A geometric shape that can create endless patterns without repeating itself: a hat

It is known that some people are far from geometry and mathematics. However, geometry and mathematics are among the most important elements of everyday life. There is no moment in life when we do not need math. Similarly, it is impossible to see a structure in which we do not encounter elements of geometry. In short, both geometry and mathematics are more important to human life than we think. Recently, a very interesting and exciting development took place in this regard. Scientists from the Universities of Yorkshire, Cambridge, Waterloo and Arkansas have discovered a geometric shape that can cover any surface without creating a repeating pattern! Let’s look at the details together.

Mathematics and geometry are two extremely important elements of human life.

In particular, geometry can be encountered at any moment of life. Triangles, hexagons, circles or rectangles… Moreover, the geometric shapes that spontaneously exist in nature allow some fascinating images to emerge. However, an extremely interesting and important event has occurred that will excite geometry lovers.

Scientists from the universities of Yorkshire, Cambridge, Waterloo and Arkansas have announced the discovery of a geometric shape that can cover a surface without repeating itself.

Tiles made with shapes that continue forever but do not repeat are called “non-periodic tiles”. Non-periodic tiling, which uses geometric shapes but never matches, has been something scientists have been working on and dreaming of for a long time. However, it was only recently discovered by the mathematicians David Smith, Joseph Myers, Chaim Goodman-Strauss, and Craig S. Kaplan.

Previously, non-periodic tiling was implemented using several different geometric shapes.

Non-periodic tiling using only one geometric shape has only recently been achieved.

The new geometric shape, met with great enthusiasm in the scientific world, was called the “hat”.

Thanks to this new geometric shape with 13 ribs, patterns can be obtained that last forever and do not repeat. According to scientists, even when the length of the sides of the hat changes, the non-periodic mosaic pattern does not disappear.

Thanks to this shape, any surface can be given “the shape of the same shape, but with a unique pattern” without gaps and overlaps. In other words, it will be possible to obtain an infinite number of patterns using one geometric figure.

The origins of research on non-periodic patterns date back to the 1970s. However, only in 2023 was it possible to discover among mathematicians a perfect geometric figure called “einstein” (German solitaire).

According to scientists, the new shape could lead to important developments in fields such as engineering, architecture and design.

However, one of the groups that made this discovery, Dr. According to Craig S. Kaplan, the geometric shape, like other unusual patterns, has a fundamental function of developing the imagination. For this reason, the scientist argues that the shape called the hat can be widely used in the field of art in the short term.

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