Curvature

How do you measure how much a curve actually curves? There are many ways to view the answer to this question, but all land you on the same mathematical quantity, known simply as "curvature".

Curvature intuition

Curvature formula, part 1

Curvature formula, part 2

Curvature formula, part 3

Curvature formula, part 4

Curvature formula, part 5

Curvature of a helix, part 1

Curvature of a helix, part 2

Curvature of a cycloid