Always wanted to have a unique bathroom or kitchen? Well, mathematicians have found the perfect tile for you.
A team from the University of Arkansas has discovered the first mold that can cover a wall without ever creating a repeating pattern.
The property is known as ‘aperiodic tiling’ and has so far only been achieved by using more than one shape.
But this one, called “the hat,” can fit into itself to produce infinite, expanding patterns.
It even retains its aperiodic tileability when the shape’s 13 sides are changed in length, allowing for even more patterns.
‘The hat’ can interlock with itself to produce infinite, extending patterns
A team from the University of Arkansas has discovered the first mold that can cover a wall without ever creating a repeating pattern (pictured)
Tiling refers to covering a flat surface with shapes that fit together without gaps or overlaps.
Aperiodic tiling is a specific type of tiling where the pattern of shapes used to cover the surface does not repeat.
This is in contrast to periodic tiling, which uses shapes to cover a surface in a pattern that repeats regularly, as with triangles and squares.
The first set of shapes that could combine to create infinitely different patterns was discovered in 1963 by the American mathematician Robert Berger.
This consisted of 20,426 unique shapes, but the finding led to further research into aperiodic tiling, to see if that number could be reduced.
The most famous aperiodic tiling set is known as the “Penrose tiling,” which consists of two different diamond shapes and was first published in 1974.
Since then, mathematicians have been searching for the elusive “einstein”; the form that can achieve aperiodic tiling by itself.
In 2010, a team from Duke University claimed to have found a shape that fit the bill, but that required using the tile plus its mirror image.
They did show that it was also possible to get an aperiodic tiling pattern without the reflected shape, but in three dimensions, not in a single plane.
For their 89-page study, published in arXivthe researchers from Fayetteville wanted to finally discover the true einstein, which means “one stone” in German.
“It has long been an open question whether such a tile exists,” they wrote.
The team first used computers to sift through hundreds of different shapes and eliminate those that clearly didn’t fit the bill.
They then looked more closely at the shapes thrown out as potential einsteins, and tried to prove mathematically that they would produce a periodic tiling.
“You’re literally looking for a one-in-a-million thing,” lead author Dr. Chaim Goodman-Strauss told me. New scientist.
“You filter out the 999,999 of the boring ones, and you’ve got something that’s weird, and that’s worth exploring further.”
“And then you start examining them by hand and you try to understand them, and you start pulling out the structure.
“That’s where a computer would be worthless, since a human had to be involved in constructing a proof that a human could understand.”
The only one they were successful with was the hat, and they managed to prove its periodicity twice.
The mathematicians hope that knowledge of their unique shape will lead to the creation of new materials that are extra strong or have other useful properties.
Repeating patterns are often seen in the molecular structures of crystalline materials and make them easy to break.
How Jack and Rose Could Both Have Fitted the Door: Mathematicians Debunk Famous Movie and TV Scenes
For most of us, when hooked on a gripping action sequence or stuck in a comedy, math is the last thing on our minds.
But some just can’t enjoy a movie or TV show knowing that Keanu Reeves wouldn’t have dodged that bullet, or Kate Winslet could have moved to let Leonardo DiCaprio watch the door.
In fact, they go off and do the equations to show how Ross Geller could have pulled the couch up, or Jack Traven’s bus couldn’t have jumped the gap in the highway.
Well, it turns out that Homer Simpson isn’t as dumb as he makes out, as he discovered the mass of the Higgs Boson in an episode of “The Simpsons.”
MailOnline reveals seven times mathematicians have debunked iconic moments in film and TV history.
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MailOnline reveals seven times mathematicians have debunked iconic moments in film and TV history
