Poohsticks and differential geometry
Random thought: Poohsticks illustrates well Lie differentiation
Joris' Theorem
A proof is given of Joris' theorem, which states that if two coprime powers of a function are both smooth, then so is the original …
When are curves tangent to hypersurfaces?
Given a curve and a hypersurface, both in Euclidean space, how can we tell if the curve is tangent to the hypersurface?
Torsion, curvature, and parallel transport
An expository note on the notions of curvature and torsion of a general linear connection on the tangent bundle.
A Characterization of Geodesics
About the Einstein-Infeld-Hoffmann theorem characterizing geodesics.
A Better Estimate of Kempner's Series
The Kempner series recently regained some notoriety due to a Saturday Morning Breakfast Cereal comic (the last panel). The observation …
Simulating Closed Cosmic Strings
One of my current research interests is in the geometry of constant-mean-curvature time-like submanifolds of Minkowski space. A special …
Shooting particles with Python
Numpy simulation of how classical and quantum particles interact with potential barriers.
Bundles and derivatives
Expository article on the geometric notion of derivatives.
Bessaga's converse to the contraction mapping theorem
A converse to Banach's fixed point theorem, due to Bessaga, is discussed.