New Math

I made it as far as calculus in college. I had no idea what I was learning, it went over my head, but I memorised the formulae and passed the tests. But I remember trigonometry, the relationship between the angles and sides of a triangle, and all those sines, cosines and tangents.

Who says that science can't renew itself? A professor realised, with Einsteinian simplicity, that we have been looking at triangles all wrong for almost two thousand years! He recast the relationships and made it all very simple. It's called rational trigonometry:

Established by the ancient Greeks and Romans, trigonometry is used in surveying, navigation, engineering, construction and the sciences to calculate the relationships between the sides and vertices of triangles.

"Generations of students have struggled with classical trigonometry because the framework is wrong," says Wildberger, whose book is titled Divine Proportions: Rational Trigonometry to Universal Geometry (Wild Egg books).

Dr Wildberger has replaced traditional ideas of angles and distance with new concepts called "spread" and "quadrance".

These new concepts mean that trigonometric problems can be done with algebra," says Wildberger, an associate professor of mathematics at UNSW.

"Rational trigonometry replaces sines, cosines, tangents and a host of other trigonometric functions with elementary arithmetic."

You can take a look at a sample chapter here. It really is, even to these out of experience eyes, awfully simple. I see an echo of the old math lesson: In a right triangle, the sum of the squares of the two sides equals the square of the opposite side. Cool!