square root of two - why the ancients

When the ancients discovered that the diagonal of a square with side length one is not a rational number, they were (apparently) shocked because it meant that it wasn’t a number at all - so there were magnitudes in nature that weren’t numbers. When we were taught this in school, we weren’t shocked at all (unless you were). It’s usually said that this is because we were in school and we were young. But it could also be due to the way we write numbers compared to the ancients. When I’m told that the square root of two is 1.4, or more precisely 1.41, or more precisely 1.414, or more precisely 1.4142, or more precisely... - I feel like this number is right before my eyes, just not fully revealed yet, like seeing a landscape through a window - I don’t see the whole thing because a wall is blocking part of it, but I can clearly see that it’s there. But when they saw that it was a little more than 1/2, but less than 3/2, or more precisely a little more than 4/3, but less than 5/3, or more precisely a little more than 5/4, but less than 6/4, or more precisely a little more than 7/5, but less than 8/5, or more precisely a little more than 8/6, but less than 9/6, or more precisely a little more than 9/7, but less than 10/7, or more precisely a little more than 11/8, but less than 12/8, or more precisely... - such a description gives the impression that this square root is eluding us, we try to catch it with fractions, but it always slips away.

comments:

2015.10.22 18:59 zibi

jak się nawalę, potrafię złapać Pi ułamkami...

back to homepage