Description
In the continuous space and time that surrounds us, our orientation is aided by tiling patterns free of gaps and overlaps.
Although calendars and maps contain many artificial elements, in many cases, the origin of these tilings is nature itself.
This lecture will focus on the tilings of three-dimensional space. We can observe beautiful examples in both animate and inanimate nature, ranging from the chambered shell of the Nautilus to cracked boulders and the membranes of human tissues. Still, the geometry of spatial tilings largely remains an enigma to this day, and over recent millennia, this mystery has inspired some of the greatest minds from Plato to Riemann, and from Aristotle to Michelangelo.
In this lecture, I will present a few ideas that fundamentally define our knowledge of spatial tilings.