Editing Differential Geometry (section)

== <span style="color: #FFFFFF;">Remembering</span> ==
* '''Differential Geometry''' — The branch of math using calculus to study smooth shapes.
* '''Tangent Space''' — The "flat" plane that just touches a curved surface at a single point.
* '''Normal Vector''' — A line sticking straight out from a surface, perpendicular to it.
* '''Gaussian Curvature''' — A measure of how much a surface curves in two directions at once.
* '''Theorema Egregium''' — Gauss's "Remarkable Theorem": curvature can be measured from "inside" a surface without seeing the 3D space it's in.
* '''Metric Tensor''' — The mathematical "rulebook" that defines distances and angles on a specific surface.
* '''Vector Field''' — An assignment of a "direction and speed" to every point in space (like a wind map).
* '''Manifold''' — A shape that looks like flat Euclidean space when you zoom in (like the Earth's surface).
* '''Covariant Derivative''' — A way of measuring how a vector changes as it moves along a curved surface.
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