u/AI_Highschool

Why do the gradients need to be parallel?
And why is “parallel” not enough—why do we still need to plug back into the constraint?

I made a short visual explanation (with 2D and 3D animation) to build intuition for Lagrange multipliers.

The goal was intuition first, formula second.

Would love feedback—especially if I oversimplified anything or if there’s a better way to explain the geometry.

https://youtu.be/fGVloOs4Lek?si=UQbjIIUpbiMjHRvh

Hi r/manim,

I wanted to share my project where I pushed Manim's 3D capabilities to explain Machine Learning mathematics.

This is a sequel to my previous gradient video, but this time I focused on transitioning from flat linear hyperplanes to complex multivariate polynomial surfaces.

You can watch the full video here:

https://youtu.be/xFF6IgU9eCw

Key animation milestones in the video:

• 0:00 Multivariate Linear Regression Made Simple
• 0:47 Visualizing Multivariate Polynomials and Nonlinear Separation
• 2:09 Intro to Gradients: Visualizing Gradients on a Bowl-Shaped Surface
• 3:29 Quick Intuition: Gradients in Linear vs. Polynomial Regression
• 4:52 Partial Derivatives Made Visual — Paraboloid Gradient (Slicing effect)
• 6:32 Comparing Linear and Polynomial (Perpendicular and Fastest)
• 7:53 Visual Proof: Gradient $\perp$ Contour Lines
• 9:55 Intuition from Partial Derivatives: The Gradient & Steepest Ascent
• 10:58 Does Gradient Always Show the Fastest Increase?

I would absolutely love to hear your feedback on the camera movements, the 3D surface rendering, or how I could optimize the rendering times for these dense vector fields.

If anyone is curious about how a specific part was coded, feel free to ask!

Hi everyone,

I’ve been creating educational videos to explain the math behind machine learning in a more intuitive and visual way.

YouTube:
https://www.youtube.com/watch?v=snIdXOjUG44

This time, I made a video about gradients—starting from the basic idea of slope, then building up to the full gradient vector intuition used in multivariable calculus and machine learning.

Topics covered:
• From derivative to gradient
• Why the gradient points in the direction of steepest increase
• What gradient magnitude really means
• Why the gradient is perpendicular to contour lines
• Visual intuition behind the math proofs

All animations were created with Manim (Python), with the goal of making abstract math concepts easier to “see.”

I’d really appreciate any feedback on both the mathematical explanation and the animation style.

Happy to answer any questions here as well!