Picturing Mathematics
a day ago
- #visualization
- #mathematics
- #fractals
- The author prefers low-tech math and trusts self-verifiable methods over computer-generated results.
- The Illustrating Mathematics workshop at ICERM in 2016 fostered a community focused on visualizing mathematical concepts.
- The author gave talks at the Illustrating Math webinar, including a eulogy for Roger Antonsen and a presentation on Ford spheres.
- Ford spheres are a 3D fractal described by Lester Ford in 1938, analogous to the more famous 2D Ford circles.
- Ford circles represent rational numbers geometrically, with their arrangement reflecting number theory principles.
- Ford spheres, like Ford circles, are dense yet sparse, illustrating the counterintuitive nature of countable dense sets.
- The author collaborated with Roice Nelson to visualize Ford spheres through cross-sections and animations.
- The animations reveal unexpected features like 'halos' and 'solar arches,' sparking further mathematical curiosity.
- The author hopes such visualizations can make math more accessible and engaging to non-mathematicians.
- The essay also touches on the author's past work with rotor-router blobs and the challenges of digital visualization.