Chaos VI: Chaos and the horseshoe

First, an old idea by Henri Poincaré (1854-1912): when studying a vector field in space, we can sometimes find a small disc that the trajectories hit repeatedly. Studying the points on the disc where the trajectories pass through is often a lot simpler than studying the vector field as a whole. We go from dynamics in continuous time to dynamics in discrete time.

Chaos VI: Chaos and the horseshoe

Associahedra: The Shapes of Multiplication

What happens when you multiply shapes? This is part 2 of our episode on multiplying things that aren’t numbers.

The Multiplication Multiverse

Multiplication of numbers is an associative property and we can make sense of “multiplication” between things that aren’t numbers but that’s not considered as associativity.

Telling Time on a Torus

What shape do you most associate with a standard analog clock? Your reflex answer might be a circle, but a more natural answer is actually a torus. Surprised? Then stick around.

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