and j where r and j generate the plane illustrated.

Definitely going to look more into roots of unity though

Anonymous

Anonymous Sat 01 Aug 2020 05:33:26 No.11959153 Report

Quoted By: >>11959165 >>11959466

>>11959103
You invented the complex numbers. Great fucking job, anon.

Anonymous

Anonymous Sat 01 Aug 2020 05:34:07 No.11959154 Report

Quoted By: >>11959158

>>11959133
I believe so, only the axis here are separated by 60 degrees and lie flat rather than existing in a true 3D space. Not sure if that exists yet, just thought the underlying algebra for such a system was elegant.

Anonymous

Anonymous Sat 01 Aug 2020 05:35:55 No.11959158 Report

Quoted By:

>>11959154
but this doesn't tell us anything new since everything here can be constructed with real and complex numbers, since it's still only 2D.

Anonymous

Anonymous Sat 01 Aug 2020 05:37:48 No.11959165 Report

Quoted By: >>11959171

>>11959153
I understand what complex numbers are and how they work, that's what I used as a basis for the creation of this. Also as another anon pointed out this could probably derived from roots of unity which I'm gonna look into. If you notice though taking the square root of -phi still takes you into a complex space assuming that phi is disconnected from the true complex plane.

Anonymous

Anonymous Sat 01 Aug 2020 05:43:20 No.11959171 Report

Quoted By: >>11959187

>>11959165
phi and psi are third roots of unity. Your number system is literally the complex numbers.

Anonymous

Anonymous Sat 01 Aug 2020 05:52:47 No.11959187 Report

Quoted By: >>11959191

>>11959171
Did some reading and indeed it is, thanks for the info. Interesting to the the behavior of roots of unity in calculus

Anonymous

Anonymous Sat 01 Aug 2020 05:55:18 No.11959191 Report

Quoted By:

>>11959187
this is complex analysis, which I recommend you read into if you're interested. it's a really fun field

Anonymous

Anonymous Sat 01 Aug 2020 06:03:41 No.11959203 Report

Quoted By:

Lmao

Anonymous

Anonymous Sat 01 Aug 2020 08:29:26 No.11959433 Report

Quoted By:

? = e^(-i*2?/3)
? = e^(i*2?/3)
1 = e^(i*0)
this is just a nonregular coordinate transformation in C or R^2 i dunno

Anonymous

Anonymous Sat 01 Aug 2020 08:51:37 No.11959466 Report

Quoted By:

>>11959153
This. At first it may look like this has $\mathbb{R}$ -dimension 3, with base vectors $1, \phi \psi$ , but the additive identity basically says that those 3 cannot be linearly independent, thus it only has dimension 2.

OP has constructed the complex numbers with a different presentation.

Anonymous

Anonymous Sat 01 Aug 2020 22:31:23 No.11961487 Report

Quoted By:

>>11959103
Look up geometric algebra

Anonymous

Anonymous Sun 02 Aug 2020 03:27:33 No.11962451 Report

Quoted By: >>11962514

>>11959146
There are no division algebras in 3 dimensions. If you're looking for a way to compute rotations in 3-space, check into William Rowan Hamilton.

Anonymous

Anonymous Sun 02 Aug 2020 03:47:57 No.11962514 Report

Quoted By:

>>11962451
prove it

Anonymous

Anonymous Sun 02 Aug 2020 04:00:50 No.11962540 Report

Quoted By:

>>11959103
just so you are aware OP, this happens every single year
Yeah amazing right, every year there is a new poster (or a couple of) who make this exact same thread because supposedly quaternions skip the third dimension. The last one I can recall used x/0 = n as a new complex number or some stuff like that and there was one about the Riemann sphere as well. I think that even Tooker tries to do something like this.

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