/sci/ - Science & Math » Thread #12716213

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Alternate coordinate systems

Anonymous Wed 17 Feb 14:10:23 2021 No.12716213 View Reply Original Report

Quoted By: >>12716231 >>12716455 >>12716467 >>12718658 >>12718695 >>12718843 >>12718903 >>12719144

I'm trying to get into a subject of alternate coordinate systems but really lack the vocabulary to search for information on this topic. Are there any non-Cartesian coordination of note that are of interest?

Anonymous

Anonymous Wed 17 Feb 2021 14:16:05 No.12716231 Report

Quoted By: >>12716239 >>12716246

>>12716213
Many articles on Wikipedia bro, even for historically used charts of the globe etc

Cartography etc.

Anonymous

Anonymous Wed 17 Feb 2021 14:19:17 No.12716239 Report

Quoted By: >>12716259

>>12716231
I don't think you understood. Let me rephrase .
Are there alternate coordinate systems that are non-cartesian that can represent also 3D Cartesian coordinate system.

Anonymous

Anonymous Wed 17 Feb 2021 14:21:59 No.12716246 Report

Quoted By:

>>12716231
I suppose by cartography you meant a Geographic coordinate system.

Anonymous

Anonymous Wed 17 Feb 2021 14:25:20 No.12716259 Report

Quoted By: >>12716322

>>12716239
any (local) homeomorphism from R^3 to itself determines a coordinate system

Anonymous

Anonymous Wed 17 Feb 2021 14:42:56 No.12716322 Report

Quoted By: >>12716513

>>12716259
In a Cartesian system that is true.

Anonymous

Anonymous Wed 17 Feb 2021 15:20:21 No.12716455 Report

Quoted By:

>>12716213
Polar coordinates. Things measured by their angle and distance from a point

Anonymous

Anonymous Wed 17 Feb 2021 15:23:58 No.12716467 Report

Quoted By:

>>12716213
Also from a statistics perspective you can apply some function to transform non linear functions to linear (like a logarithmic function) . Similarly, you can change the coordinates to be logarithmic to make your object/data appear linear when it’s not.

Anonymous

Anonymous Wed 17 Feb 2021 15:39:10 No.12716513 Report

Quoted By:

>>12716322
it's true without any assumptions about a coordinate system

Anonymous

Anonymous Thu 18 Feb 2021 01:49:13 No.12718634 Report

Quoted By:

polar coordinates
cylindrical coordinates
spherical coordinates
etc

Anonymous

Anonymous Thu 18 Feb 2021 01:55:19 No.12718658 Report

Quoted By:

>>12716213
This one only works for three or less dimensions:
Use your finger to point out the place you are trying to address.

Anonymous

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Anonymous Thu 18 Feb 2021 02:08:18 No.12718695 Report

Quoted By: >>12718779 >>12719110

>>12716213
I had in mind a spherical type system that makes
this sort of mesh on the surface. Not geographical,
somewhat polar, but easily done parametrically.
In terms of Cartesian coordinates, parametric
works out fine with the proper associations.

The next post is an umbilic torus with equations.

Anonymous

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Anonymous Thu 18 Feb 2021 02:32:17 No.12718779 Report

Quoted By: >>12719068 >>12719718 >>12719776

>>12718695

$x=\sin(u)\left(7+\cos\left(\frac{u}{3}-2v\right)+2\cos\left(\frac{u}{3}+v\right)\right)$ $y=\cos(u)\left(7+\cos\left(\frac{u}{3}-2v\right)+2\cos\left(\frac{u}{3}+v\right)\right)$ $z=\sin\left(\frac{u}{3}-2v\right)+2\sin\left(\frac{u}{3}+v\right)$

Anonymous

Anonymous Thu 18 Feb 2021 02:58:07 No.12718843 Report

Quoted By:

>>12716213
Polar, cylindrical and spherical are the big ones

Anonymous

Anonymous Thu 18 Feb 2021 03:16:42 No.12718903 Report

Quoted By:

>>12716213
geodesics?

Anonymous

Anonymous Thu 18 Feb 2021 04:26:55 No.12719068 Report

Quoted By: >>12719718

>>12718779
That's hot.

Anonymous

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Anonymous Thu 18 Feb 2021 04:42:23 No.12719110 Report

Quoted By: >>12719776

>>12718695
In somewhat same vein. I was thinking of a harmonic frequency that would represent a sphere. The center point to some arbitrary length on the wave would give a vector

Anonymous

Anonymous Thu 18 Feb 2021 04:53:05 No.12719144 Report

Quoted By:

>>12716213
Cylindrical (circular, parabolic, etc)
Spherical
Ellipsoidal (prolate and oblate spheroidal in particular)
Toroidal
etc
Literally any decent text on electromagnetism should cover most or all of them

Anonymous

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Anonymous Thu 18 Feb 2021 09:06:28 No.12719718 Report

Quoted By:

>>12718779
>>12719068
Here's something hotter, a more twisted umbilic
torus.

Anonymous

Anonymous Thu 18 Feb 2021 09:31:27 No.12719776 Report

Quoted By:

>>12718779
>>12719110
Oh, then spherical harmonics might be interesting
to you.

Anonymous

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Anonymous Thu 18 Feb 2021 14:24:52 No.12720278 Report

Quoted By:

Finally, /sci/ gets it.

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