However, for these four researchers, the victory is more than just decoration, as it solves an age-old mathematical problem.
This is because their formation represents, in plane geometry, the first truly exponential monotile: unlike a sequence of triangles or squares, this unique block of shapes can be terminated without forming a monotony. They solved the problem Ian Stein (
a stonein German) which deals with the ways in which a program can be overridden.
Intuitively, a tessellation consists of dividing a plane into slices without gaps or overlaps. Examples abound in nature, for example in human creations such as bees or checkerboards.
All these examples of tilings are periodic, which means they are called symmetrical
We can imagine taking an infinite checkerboard, sliding it into a square, and then putting it back down again, each piece fitting perfectly into the shape of the checkerboard.Explains a press release from the University of Arkansas, in which one of the researchers, mathematician Sime Gutman-Strauss, is associated.
The first examples of abiotic shells were created in the 1960s, and 20,000 different shapes were required. This number gradually decreased until the 1970s, when the famous British mathematician Roger Penrose created a collection of aperiodic tiles that used only two shapes.
Since then, the goal has been to bring the aperiodic tileset back to a uniform format. The feat was accomplished by a quartet that included Craig Kaplan, a computer science professor at the University of Waterloo in Canada.
We present the first truly aperiodic monotile, which implements exponentials only through geometry without additional constraints. […] We demonstrate that this form, the so-called “cap” polychite, assembles into shells based on an alternating mechanism.Professor Kaplan says.
The cap has a 13 sided shape. This discovery will eventually lead to tangible applications in materials science and will often attract the attention of visual arts specialists.
Something I never expected in my lifeProfessor Edmund Harris, one of the members of the committee, is delighted.
The details of this work would be the subject of a scientific paper (new window) Will be released in the coming months.