This 13 sided shape is also referred to as an "aperiodic monotile" which is a specific shape - one shape to that can cover a plane without repeating the pattern. The term Einstein does not refer to the famous physicist. Instead, it refers to the German term for one stone. Furthermore, all the conditions for this shape are found in geometry and has no additional constraints inflicted via matching conditions.
This shape also known as a polykite aka The Hat because it vaguely resembles a fedora hat and it assembles tiles in through substitution. Originally, they had over 20,000 tiles but that has been decreased to 2 back in 1974 but at that point couldn't get it down past the two. Then around 2016, someone became interested in it and found the solutions. To prove it, they used computer coding using software that had recently been written. Prior to this software being written, they would have had trouble proving it. They also discovered that the doesn't lose its aperiodic nature when the sides of the shape are changed.
Furthermore, it stands between order and disorder. The shapes fit neatly together but the pattern can never repeat itself and that is what makes it an einstein shape. It is actually a two dimensional shape with straight edges so its classified as a polygon. This particular discover can be used in physics, chemistry, and even in the study of crystals.
Most mathematicians love the idea because it is so simple, easy to visualize and understand. Let me know what you think, I'd love to hear. Have a great day.
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