perturbations of a chaotic map

#mathsky

Euclid’s Elements is the second-most printed and studied book in history — after the Bible.

Written around 300 BC in ancient Greece, this edition is its first English translation (1570). It remained a core math textbook well into the 20th century.

Euclid, Newton & Turing

This weekend, at the John Rylands Library in Manchester, I finally found a historical copy of Euclid’s Elements.

And right next to it: Newton’s Principia and Turing’s handwritten notes. Completely overwhelming.

And they work in real life too :)

Smooth-rolling objects require virtually no force to start moving – even with low friction, they roll.

An object is “smooth-rolling” if its center of mass remains at a constant height while it rolls.

We created knots with this property by combining Morton’s knots with Two-Disk Rollers.

Smooth-rolling knots!

At @markpauly.bsky.social’s lab, we found a way to optimize knots for smooth rolling.

I presented our work at Bridges 2025 – the conference for #MathArt.

More below ↓

Here are the first 8 million integers, rendered by John Healy.

johnhw.github.io/umap_primes/...

What is the hidden structure of the natural numbers?

In the UMAP paper, @lelandmcinnes.bsky.social et al. embedded the integers as binary vectors of their prime factors.

This UMAP visualization of 30 million integers reveals a fractal-like geometry.

#UMAP #mathart #dataviz #numbertheory