Differential Geometry - 11 - Gauss Map x Gauss Curvature

What is Differential Geometry? Curves and Surfaces is a course in basic differential geometry focused on problem solving and aimed towards research level geometry.
arxiv.org/abs/...
This video was animated using the Manim extension of Python, developed by the Manim community, and originally created by Grant Sanderson: github.com/Man...
The code used for this video can be found in the repository: github.com/zam...
Music:
The Memories I Never Had - Synthetic Tides
Midnight Rider - The Big Let Down
Night Light Speed - The Big Let Down
Polygon - Ben Elson
The creation of this video was partially supported by Penn State University

[@nikolaskaarsberg7754]

This is easily the best video I've seen on this topic. Great explanations and the visuals help so much. Great video!

[@mightyowl1252]

These videos are really well made, I hope you make more of them. The explanations are very clear and the visual examples are great

[@hyperduality2838]

Positive curvature (dark matter, synergy) is dual to negative curvature (dark energy). Curvature is dual. Contravariant is dual to covariant -- vectors or functors -- dual basis. Attraction is dual to repulsion -- forces are dual! "Always two there are" -- Yoda.

[@jjw4832]

Really well made. Concise and clear explanations.

[@MertowVA]

Fantastic visualizations. Great work! Also great use of manim.

[@tim-701cca]

7:06 = that shows the relations to Normal Curvature and 2nd fund.form. This helps!

[@TheJara123]

Marvelous man...keep.up

[@unkn0wnus3r97]

excellent video!

[@user-jy7gn2xe5r]

High quality