Debates over how geometry is understood and learned date back at least to the days of Plato, with more recent scholars ...

Geometric objects take on different properties depending on the space in which you visualize them. Using techniques from an upstart field called tropical geometry — which analyzes complicated shapes ...

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 ...