Books/
see also unconcisemath.com
Jason M. Osborne
mathematician + educator + creative tinkerer + writer
This is the book (our latest, not Div but Grad and Curl) you will want to read if you wish to start at the beginning to build a foundation with the fundamental concepts of points, vectors, and dual vectors which underpin much of differential geometry
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more books by
jason m osborne
unconcise/math
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In A Curvature Story the concept of Curvature is introduced in pictures and animations with minimal use of or appeal to formulas. Many of the mathematical ideas used in following books are introduced as Graphical Definitions in this first book in the series.
The second book On Tensors: From Linear Algebra to Surface Curvature supplements the imagery of A Curvature Story with the mathematical machinery of tensors needed for a thorough treatment of both the intrinsic and extrinsic computation of surface curvature. The building of this tensor infrastructure is laid down on a solid Linear Algebra foundation that is motivated by an appeal to Color Vectors and Data Storage
From the book On Tensors, one of the we learn from Gauss' Theorema Egregium that curvature is Intrinsic, whereby curvature can be defined completely in terms of The Metric Tensor. In this third book, we focus on illustrating the concept of intrinsic geometry and show how the elevation data of a topo map can be encoded in the metric tensor to obtain intrinsic distance and angle computations on a surface
With the geometric and computational understanding of curvature gained from the first three books, we delve deeper in this fourth book On Geodesic Triangles into a geometric treatment of Geodesics (on surfaces of revolution with the sphere as a special case) and show how the sum of the angles of these triangles are related to curvature
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