| |
|
Irrational numbers have a great history. The story goes (all this could be false, of course, but everyone tells the story anyway) that the ancient greeks believed all numbers - all lengths of things in the world, say - to be the ratio of two whole numbers. A whole number divided by another is a rational number.
But they found - often attributed to Pythagoras, though Euclid is generally given credit - that there are some numbers which aren't rational. Take a square of side length 1, then the diagonal has length the square root of two, which is irrational. (Incidentally, this may be why Pythagoras theorem is usually stated in that god-awful way to do with squares on sides. Because if you look at the squares, you never have to confront an irrational number.)
So irrational means not rational, not a ratio. But due to the cod history that people learn, it also has to do with "doesn't make sense, arrgghhh!!! Not rational!".
If you are interested, have a look at this wikipedia page. The proof that the square root of 2 is irrational is Euclid's proof, and is one of the prettiest things in math (forget utility, btw, its all about pretty arguments). Its a little tricky, at first, but very rewarding. |
|
|
