## 17/09/2005

### No more classical Trigonometry? Here comes Rational Trigonometry

At least that’s what an australian academic, Dr Norman Wildberger, says. He says he managed to rewrite the classic geometry theorems and formulas without using trigonometric functions. His book might be worth a look.

From his introduction:

Rational trigonometry

The new form of trigonometry developed here is called rational trigonometry, to distinguish it from classical trigonometry, the latter involving cos θ, sin θ and the many trigonometric relations currently taught to students. An essential point of rational trigonometry is that quadrance and spread, not distance and angle, are the right concepts for metrical geometry (i.e. a geometry in which measurement is involved).

Quadrance and spread are quadratic quantities, while distance and angle are almost, but not quite, linear ones. The quadratic view is more general and powerful. At some level, this is known by many mathematicians. When this insight is put firmly into practice, as it is here, a new foundation for mathematics and mathematics education arises which simplifies Euclidean and non-Euclidean geometries, changes our understanding of algebraic geometry, and often simplifies difficult practical problems.

Quadrance measures the separation of points, and spread measures the separation of

lines. It turns out thatquadrance = (distance)^2

spread = ( sin (angle))^2although the actual definitions used in this text are independent of distance, angle and the trigonometric functions. They are ultimately very simple, based on finite arithmetic and algebra as taught in schools.

no more cosθ and sinθ ? One thing’s for sure…he will be strictly judged by millions of mathematicians for every word he’s written…math people are crazy people and they don’t like others playing smart on them…

good luck to Dr Wildberger…

Filed by kargig at 20:10 under maths

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