# Mathematicians Invent a New 13-sided Shape with Incredible Probabilities

The curious tile was discovered by computer experts. The only shape that can cover an entire plane without repeating a pattern is known as "einstein". And this unique design only needs 13 edges.

In mathematics, "aperiodic monotile", also called "einstein" because it means solitaire in German, is a shape that can cover a plane but never repeat.

Craig Kaplan, one of four authors and professor of computer science at the University of Waterloo, says: “In this paper, we present the first truly aperiodic monotile, a shape that forces periodicity through geometry alone, without additional constraints imposed through matching conditions.

We have shown that this polycyte shape, which we call the "hat", must come together in tilings using a technique of substitution.

According to team member and University of Arkansas professor Chaim Goodman-Strauss, "you're looking for something that's literally seen in a millionth." “After eliminating the 999.999 boring ones, what's left is a strange one that's worth further investigation. Then you begin to examine, understand and reveal their structure with your hands.

Such a breakthrough had never occurred in the history of aperiodic tile. Kaplan tweets that the first aperiodic sets contained more than 20.000 tiles. Later work reduced this figure to 92, then six, and finally two-dimensional clusters in the form of the famous Penrose tiles. However, Penrose tiles date back to 1974.

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Others have since created 2D sets, but no one has been able to discover an "Einstein," a single shape that periodically tiles the plane, according to Kaplan. Could such a shape exist?

It is now.

The aperiodic character of the design was demonstrated by the researchers using computer programming, and as an intriguing side note, the shape remains so even when the length of its sides changes.

Kaplan says: “We've finally found one!”

It's time to rebuild the bathroom.

Source: popularmechanics – TIM NEWCOMB

Günceleme: 31/03/2023 17:21