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 ...

Interior angles in a triangle add up to 180˚. Triangles close triangleA polygon with three straight sides. have three sides, therefore they have three angles. Interior angles in a triangle sum to a ...

Parallel lines close parallel lines Lines which never meet and stay the same distance apart. Parallel lines are indicated by a pair of arrows. are two or more straight lines that remain the same ...

In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...