Curvature, in all of its aspects is at the core of geometry. Going straight is central to geometry, but it is also a fiction, since we live in a curved world with gravitational attraction in landscapes of mountains, valleys and planes. Nevertheless it is a very useful fiction, and the basis of Euclidean geometry and our science. How then to define being curved, intrinsically and/or as a deviation from planarity? This is one of the central questions in mathematics and geometry; we have derived Euclidean geometry, one geometry that is in accordance with our intuition and our position on earth (with its gravitational field).
Sectional Curvature Gaussian Curvature Principal Curvature Chebyshev Polynomial Euclidean Geometry
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