When most people think of shapes, they imagine a triangle, a rectangle, or maybe even a fancier-sounding rhombus or trapezoid. But to mathematicians, shapes encompass a vast universe of surprising ...

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In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space. When you gaze out ...

“Topology is the study of whether there are holes in a space,” says mathematician Dennis Sullivan of the City University of New York Graduate Center. He just won one of the most prestigious awards in ...