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Graphics Archive — Special Topics: Hyperbolic Geometry

“Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.” — The Poincaré Conjecture.

“Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.”

- The Poincaré Conjecture photo credit : https://bit.ly/2KDYLoC

If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing…


Comments to: [email protected] Created: Tue Feb 11 7:10:27 CST 1997 — Last modified: Tue Feb 11 7:10:27 CST 1997.

Copyright © 1990–1995 by The Geometry Center, University of Minnesota. All rights reserved. For permission to use these images, please contact [email protected].

Blue Origin, SpaceX, ULA win $5.6 billion in Pentagon launch contracts

Join our newsletter to get the latest military space news every Tuesday by veteran defense journalist Sandra Erwin.

The three companies will compete for orders over the contract period starting in fiscal year 2025 through 2029. Under the NSSL program, the Space Force orders individual launch missions up to two years in advance. At least 30 NSSL Lane 1 missions are expected to be competed over the five years.

Physicists use machine learning techniques to search for exotic-looking collisions that could indicate new physics

One of the main goals of the LHC experiments is to look for signs of new particles, which could explain many of the unsolved mysteries in physics. Often, searches for new physics are designed to look for one specific type of new particle at a time, using theoretical predictions as a guide. But what about searching for unpredicted—and unexpected—new particles?