To Domokos, 61, a professor on the Budapest University of Technology and Economics, this bizarre rocky outcrop is a wellspring of mathematical questions.
Inspired by rock cracks, Domokos devised a brand new framework for classifying polygonal tessellation that’s versatile sufficient to accommodate messy pure patterns, however rigorous sufficient to be helpful. Applied in geology, it reveals common patterns within the geometry of fractures at each scale from mud cracks to the tectonic jigsaw, and it’s now serving to NASA scientists perceive the surfaces of different worlds. His work on the geometry of pebbles has helped hint erosion on Earth and Mars. In the palms of MIT researchers, Domokos’s work on the balancing factors of 3D varieties impressed the design of a self-orienting tablet capsule for delivering vaccines to the abdomen. And most lately, Domokos teamed up with chemists to make use of his rock fracture geometry to foretell how molecules assemble into “2D” sheets—a notoriously cussed drawback often left to supercomputers.
“Gábor’s problems are somehow topological, somehow geometric, somehow mechanics, partial differential equations. Some [are] crazy,” says Sándor Bozóki, a mathematician on the Institute for Computer Science and Control in Budapest, who has printed with Domokos. “He’s not a leading figure in any of these fields,” says utilized mathematician Alain Goriely of Oxford University. But, he provides, like the most effective utilized mathematicians, “he is using them in the most clever and beautiful way.”
“The first thing that people do when they understand something: give it a name,” Domokos says. “And shapes don’t have names.”
Krisztina Regős, mathematician
Best recognized for co-discovering the gömböc—the primary convex 3D form with simply two balancing factors—Domokos goals to grasp the bodily world by describing its varieties within the easiest potential geometry.
He typically begins new tasks by concocting unique methods to categorise shapes. To show that the gömböc existed earlier than they discovered it, he and Péter Várkonyi launched mathematically exact definitions of flatness and thinness. To categorize pebbles, Domokos counts their variety of secure and unstable balancing factors. And to explain tessellating patterns in rock cracks or nanomaterials, he calculates simply two numbers: the common variety of “tiles” assembly at every vertex within the “mosaic” and the common variety of vertices per tile.
The level is to search out “a new language” to explain the shapes, says mathematician Krisztina Regős, one among Domokos’s graduate college students. “The first thing that people do when they understand something: give it a name,” Domokos says. “And shapes don’t have names.”
But with the precise language, it’s potential to start out asking questions: Do homogenous 3D shapes with simply two balancing factors exist? Yes. These shapes decrease flatness and thinness, and one is the gömböc—which, due to its geometry, all the time rights itself irrespective of how it’s set down. What occurs to pebbles as they erode? They lose balancing factors, getting rounder after which flatter over time. What does the Earth break into when it falls aside? Plato was proper: on common, it breaks into cubes.
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Of course, fields like geomorphology have already got schemes for classifying objects of research—there are a number of methods of cataloguing pebbles, as an illustration, says Mikaël Attal, a geomorphologist on the University of Edinburgh. But as a perpetual outsider, Domokos both doesn’t know or doesn’t care about upsetting conference. Even inside arithmetic, he doesn’t match right into a self-discipline.