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 scalene triangle has 3 sides of different lengths and 3 unequal angles. An isosceles triangle has 2 sides of equal length. The dashes on the lines show they are equal in length. The angles at the ...

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 ...

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 ...