Posts-2022
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
Post Zero: A Cascading Collection of Caveats
06 June
Here we make our introductions and discuss the animating ideas behind these collections of posts.
additional resources:
A Pattern Language and A Curvature Story
08 June
How A Pattern Language has informed the design and organization of my current approach to writing about mathematics. In the process we introduce our animated graphic novel A Curvature Story (available by clicking the Apple icon).
additional resources:
A Basic Website in RMarkdown (with an R renderscript)
05 July
Just because it’s a basic website doesn’t mean it’s not an effective website. A process is discussed that helped me understand the building of a basic website in RMarkdown. Many of the basic ideas shown in this post (e.g. YAML spacing, using YAML scalar and array variables, R script for rendering, etc.) were also used in the building of this blog you are now reading.
additional resources:
The Cost of Curvature
16 August
An attempt is made to re-cast the curvature of a sphere in terms of area (meters squared) and money (dollars). It turns out that, in one sense, the curvature of the earth doesn’t cost that much. Some of the mathematical ideas touched on in this post are surface area, arc-length, and great circles.
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On Geodesic Triangles and a Euclidean Limit
26 August
In this post we illustrate the interest that Differential Geometers (those folks who like to mix Calculus with Geometry) have with the concepts of curvature and geodesics. We illustrate curvature as that deviant quality inherent to a sphere which deforms the standard Euclidean result requiring angles of a triangle to add to 180 degrees. We also see that in defining the Differential Geometric equivalent of straight lines (geodesics), the mathematical and computational complexities increase drastically. This is the first post which illustrates the Maple package I have written (called tensorAddOns) whose purpose is to handle the difficult computations involving many of the higher dimensional objects in Differential Geometry.
additional resources:
Maple Conference 2022
25 October
A short introduction to the Maple package tensorAddOns which fascilitates many tensor computations in differential geometry and physics.
additional resources:
Tensor Computations with tensorAddOns
25 October
