Bramblethorn
Sleep-deprived
- Joined
- Feb 16, 2012
- Posts
- 18,623
Think of it as a haiku for mathematicians. Yes, it would be much easier to just take a photograph of that lovely autumn day instead of trying to describe it in just three short lines, but working within the constraints of the form is part of the challenge.Pardon us non-mathematicians. But can't you do this by putting a ruler on top of the rectangle, measuring how long it is from side to side, dividing it into three, and drawing lines down accordingly? I don't even know how to deal with vectors and coefficients and what not.
Besides, rulers don't give an exact measurement. If my rectangle is 51.2002 cm wide, the best I can get with a standard ruler is "about 51.2 cm". One-third of that is seventeen and one-fifteenth centimetres, but my ruler doesn't have markings for fifteenths of centimetres, so again the best I can do is approximately one third.
If you're trying to build a house or whatever, "approximately" is fine. Leave the Euclidean geometers at home, they'll only get in your way and drink your wine. But part of the aim of this kind of exercise is to develop the kind of intellectual rigor that distinguishes between "approximately" and "exactly", between "looks like this construction works for this particular rectangle" and "this construction will work for any rectangle".