When you hear the words "rational" and "irrational," they might bring to mind the relentlessly analytical Spock in "Star Trek." If you're a mathematician, however, you probably think of ratios between ...

Most people rarely deal with irrational numbers—it would be, well, irrational, as they run on forever, and representing them accurately requires an infinite amount of space. But irrational constants ...

Imagine being asked to pick a number from 1 to 10. You are quite likely to pick a whole number; I have never seen someone do otherwise. But you could also pick the number pi, whose decimal expansion ...