To Domokos, 61, a professor on the Budapest College of Know-how and Economics, this atypical rocky outcrop is a wellspring of mathematical questions.
Impressed 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. Utilized 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. Within the palms of MIT researchers, Domokos’s work on the balancing factors of 3D types impressed the design of a self-orienting tablet capsule for delivering vaccines to the abdomen. And most just 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 downside often left to supercomputers.
“Gábor’s issues are someway topological, someway geometric, someway mechanics, partial differential equations. Some [are] loopy,” says Sándor Bozóki, a mathematician on the Institute for Laptop Science and Management in Budapest, who has revealed with Domokos. “He’s not a number one determine in any of those fields,” says utilized mathematician Alain Goriely of Oxford College. However, he provides, like the most effective utilized mathematicians, “he’s utilizing them in essentially the most intelligent and delightful means.”
“The very first thing that folks do once they perceive one thing: give it a reputation,” Domokos says. “And shapes don’t have names.”
Krisztina Regős, mathematician
Finest identified 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 types within the easiest attainable geometry.
He usually 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 purpose is to search out “a brand new language” to explain the shapes, says mathematician Krisztina Regős, certainly one of Domokos’s graduate college students. “The very first thing that folks do once they perceive one thing: give it a reputation,” Domokos says. “And shapes don’t have names.”
However with the appropriate language, it’s attainable to begin asking questions: Do homogenous 3D shapes with simply two balancing factors exist? Sure. These shapes reduce flatness and thinness, and one is the gömböc—which, due to its geometry, at all times rights itself regardless 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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In fact, fields like geomorphology have already got schemes for classifying objects of examine—there are a number of methods of cataloguing pebbles, for example, says Mikaël Attal, a geomorphologist on the College of Edinburgh. However 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.