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 ...

A technician often has to sketch or design ductwork and the other parts of an HVAC system. Sometimes you have to sketch the room or building you are working with. This means working with lines, angles ...

Polygons can be regular or irregular in shape. A polygon is a closed 2D shape with at least three sides. A regular polygon is a polygon with all equal sides and angles. An irregular polygon is a ...

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 ...

A road bike frame is essentially three big tubes stuck together in a triangle, four thinner ones to support the rear wheel and a fork to hold the front wheel and allow it to turn. But it’s a lot more ...