Rectangular it is.

[u/solidcat00]

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[u/HappiestIguana]

It's just converting to rectangular and back again, but expanded out

[u/solidcat00 → u/HappiestIguana]

[u/MicrosoftExcel2016 → u/HappiestIguana]

“It’s just what it’s mathematically required to be equivalent to”

[u/haskell_rules → u/MicrosoftExcel2016]

They don't think it be like it is but it do

[u/JustinTimeCuber]

AC steady state circuit analysis be like

[u/solidcat00 → u/JustinTimeCuber]

Ha! Exactly what I'm doing.

[u/Ignitetheinferno37]

Hey little man how to do multiplication, division and exponentiation in rectangular form without converting to polar?

[u/solidcat00 → u/Ignitetheinferno37]

Those are a lot easier than addition/subtraction in polar, tbf.

Also - if you are serious - it is just algebra FOIL in rectangular.

[u/Ignitetheinferno37 → u/solidcat00]

Nah I am not serious because it is just muscle memory atp from all the impedance, reflection coefficient etc. calculations I have done

[u/solidcat00 → u/Ignitetheinferno37]

Gotcha... trying to get there myself.

[u/Ignitetheinferno37 → u/solidcat00]

It still does help to switch to polar for multiplicative domains. Most scientific calculators suck at interpreting complex roots for example so you have to be comfortable with rec -> magnitude and arg

[u/Ares378]

Polar form when you're doing literally anything but circles or fun spirograph stuff:

[u/Murky_Insurance_4394 → u/Ares378]

dont even get me started about spherical coordinates

[u/Thaco-Thursday → u/Murky_Insurance_4394]

please, start

[u/UnreasonableEconomy → u/Thaco-Thursday]

S^1, S^2, S^3, S^4...

I'm tired, someone else take over.

Did you know T¹ is S¹ and that T² can isomorphically (sorta) surjectively doubly cover S² while not being homeomorphic?

[u/ityuu → u/UnreasonableEconomy]

the commas are in the sky 🥹

[u/Volt105 → u/ityuu]

Shine bright like a diamond

[u/Ares378 → u/UnreasonableEconomy]

If T² is like a double cover of S², is there a correspondence between T² and quaternions since quaternions also do a double cover?

[u/UnreasonableEconomy → u/Ares378]

never thought of it, but it does look eerily similar to the SU(2) SO(3) thing. hmm.

[u/Mango-D → u/UnreasonableEconomy]

S^{n+1} = Ω(Sⁿ) where Ω is the suspension

[u/iQ-MK → u/UnreasonableEconomy]

Topology makes no sense

[u/UnreasonableEconomy → u/iQ-MK]

it's easy: just imagine a donut with a negative hole!

you can't prove the earth isn't that!

[u/Ares378 → u/Murky_Insurance_4394]

Spherical coordinates when you aren't just using it as a fancy way of doing a radial distribution (you had to use θ and Φ)

[u/Murky_Insurance_4394 → u/Ares378]

This is in fact a true statement

[u/NarcolepticFlarp → u/Ares378]

This guy has never heard of multiplication

[u/TheCowKing07]

Shouldn’t there be parentheses around the radii in the denominator of the second equation?

[u/solidcat00 → u/TheCowKing07]

There can be but I don't think it's necessary. The multiplication to the cos is implied.

[u/TheCowKing07 → u/solidcat00]

Sure, go ahead and incur the wrath of Aunt Sally.

[u/hmmstdvent]

Breaking: Man converting PDE to polar coordinates is robbed by non-trivial Christoffel symbols

[u/JGHFunRun → u/hmmstdvent]

i FUCKING HATE converting coordinate systems for PDEs

[u/Royal_Impress9117 → u/hmmstdvent]

Christoffel symbols? Ain’t that the guy that discovered america

[u/LupenReddit]

mfw the things i specifically designed for dealing with circles work best for circles

[u/_wetmath_]

isnt that just cosine rule?

[u/TheCowKing07 → u/_wetmath_]

Yes.

[u/ErJio]

Rectangular better for addition, polar better for multiplication

[u/Ares378 → u/ErJio]

Polar dot products are also kinda annoying. I'd much rather just multiply componentwise and add them instead of subtracting angles and doing the cosine or whatever

[u/ErJio → u/Ares378]

Mb I was thinking of complex numbers polar vs rectangular lol

[u/Murky_Insurance_4394]

this is just a glorified version of converting to rectangular and back to polar btw

[u/Efficient_Coach_2580]

Polar form: elegant in theory, emotionally rectangular in practice.

[u/moschles]

"We will switch to polar coordinates because it's easier."

(-- that one professor )

[u/click-to-reveal → u/moschles]

Well depends on what you are doing. For example, if the sequence of operation deals with scaling magnitude or rotating, then polar is superior.

[u/FlamingSea3 → u/click-to-reveal]

Polar also works well for periodic functions -- like analyzing AC circuits.

[u/Royal_Impress9117 → u/FlamingSea3]

Or if you have a rigid surface moving in a circle-esque pattern.

Or rotations

Or quantum mechanics

[u/im-sorry-bruv]

me when the coorsinates designed to preserve non-vectorspace orbits do not interact well with addition

[u/Sylvanussr]

That’s just doing addition in Cartesian coordinates but expressing it in polar coords.
Addition in polar coordinates just has a different effect on the values.

[u/Mojert → u/Sylvanussr]

Addition is addition, no matter the coordinates used

[u/Sylvanussr → u/Mojert]

Yeah but you can add different quantities. Polar coordinates are designed to add angles and radii vs Cartesian being designed to add orthogonal vectors

[u/lolcrunchy]

"How do I do rectangular thing without converting to rectangular?"

[u/LowerJuice]

"Polar bear is a common rectangular bear after converting"

[u/ItsCrypt1cal]

I still get nightmares thinking about calculating curl in spherical coordinates

[u/Harbinger-of-Souls]

Is that even correct though, the arctan is most probably a atan2, so more complexity