Tuesday 15 October 2019

More on the $3 Tensor

Here are two relevant lectures on the algebraic and differential geometry behind tensors. See The Power of ThoughtWildberger on ChromogeometryAll About e and Tensor Calculus.

First the history, going back to Huygens and the use of involutes and evolutes and how these ideas led to Gauss' characterization of the curvature of a surface.


The next extends these basic ideas to ideas of Tangent Spaces


And the second half of the last lecture connects back to discrete spaces and all the way back to Euclid and the idea of solid angle.


Now you be able to see how dual spaces of polynomial approximations  give you the objects in Tensor Calculus


These lectures give a clear idea of the connection between parametric splines and polynomial approximations




See The Power of Thought, for more on splines and numerical methods.

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