Differential Geometry, Ch. 2 Gaussian Curvature

Note date change: Apr 28 -> Apr 21

### Can a Surface Detect Its Own Curvature?

What if you were confined to a surface—with no outside view—could you still tell if it’s curved?

We’re studying Visual Differential Geometry and Forms — Tristan Needham, focusing on intuition first, formulas second.

Last meeting: curved geometries, spherical vs. hyperbolic space, angular excess, and geodesics as “straight” and “short.”

This meeting: Gaussian curvature—how a surface detects its own curvature using only internal geometry—completing Act I.

### What to Expect

• Calculus required
• Reading Chapter 2 encouraged
• Reviewing problems is helpful
• Discussion-based (not a lecture)

### Why It Matters

Curvature underlies:
• General relativity
• Gauge theory
• Machine learning & data geometry

### Important

Discussion will stay focused on the agenda.
For casual physics conversation, see other group meetings.

### Optional References

Weeks • Baez & Muniain • Greenberg • Isham

### More in Physics With Friends

This event is one of many collaborative study tracks in our Physics With Friends community.
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Join anytime — come prepared to think.