© | Dror Bar-Natan's Image Gallery: Knotted Objects:

Planet Hopf

Hopf says that 3-space fibers over the 2-sphere, the Greeks say the 2-sphere is planet Earth, and Copernicus says it spins.
The consequences are ridiculous.

Swap Image / Video

Alternative version

Image/Video Downloads: PlanetHopf.png (2400x2400), PlanetHopf_720.png (720x720), PlanetHopf.ogg (720x720), PlanetHopf_240.ogg (240x240). Source files: Academic Pensieve: Projects: PlanetHopf.

See all 360 video frames at higher quality

What's shown? The pullback to S3 of a (partial) map of (spinning) planet Earth, via the Hopf fibration S3→S2, projected down to R3 by the stereographic projection. Much like the cheese wheel on the left, a wedge-shape of openning 80o is cut out of R3. The whole map of Earth can be seen on both sides of the cut (each in itself, a half-plane), with an 80o rotation between the sides. For improved visibility, the full pullbacks of only the G8 countries are actually shown, and only the pullbacks of Canada, Japan, and Italy are continued through the cut, in a translucent form.
A home made cheese wheel by David Fankhauser.