On 9/18/05, Robert G. Seeberger <[EMAIL PROTECTED]> wrote: > > http://physorg.com/news6555.html > > 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. > > What's more, his simple new framework means calculations can be done > without trigonometric tables or calculators, yet often with greater > accuracy. > > 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." > > "For the past two thousand years we have relied on the false > assumptions that distance is the best way to measure the separation of > two points, and that angle is the best way to measure the separation > of two lines. > > "So teachers have resigned themselves to teaching students about > circles and pi and complicated trigonometric functions that relate > circular arc lengths to x and y projections – all in order to analyse > triangles. No wonder students are left scratching their heads," he > says. > > "But with no alternative to the classical framework, each year > millions of students memorise the formulas, pass or fail the tests, > and then promptly forget the unpleasant experience. > > "And we mathematicians wonder why so many people view our beautiful > subject with distaste bordering on hostility. > > "Now there is a better way. Once you learn the five main rules of > rational trigonometry and how to simply apply them, you realise that > classical trigonometry represents a misunderstanding of geometry." > > Wild Egg books: http://wildegg.com/ > Divine Proportions: > web.maths.unsw.edu.au/~norman/book.htm<http://web.maths.unsw.edu.au/~norman/book.htm> > > > xponent > Wonders How This Will Affect Power Factor Correction Maru > rob >
Doesn't this scheme make it really hard to calculate distances? From the looks of it, it involves a lot of square-rooting. ~Maru
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