Cardinal

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Cardinal

Jul 25, 2021 00:44

Cardinal

Jul 25, 2021 00:44

I have to check on you guys every now and then.

Cardinal

Jul 25, 2021 00:43

I hope, you are doing well.

Cardinal

Jul 25, 2021 00:43

what's cracking with you guys?

Cardinal

Mar 2, 2021 19:06

@GWarner Thank you! Good suggestion!

Cardinal

Mar 1, 2021 17:16

However, I do not get the Europe reference at all

Cardinal

Mar 1, 2021 17:16

I get the general meaning which is his perseverance and dedication.

Cardinal

Mar 1, 2021 17:15

> Hit Europe, kicked the door in, put a foot through it

Cardinal

Mar 1, 2021 17:15

What does "Europe" mean in Eminem's new song lyrics:

Cardinal

Mar 1, 2021 17:15

Hello mates.

Cardinal

Sep 10, 2020 04:50

I'll catch up with you guys later.

$Mathematics$ Mathematics

Associated with Math.SE; for both general discussion & math qu...

Cardinal

Feb 11, 2021 15:58

It was a good chat guys, thanks. I have to go. I wish you a good rest of day. take care.

Cardinal

Feb 11, 2021 15:56

hmm, i don't know, by definition rho depends on x and y not the other way around. even any radial line from the origin would have two unique dimensions of the tangible space

Cardinal

Feb 11, 2021 15:52

@Astyx No, a dimension of space is a singular entity. I suppose it could not have two constituents.

Cardinal

Feb 11, 2021 15:50

Compared to x and y and z, which all three do.

Cardinal

Feb 11, 2021 15:50

a single unique dimension

Cardinal

Feb 11, 2021 15:50

@Astyx I mean, rho does not represent a unique dimension of the space on its own.

Cardinal

Feb 11, 2021 15:44

@Astyx No, I say that because they constitute the spherical and cylindrical systems

Cardinal

Feb 11, 2021 15:44

Perhaps, in some geometry using "phi" unit vector instead of "rho" unit vector would make the mathematical expressions less lengthy

Cardinal

Feb 11, 2021 15:42

@Semiclassical Thank you, yes.

Cardinal

Feb 11, 2021 15:42

I see, meanwhile, this relativeness also exists with respect to phi and rho in my opinion.

Cardinal

Feb 11, 2021 15:40

:embarrassed:

Cardinal

Feb 11, 2021 15:40

I mean, x y z are genuine, the rest of systms for the three-dimensional space are fake

Cardinal

Feb 11, 2021 15:40

OK, my discussion is a bit philosophical than technical.

Cardinal

Feb 11, 2021 15:38

maybe "stand alone" is a better terminology than unique

Cardinal

Feb 11, 2021 15:38

I don't know, I can say z is a unique direction but I could not say that for "rho" since it depends on x and y

Cardinal

Feb 11, 2021 15:37

I meant unique unit vectors (my bad)

Cardinal

Feb 11, 2021 15:36

I mean, they just created to make them for sake of mathematical tractability

Cardinal

Feb 11, 2021 15:36

I think I now could fathom what is the idea behind in such definitions.

Cardinal

Feb 11, 2021 15:34

I mean, they are just a definition to make things read better

Cardinal

Feb 11, 2021 15:34

I think both of $rho$ and $phi$ directions are not actually unit vectors if we look at them carefully, because they are not unique they are dependable on x and y.

Cardinal

Feb 11, 2021 15:31

from the vector analysis though, I would say you only need the coordinates and either one would do the job.

Cardinal

Feb 11, 2021 15:30

I see what you are saying.

Cardinal

Feb 11, 2021 15:29

Literally this semester LoL

Cardinal

Feb 11, 2021 15:29

Yes, I am teaching Emag to the Undergrads

Cardinal

Feb 11, 2021 15:29

Hmm, for X-Y plane, I would say I don't agree with you

Cardinal

Feb 11, 2021 15:28

one is redundant in general

Cardinal

Feb 11, 2021 15:27

I mean, either \phi or \rho

Cardinal

Feb 11, 2021 15:27

What do you mean, it is not universal? It works for all the points on the X-Y plane

Cardinal

Feb 11, 2021 15:26

What I see is, any point on the X-Y plane can be completely described by the "\rho" unit vector

Cardinal

Feb 11, 2021 15:24

having a unit vector for $\phi$ does not make sense to me

Cardinal

Feb 11, 2021 15:24

I meant, only the $\rho$ direction does the job

Cardinal

Feb 11, 2021 15:23

I didn't say the whole cylindrical system is pointless

Cardinal

Feb 11, 2021 15:20

I suppose it's just a pure mathematical definition and there is no actual point in it !! :sweating: :embarrassed:

Cardinal

Feb 11, 2021 15:19

I'll appreciate if you discuss your takes.

Cardinal

Feb 11, 2021 15:19

Q: What is the point of having a unit vector $\hat{\phi}$ in the cylindrical or polar coordinates?

As we know in the cylindrical (or polar) coordinate system we have: $$\hat{\rho} = \cos{\phi} \hat{x} + \sin{\phi} \hat{x}$$ $$\hat{\phi} = -\sin{\phi} \hat{x} + \cos{\phi} \hat{y}$$ Now lets consider a given point $\mathcal{P}$ in the cylindrical coordinate as $\left(\alpha, \beta, 0\right)$. Us...

Cardinal

Feb 11, 2021 15:18

It's here:

Cardinal

Feb 11, 2021 15:17

I got a question for you.

Cardinal

Feb 11, 2021 15:17

Hope you are doing well.

Cardinal

Feb 11, 2021 15:17

Hello guys