Sometimes I find a particularly nice idea or way of looking at something. A proper subset of those times I write something down, and in a further proper subset I am proud of the resulting writeup. Below, I've listed some documents in that latter category.

• Intuitive way to understand the Gauss-Bonnet Theorem (high-effort Stackexchange answer). Nominally this is about the Gauss-Bonnet theorem, but really it's about the relationship between (Gaussian) curvature, angular excess of triangles (that is, the sum of the angles minus pi) and parallel transport around small loops. It's an amazing story. 

• Automorphisms of Isom(X) Let X be a metric space. Here's a fairly general strategy for computing Aut(Isom(X)): characterize point stabilizers algebraically, so that automorphisms send point stabilizers to point stabilizers. The resulting map X→X often preserves some structure on X. The group Aut(Isom(X)) will be the group preserving this structure. This gives satisfying geometric computations of Aut(Isom(X)) for X hyperbolic space, regular trees, Euclidean space and more.  

• The Godbillon-Vey class as "helical wobble" The Godbillon-Vey class is a cohomological invariant of codimension-1 foliations. In his paper "Noncobordant Foliations of S^3", Thurston described this invariant as measuring the "helical wobble" of the leaves of the foliation. I found this both confusing and enticing. This is the explanation I eventually came up with.