Notes

Note: Integral Axioms Values:

Note: 2D Geodesic Cheatsheet:

Note: Quadratics for Grown Ups:

Note: Graph Geodesics Extrinsic:

Note: Graph Geodesics Intrinsic:

Note: Differential Forms Cheatsheet:
Tricks for working with the Laplacian using Differential Forms

Note: Hyperbolic Dodecahedra Ball Model:

Note: Hyperbolic Dodecahedra:

Lie Derivative, Geometrically:

Note: Lie Derivative Example:

Symmetries and Conserved Quantities along Geodesics:

Note: Ode Existence Uniqueness:

Note: Ode for Exponential:

Note: Ftc From Axioms:

Note: Exponential Integration:

Note: Exponential Differentiation:

Note: Exponential Properties:

Note: Gravity Along Curve:

Note: Laplacian Discovering Preharmonics:

Note: Laplacian Preharmonic:

Note: Laplacian Spherical Symmetry:
Finding Fundamental Solutions in metrics with spherical symmetry

Note: Laplacian Isometries:

Note: Laplacian Chain Rule:

Note: Laplacian Constant Curvature:
Finding Fundamental Solutions in Euclidean, Spherical and Hyperbolic Geometry

Linking Number:
Gauss' linking number of closed curves and algebraic topology.

Winding Number:
Understanding the Algebraic Topology underlying the winding number of a closed curve in the plane.

Note: Gx Developing Pair:

Hyperbolic Springs:
Deriving the ODE for a spring which is pushed in hyperbolic geometry (it oscillates!)

Convolution and Differentiation of Distributions:
If F is a distribution and g is a function, why is (DF)*g equal to F*Dg?

Topologizing The Space Of Distributions:
Why do we need to require convergence of the derivatives when defining a topology on the set of distributions?

Note: Hyperbolic Heptagons:

Note: Hyperbolic Hexagon Realizations:

Note: Hyperbolic Hexagon Moduli:

Note: Hyperbolic Pentagon Realization:

Note: Hyperbolic Pentagon Moduli:

Deep Time:
Some thoughts on the importance of appreciating the immensity of earth's history.

Life in Hyperbolic Space:
The dangers of life in a negatively curved space

Cassini:
Saying goodbye to my favorite space craft, on the eve of its entry into Saturn's atmosphere.

Cubics and Braids:
The bridge between the 3-strand braid group and the trefoil knot complement

Hopf:
An old note, from my early graduate school days, explaining the hopf fibration.

Lattices:
Lattices in the Plane and the Trefoil Knot

Convolution:
A note I wrote to myself in undergraduate, when trying to understand the definition of convolution.

Geometric_series:
A note from early college explaining the summation of infinite series.

Divergence:
Notes to myself from early college about what divergence means.

The Quadratic Formula:
A derivation of the quadratic formula interpreting monomial expressions as lengths and areas.