Saturday, September 17, 2005

No need for sine (and cosine)?

If you have slightest interest in geometry, you have to read this. It's the first chapter of a new book called "DIVINE PROPORTIONS: Rational Trigonometry to Universal Geometry" in which the author proposes new system to handle Euclidean geometry without need for angles (and sin, cos, tan etc...). Lengths and angles are replaced by "quadrance" and "spread", which might seem like crazy idea at first, but has the effect of anyone being able to calculate trigonometry problems by hand, using rational numbers, without need for tables or calculators.

Not only is it "interesting bold idea", it could also be applied to computer software, possibly making things like realtime raytracing more feasible (although most in-game trigonometry today is done using pre-computed tables, I'm afraid).

6 comments:

Tomas L said...

This guy seriously thinks he found some 'divine' stuff. I wasn't reading the book but i do not see why one should forget sins. As long as i play with triangles it is probably fine, however, once going into something periodic (e.g. quantum mechanics) the angle is the right thing. This is just because it is the natural measure of separation, unlike spread. To conclude: math likes to be divine but physics not.

Anonymous said...

Tomas you're right on this one. There's no reason why anyone should forget sins...

Fuxoft said...

Except Jesus, of course!

stenlis said...

I don't know how about you, guys but at my next confession I am going to tell the priest I replaced my sins with simple arithmetics.

Tomas L said...

I am going to replace my sins with coses, according to cos^2=1-sin^2, to have my warm bed in Heaven guaranteed.

Jan Vaněk jr. said...

I found some discussion of it at Luboš Motl's blog. They didn't go very deep and certainly didn't bother explaining for the lay audience, but as far as I understand it, the author just takes an obvious though obscure idea in a related abstract field and makes an academic exercise of developing it (kind of like suggesting everybody switches to hexadecimal numbers from now, with obvious advantages). And he's very good at marketing. Well, when the book is out, a better evaluation should appear.