“The einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles, that is, a shape that can tessellate space, but only in a nonperiodic way. Such a shape is called an einstein, a play on the German words ein Stein, meaning one stone.”

https://en.m.wikipedia.org/wiki/Einstein_problem

Penrose discovered the ‘Penrose Tiles’ 50 yrs ago, which was a phenomenal mathematical feat, for the past 50 years, even though it was two shapes, kites and darts.
Then this tinkerer came along and developed a single 13 sided shape that is non-repeating, based upon a hexagonal (honeycomb) pattern.

https://www.sciencenews.org/article/mathematicians-discovered-einstein-tile

It just amazes me that here it is 1/4 of the way through the 21st C and we have super computers and it’s taken all this time for one of us to figure out how to make a single shape that makes a non-repeating pattern.

Math is beautiful.



Edited 1 time(s). Last edit at 03/27/2023 10:11PM by schrodingerscat.

Mathematicians have been working on Goldbach's Conjecture (all even numbers greater than 2 can be written as the sum of two prime numbers) for almost 400 years, any nobody has been able to prove that it is true or false, though computers have tested it out into the trillions and all cases have been true so far.

It took about 2,500 years of trying to square the circle using straight edge and compass, until the 1800s, when it was proven to be impossible.

Humans have been counting for tens of thousands of years, but it wasn't until the late 1800s that a rigorous definition of integers was formulated. While everybody intuitively knows what an integer is, it was surprisingly difficult to really nail down the concept. Look up "Peano Postulates" if you want to see some serious math gobbledygook.

There are lots of problems that took a long time to solve, and many that are not yet solved (and may never be), and some that have been proven impossible to solve, which is a sort of solution in its own right.


But yeah, non-periodic tilings are very clever tricks to pull off.