Mathematics can be fascinating, especially when it comes to patterns and symmetry. For years, mathematicians have been searching for a pattern that never repeats, and they finally found the answer. Let's find out together what makes this discovery so important.
“The hat”: the unique shape that creates a special mosaic
The pattern that never repeats itself has been identified by mathematicians as a 13-sided shape that they have dubbed “the hat”. This shape is the first real example of an “einstein”, a unique shape that generates a special mosaic of a plane that can cover a complete surface without gaps or overlaps, with a pattern that never repeats.
The new aperiodic monotile discovered by Dave Smith, Joseph Myers, Craig Kaplan, and Chaim Goodman-Strauss, rendered as shirts and hats. The hat tiles are mirrored relative to the shirt tiles. pic.twitter.com/BwuLUPVT5a
Mathematicians understood that “the hat” was composed of eight comets, four-sided polygons with two pairs of adjacent sides of equal length. Although this shape is simple, it is extremely complex, and scientists thought the shape would be much more complex before the discovery. This discovery could lead to research in materials science, as shapes that form mosaics that never repeat could help design stronger materials.
Why is this so important?
Understanding “the hat” is important because it solves a mathematical mystery that has puzzled mathematicians for years. Repeating patterns have translational symmetry, which means that one part of the pattern can be changed and it will overlap perfectly with another part, without rotation or reflection. However, “the hat” does not have translational symmetry, each section of its pattern appears different from each part that precedes it.
Furthermore, this discovery may inspire people to explore mathematics and shapes in new and creative ways. Who knows, maybe it will lead to another great mathematical discovery in the future.
The discovery of “the hat” is an important step forward for mathematics and materials science. It is a proof that the curiosity and perseverance of mathematicians can solve puzzles that have persisted for years.
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