Posts-2023
The first principle is that you must not fool yourself
and you are the easiest person to fool.
Richard P.
Feynman
the writing process: a safeguard against
this first principle
Level:
general audience
approachable
calculus
advanced
Intrinsic v. Extrinsic Geometry and the Metric Tensor Illustrated
06 March
We illustrate the metric tensor as a mathematical book-keeping device which accounts for the variable change necessary in converting ground-distance to hiking-distance in a topographical map. Calculations are done in topographical maps to re-enforce the intuitive explanation given of intrinsic and extrinsic geometry.
additional resources:
An unConcise/math Vision for eBooks
11 May
a fixed layout ePub comprised of self-contained text/animation/assignment layers
additional resources:
On Tensors
11 Sept
From Linear Algebra to Surface Curvature: The Mathematics of a Curvature Story. Starting from introductory Linear Algebra (matrices, vectors, and multiplications thereof) we develop the Kernel-Index or Tensor Notation as written about by J.A. Schouten in the book Ricci-Calculus. Concepts from Linear Algebra are motivated by way of Colors and Tensors are motivated as a means of Storage. The Linear Algebra and Tensor machinery converge with a treatment of the computation of Surface Curvature from both an intrinsic and extrinsic point of view. We conclude with both graphical and computational illustrations of Gauss’ Theorema Egregium.
additional resources:
Conversion of Maple Output to Mathematica Input
15 Sept
