# Jonathan Hanke's Website

Research and Software in Number Theory

## Nice Animations

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Below are some interesting mathematics animations/visualizations of various fibrations.

The Hopf Fibration — This beautiful representation of the (quaternionic) Hopf fibration $S^3 \rightarrow S^2$ was created by Niles Johnson. His description of the mathematics behind this animation can be found here.  For the brave, he also has an introduction and visualization of the (octonionic) fibration $S^7 \rightarrow S^3$ here, which was first presented at John Milnor’s 2012 Abel Prize conference.

The Modular Fibration — This is a fibration of $S^3 \rightarrow S^2 \cong P^1(\mathbb{C})$ using the modular $j$-function, created by Ihechukwu Chinyere while attending the African Institute for Mathematical Sciences (AIMS) in South Africa. His well-written paper describing the mathematics can be found here. It is based on the computer code written by Niles Johnson to visualize the Hopf fibration above.

Written by jonhanke

February 10th, 2013 at 8:33 pm

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