# Niles Johnson

## Department of Mathematics

### The Ohio State University, Newark

Here you will find a few pictures and some information about my recreational projects.

## Artistic Projects

Most of what I do has some kind of artistic component; it's more apparent in some projects than others.

### Papercraft

Some fun during the holidays! Click through for descriptions, animated gifs and interactive spinners!

### The 120-cell

During a discussion of the 120-cell I used the Sage Single-Cell server to make an interactive model of the relevant Hopf fibers, based on my earlier Hopf fibration project.

Fibers showing the 12 cores for rings of dodecahedra making up the 120-cell. The view shown here is looking straight down the z-axis.

### Constructing a spectral sequence

Here is a colored-pencil illustration to accompany the construction of a spectral sequence for a filtered chain complex. The longest part of this, by far, was drawing all those parallel lines.

### Visualizing seven-manifolds

In January 2012 I finished an animation Visualizing Seven-Manifolds based on Milnor's 1956 construction of exotic 7-spheres. This 9-minute video is my longest to date!

A slice of the seven-sphere, computed using Sage and Tachyon.

### Hopf animation

My first major video project was an animation of the Hopf fibration, inspired by Ken Shoemake's famous picture. Check out the result on my Hopf video page!

A raytraced visualization of the Hopf fibration, computed using Sage and Tachyon.

A second version, showing the base 2-sphere and the special fibers over the North and South poles.

### Aperiodic tilings

An aperiodic tiling fills the plane without ever repeating!

### Pythagorean triples

Learn how to derive a formula for Pythagorean triples. It's based on finding rational points on the circle!

## Even more

Here is a list of other projects, and other things I think are neat.

• My incomplete, anecdotal notes about applying for jobs.
• Some time I'd like to learn how to use trackbacks. Then I could send links to the arXiv.
• I use MathJax to display LaTeX on my webpage: $\int_{- \infty}^\infty e^{-x^2} \, dx = \sqrt{\pi}$
• I use TeX4ht to generate pdf and html versions of my CV from the same source file.
• I have implemented a JavaScript feature which you can use to send me an RSA-encrypted message using my public key, in case that was something you needed to do. In the HTML source there, you can also read how to set up a function like this for yourself, using your own public key.
• A QR code:

Where does it point? Well, that's for you to figure out :) Here is one link which will let you generate your own.

• I've started to be a regular user of TikZ, and now I have my own TikZ demo page.
• My Erdős number is at most 4. I've collaborated with Brian Boe, Nick Gurski, and Dan Nakano, all of whom have Erdős number at most 3