I made an animation to show the intuition behind Prince Rupert's Cube using Manim library.

Link: https://youtu.be/75Bvw3o9Dac?si=OnEM_z-GTlB1BQ5D

#Math #Mathstodon #Geometry #Manim #Python #MathAnimation #VisualMath #SciComm #Mathematics

Watch at: https://youtu.be/LvFyHqzaIZ0
Play at: https://www.desmos.com/3d/d2eetcw1bz

#youtube #youtuber #youtubechannel #desmos #desmosart #desmosanimation #desmos3d #christmas #christmas2025 #christmasTree #christmasEve #merrychristmas #merryxmas #merrychristmas2025 #xmas #xmas2025 #xmastree #animation #animated #animation3d #3d #3dart #3danimation #nerd #geek #math #maths #mathart #mathanimation #graph #equation #art #artist #artistsonmastodon #snow

3Blue1Brown angrily lashes out at you for being bad at math (POV)

https://peertube.ichigo.everydayimshuflin.com/w/4H3XRkPRRVquaYX5q7yUWZ

I didn't understand much of it - and still found this animation amazing².

(I must've been under a rock 2 years ago)

https://m.youtube.com/watch?v=B1J6Ou4q8vE

#math #animation #mathanimation #stickfigureart #stickfigures

USM is a single, systematic framework that unifies trigonometric, hyperbolic, and complex-exponential substitutions into one coherent method. No more hunting through a dozen separate “recipes” for different radicals or inverse-trig integrals—you rewrite x + b as e^(±i α) (or e^θ), track sign/branch choices algorithmically, and reduce everything to a rational (“polynomish”) integral in a new variable.

Why USM shines for ∫ e^(arccos(x)) dx:
• Transforms e^(arccos(x)) into simple powers of t = e^(–i arccos(x))
• Eliminates the usual integration-by-parts slog
• Integrates term-by-term in one shot, then back-substitutes for a crisp final form

📄 Dive deeper! Check out my draft article “A Unified Substitution Method for Integration” for full proofs, more examples, and the USM’s broader scope (link in bio).

#UnifiedSubstitutionMethod #USM #Calculus #Integration #MathAnimation #Manim #MathHack #STEM #Education #InstaMath #LearnWithAnimation #MathLife #GarciaUSM #ReadTheDraft

I don't do a lot of animations, but couldn't resist with this one. This traces the path of 25 iterations of the system

x ↦ x - 0.4 sin(y + sin(0.4y))
y ↦ y - 0.4 sin(x + sin(-2x))

with initial (x, y) the set of points on a circle of radius 12, as the center moves from (-5, -0.4) to (+5, -0.4).

#mathart #mathanimation #fractalanimation #trippy #iteratedfunctionsystem #generativeart #ffmpeg

#MathAnimation: #ParallelTransport

https://buster.me.uk/globe/

An animation (HTML5 canvas and Javascript) made for a very small, very informal talk, which was supposed to be about gauge theory but only got as far as talking about connections and #ParallelTransport. The audience already knew all about it but they were very indulgent (both of them)!