Newswise — New Brunswick, N.J. (Nov. 30, 2020) – The artist M. C. Escher brought complex mathematical ideas to life through dizzying illustrations like Circle Limit IV (Heaven and Hell), in which angels and demons soar through an infinite, bowl-shaped space. Their winged bodies form a pattern that mathematicians call a lattice.

In December, a Rutgers University-New Brunswick mathematician will co-host a workshop, convened by the American Institute of Mathematics and National Science Foundation, to ask, among other things: How would those angels and demons look if Escher’s drawing were 22-dimensional? Or 1,001-dimensional? Or in any number of other dimensions?

Welcome to the world of “hyperbolic reflection groups,” the name for the type of geometric space Escher depicted in his Circle Limit engravings. They represent what you’d see if you placed a single object – say a single angel-devil picture – at the bottom of a bowl and surrounded it by mirrors to make the image reflect itself, over and over, infinitely. “It’s not unlike what you see when you’re surrounded by mirrors in a dressing room or barbershop, but in a barbershop you’re standing on flat ground, not the bowl-shaped hyperbolic space that Escher depicted. That gives a completely different geometry for the ways your reflections will line up with each other and the patterns they’ll create,” said Alex V. Kontorovich, a professor of mathematics at Rutgers-New Brunswick’s School of Arts and Sciences and an organizer of the “Arithmetic Reflection Groups and Crystallographic Packings” workshop which begins Dec. 14.

The full story, with images, is here.

A WikiArt image of Escher’s Circle Limit IV: Heaven and Hell can be found here.

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