Taking a stroll through the space of right angled hexagons in hyperbolic geometry can be mesmerizing (math to follow!) 1/n If somebody hands you a shape with all right angles, you can proceed to tile the space around you by just flipping it over and over, reflecting through its edges. In the euclidean plane, such shapes are called 'rectangles' and all have four sides. 2/n

I’m back! Having a busy month moving and settling in @Stanford, but this hasn’t totally kept me away from making cool pictures :) Here’s a depiction of an Anosov mapping class on a torus 1/n Let’s unpack a bit what this means. One way to picture a homeomorphism from the torus to itself is a way of “putting clothes” on the torus: if the domain is some toroidal Christmas sweater and the codomain our torus, a homeomorphism tells us which part of the sweater goes where.

Better video (and explanation!) of this week's mathematical conspiracy; a thread. 1/n The space of quadratic polynomials can be identified with R^3; we think of the function ax^2+bx+c as the point (a,b,c). The polynomials with integer coefficients form the cubical lattice. 2/n