This video discusses the discovery of a new type of shape called an Einstein Tile, which is a shape that can cover a surface without repeating in a predictable pattern. Mathematicians had been searching for such a shape for over 50 years, and in March of the year this video was published, it was finally found by a retired printing technician named David Smith. This discovery led to the development of multiple aperiodic monotiles, including one called the Spectre, which has practical applications in materials science. These aperiodic patterns behave differently from periodic ones and are being explored for various purposes.
1. The episode is sponsored by Brilliant.
2. The episode discusses the discovery of a shape that can completely cover a surface without a predictable repeating pattern.
3. This shape was unknown to mathematicians until recently.
4. Mathematicians had been searching for this shape for over 50 years.
5. The discovery of this shape was announced in March of the current year.
6. The discovery has caused excitement within the mathematics community and a festival was held in its honor.
7. The shape is referred to as a nonperiodic tiling in mathematics.
8. Nonperiodic tilings are when a shape or set of shapes can cover a plane without any gaps, but it's impossible to create a repeating pattern.
9. The shape is called an aperiodic tile.
10. The first set of aperiodic tiles was discovered in 1964.
11. The original set of tiles had 20,426 different tiles.
12. Over time, the number of tiles was reduced until a set of six tiles was found.
13. Roger Penrose's work reduced the number of tiles to two.
14. The episode mentions a video by Veritasium about Penrose tiles.
15. The episode discusses the discovery of a single shape that can only tile aperiodically, known as the Einstein Tile.
16. The discovery of the Einstein Tile was made by a retired printing technician, David Smith.
17. Smith discovered a simple shape that behaved strangely and was named a polykite.
18. Smith emailed computer scientist Craig Kaplan about his discovery and they worked together to prove the shape's aperiodicity.
19. The proof used a technique called the unique hierarchy method.
20. The hat tiling was proven to be aperiodic by showing it must be built in a unique hierarchy.
21. Smith discovered another aperiodic monotile, the turtle, shortly after finding the hat.
22. Smith found that the turtle and the hat were related and could be morphed into each other.
23. This discovery resulted in an infinite continuum of aperiodic monotiles.
24. The result was published in March, 2023, just five months after Smith discovered the hat.
25. The episode mentions that aperiodic patterns are being used to make new materials.
26. Physicists are excited about the properties of aperiodic lattices.
27. Scientists are experimenting with aperiodic lattices and have found that they behave differently than their periodic counterparts.
28. Smith has suggested that the hat and the turtle could be used to tile a bathroom floor.
29. Smith has contributed to a groundbreaking discovery without any formal training in mathematics.
30. The episode encourages viewers to join