A Hopf map is an interesting way to explore a 4-dimensional structure: it maps each point in a sphere (bottom) to a circle in a 4-dimensional sphere. replaynext - 1/4

A set of points along the equator unveil an interesting structure: the flat torus. A torus that you can flip upside-down.

replaynext - 2/4

replaynext - 2/4

You are probably now thinking "but what does a 4D sphere actually look like?" You can't really *see* it, but here we use a stereographical projection to show some points of a 4D sphere into 3D space.

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replaynext - 3/4

Hover and click the sphere below to add new rings to the structure and explore the Hopf fibrations!

clear points restore points

clear points restore points

Argh, your machine doesn't support the features in this viz. Here's an image of what you're missing!

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