## Tag: torus

## 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.

## 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.

## What Does It Mean to Be a Number? (The Peano Axioms)

If you needed to tell someone what numbers are and how they work, without using the notion of number in your answer, could you do it?