“Mathematics students have cause to celebrate. A University of New South Wales academic, Dr Norman Wildberger, has rewritten the arcane rules of trigonometry and eliminated sines, cosines and tangents from the trigonometric toolkit. “ – read the rest of the article on physorg.com. It looks fascinating stuff.
Too bad it’s not yet available on Amazon.com, but you can get it from the publishing house directly (book to be launched on Sept 20th). Chapter 1 may be downloaded online: it’s on my reading list tonight.
“ Rational trigonometry
This remarkable new theory, revealed here for the first time, dispenses with all the usual complicated trigonometric functions and relations and establishes a trigonometry based entirely on elementary arithmetic and algebra. The essential quadratic aspects of geometry are brought to the fore, with the key concepts of quadrance and spread replacing distance and angle. The two subjects of geometry and periodic motion are cleanly separated; it is neither necessary nor desirable to have a theory which merges the two.
In Divine Proportions: Rational Trigonometry to Universal Geometry, Associate Professor N J Wildberger of the School of Mathematics at the University of New South Wales shows how to solve even complicated geometric problems without tables or calculators, with more accurate answers. Many engineering, surveying and physics problems are solved in this book, illustrating in detail the advantages of this new approach. For large scale problems, rational trigonometry harnesses modern computational power more efficiently.”