kamalktk
Antediluvian
- Joined
- Feb 5, 2011
- Messages
- 7,226
"Researchers proved the existence of a kind of shape that'd only been predicted to exist by theory."
https://gizmodo.com/new-13-sided-shape-the-hat-tiles-aperiodic-monotile-1850268575
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The hat is what’s known as an aperiodic monotile, which means that a single shape can tile a surface without any translational symmetry, or without its pattern ever repeating. The famous Penrose tilings are an example of aperiodic tiling, where the pattern is aperiodic but uses two different shapes.
The hat tiling only uses one shape, an “einstein,” which is German for “one stone,” making the pattern an aperiodic monotile. The 13-sided hat is a polykite shape, consisting of eight kites connected at their edges. The existence of an aperiodic monotile was purely theoretical until a research team led by mathematician David Smith and colleagues proved its existence in a preprint paper posted online this month.
https://gizmodo.com/new-13-sided-shape-the-hat-tiles-aperiodic-monotile-1850268575
--------------------------
The hat is what’s known as an aperiodic monotile, which means that a single shape can tile a surface without any translational symmetry, or without its pattern ever repeating. The famous Penrose tilings are an example of aperiodic tiling, where the pattern is aperiodic but uses two different shapes.
The hat tiling only uses one shape, an “einstein,” which is German for “one stone,” making the pattern an aperiodic monotile. The 13-sided hat is a polykite shape, consisting of eight kites connected at their edges. The existence of an aperiodic monotile was purely theoretical until a research team led by mathematician David Smith and colleagues proved its existence in a preprint paper posted online this month.
