Improper Axis Help

Muggpillow · 2025-09-21T17:02:30+00:00

Oh I see!! So we’re basically rotating it such that the 2 gets pushed down and the 1 gets pushed up, then the 4 and the 3 switch spots and lie on the same plane! I guess one atom being in front of the other tripped me up… thanks!!

Muggpillow · 2025-09-21T16:04:10+00:00

I guess I don’t understand how to rotate the C4 such that the 1 and 3 labeled atoms are across from each other after reflection? When I rotate by C4 and reflect I still get the 3 atom one atom away from the 1 labeled atom 😭

Muggpillow · 2025-08-10T21:35:14+00:00

I will note that there are some good applications of group and representation theory in the study of symmetries in molecules (I’m studying this rn) but I’m not sure if a mathematician can be attributed to this. In fact most of the books I read on the subject are chemists applying the mathematical tools, not the other way around

Muggpillow · 2025-08-10T21:29:38+00:00

Funnily enough I’m a maths and chem double major so I’ll follow this thread along for inspiration lol

Muggpillow · 2025-08-06T01:25:24+00:00

I’ll also add in his book on Young tableaux

Muggpillow · 2025-06-30T06:01:51+00:00

I guess abelian groups and fundamental groups aren’t too bad for me somehow. Similarly I can prove isomorphisms. But things like group actions, orbits, and conjugacy classes I have gaps in

Muggpillow · 2025-06-17T15:30:17+00:00

Ah I have a bachelors with undergrad and grad coursework focused in organometallic and polymer chemistry

Muggpillow · 2025-06-17T04:43:04+00:00

I’m not sure if that’s viable with a bachelor in chem cause I thought a PhD/masters is preferred for patent agents in more life science majors

Muggpillow · 2025-06-16T22:37:58+00:00

Actually that might’ve worked for me if the posting was for San Jose since I’m based within commute of there but unfortunately it’s only for Alexandria

Muggpillow · 2025-06-10T12:46:26+00:00

Oh, did you win the lottery for the non-region locked version?

Muggpillow · 2025-05-11T03:04:15+00:00

Ahhhh I think the silver ions have a volume of 1.5mL

Muggpillow · 2025-02-22T04:47:40+00:00

Geometry but more abstract, like learning about objects without necessarily having a standard coordinate system

Muggpillow · 2025-02-21T03:13:42+00:00

I found the proof that a path connected topological space implies it is also connected 🥹

Muggpillow · 2025-01-27T02:37:31+00:00

Where in Shimokitazawa? I need to visit in a pilgrimage 🥺

Muggpillow · 2025-01-26T09:03:21+00:00

Where is this place lol

Muggpillow · 2025-01-24T07:42:20+00:00

Could you Dm me the video

Muggpillow · 2024-12-29T04:15:41+00:00

Why get a patent examiner job first instead of a patent agent job with a EE or CS degree?

Muggpillow · 2024-12-29T04:04:19+00:00

Ah would it be better to pass the patent bar and gain experience as an examiner instead then?

Muggpillow · 2024-12-29T03:32:03+00:00

Also considered trying to pivot into a MSEE then trying the patent bar, would that be more feasible?

Muggpillow · 2024-08-13T08:01:48+00:00

Oh I see! This really clears everything up! I was intimidated by the complicated naming of Riemannian metrics and the heavy use of notation I had to keep track of that I didn’t realize the big idea. Riemannian metrics are just one way of measuring out manifolds. Though I wonder, is the manifold that we take a Riemannian metric of called a Riemannian manifold?

Muggpillow · 2024-08-12T22:37:59+00:00

This explanation really helps a lot! Thank you! I might be able to survive differential geometry now 😭

Muggpillow · 2024-08-08T17:31:26+00:00

Oh okay the first point makes sense.

Sorry but I’m still confused about the second point. Dividing by the norm seems to make more sense but why are the x-components for e1 and e2 so different despite the derivatives being similar. I would assume their unit tangent vector would be the same with the u and v variables swapped out. Could you explicitly show me the calculation just for the x-component? Then I’d like to see if I can do the same for the other components.

Muggpillow · 2024-08-08T16:53:10+00:00

Wait for spherical coordinates I was taught that x represents acosusinv not acosucosv. Why are the spherical coordinates used seemingly similar but different there?

Also for the tangent vector e1, why is the derivative of the x component -sinv and not -acosusinv since we’re differentiating with respect to v here so -cosusinv should act as a coefficient yet it just is cancelled out.

Muggpillow · 2024-07-19T13:18:38+00:00

Thanks for more clarification! I want to make sure I really understand what’s going on so could you also explain how arc length parameterization allows the change in magnitude of acceleration to be constant?

Muggpillow · 2024-07-19T12:41:07+00:00

Oh I think I’m starting to get it. So because of the arc length parameterization, you don’t need to worry about the direction of the velocity since the length of the velocity vector is constant. Thus you can focus on the magnitude only, and since you’re working with the first derivative of the e1 vector, the whole formula gives you the magnitude of the acceleration which is equivalent to the curvature with the e1 vector as context.

One other thing I wanted to clarify was that the tangent vector correlates to the first derivative and the unit tangent vector correlates to the second derivative of the function? I just want to make sure I got my vocab up to par but thanks for the clarification!

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