Volume of a Hypersphere

[tibees]

🦜 Big R refers to the radius of the cylinder, whilst little r refers to the radius of the sphere. R can be expressed in terms of r during the integral

[andrewz]

Calculus is so elegant. It looks messy but the fact that we can communicate the structure of such a theoretical object in meaningful language always amazes me. One of my favorite things was revolution of solids. Realizing we can create higher dimensional structures just by rotating lesser dimensional ones.

[Ty-]

Most of the times, I have no idea what she is saying, but I can’t stop watching her. It’s so fascinating, especially when she is talking about different dimensions !

[ktkatte]

I wanna drift endlessly in space while contemplating how to meet someone very far away by traversing a 4D sphere now

[SnakeWasRight]

I get chills even seeing someone on my phone draw on a chalk board

[jacobhempel]

The volume integral of a d-dimensional sphere is super helpful in statistical mechanics where you frequently find yourself integrating over 3N (N=number of particles) spatial and momentum coordinates.

[xydya]

Your voice is just so calming! I would so watch a longer lecture or even a Math ASMR

[YourCrazyOverlord]

I'm so glad we're getting more of these. I want like an hour long lecture in this style

[TheTatva]

She is a 5D Goddess, teaching us 4D by incarnating in 3D 🥹

[davidrobertson]

I am so close to understanding a 4th spatial dimension while also remembering the great series Little House on the Prairie

[mialotusmusic]

Ok but can we talk about the fact that you have the hair and look of a real life Disney princess?!

[ScotchVX]

Her calm obsession with 4D objects is out of control!

[tomtomdishman]

You amaze me every time Tibees! - Thank you! Tom- Mooresville NC.

[soar_on]

i listen with my ears and not my brain, awesome content

[callmejackaroo]

Whoa! Calculate the volume of that braid!!

[solomonafework]

You took the phrase, "she lives in a diffrent dimension" to a whole new level ❤

I don't know why 4th Dimensional Fairy Lady keeps getting recommended to me, but I don't mind it one bit, even if I don't really understand much maths at all

[YoungGandalf]

The mathematical formula doesn't seem too complex, but...trying to conceptualize a hypersphere is out of this world.

[jucom]

And by writing this as a shell integration we can find the surface volume of a 4d hypersphere: integ(0, r, V(R)dR)=pi²r⁴/2 so V(r)=d(pi²r⁴/2)/dr=2pi²r³.

[MegaUpMan]

Genuinely these have helped me reinvigorate my love for math ever since graduating college. Might have to go to grad school soon to study more of this, it’s seriously that interesting!!! Hahaha