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Steve Trettel

23 Oct, 3 tweets, 1 min read

The (2,11) torus knot complement. At first I figured making nice images of torus knots might look “boring,” but I think this is my favorite knot so far!

Here as well the picture is drawn by finding a parameterization to the normal tube (of some small radius) about the knot with respect to the spherical metric on S^3, then stereographically projecting from a point on the knot so we are viewing from “inside” the knot complement.

And here’s the (4,11) torus knot as well!

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Steve Trettel

@stevejtrettel

29 Jan 20

@Stanford

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.

There are an infinite number of ways to put our torus in its Nordic knit - but this infinitude comes in two flavors. First - having already put the sweater on the torus, many new “clothings” can be built by bunching it up a little here, or stretching a little there.

Read 24 tweets

Steve Trettel

@stevejtrettel

8 Nov 19

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

The discriminant of ax^2+bx+c, namely b^2-4ac determines whether the polynomial has two real roots (positive discriminant) or complex conjugate complex roots (negative discriminant). The discriminant=0 surface is a cone. 3/n

Read 10 tweets

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