Picture math class without those confusing sines, cosines, and tangents. Picture an architect working out the surface area of various building structures without having to work through a range of degrees. In short, how much simpler trigonometry would be if we could remove the complicated bits and distil it down to crystal clear calculations.

University of New South Wales mathematician Norman Wildberger has done just that and espouses the theory that a rational, algebraic approach to trigonometry could open the way to a universal geometry. His is a revolutionary text, essentially overwriting centuries of tedium with a crisp new approach that is bound to raise hackles among conventionalists. However, Wildberger is not discarding the foundations of mathematics, instead he is constructing an architecturally sound new geometry that unites number theory and algebra and simplifies many geometrical problems.

In “Divine Proportions”, Wildberger (an alumnus of Toronto and Yale) clearly lays out the required definitions and theorems and illustrates tehm with useful formulae, diagrams and exercises.

If you’re a professional mathematicia, scientist, engineer, or a student who wants a different take on their studies, this book could change your understanding of mathematics.

Jim, I’d have to defer answering that question to someone in that area of expertise, sorry.

David,

I’m curious about the application of your trigonometric approach to EKG signal detection. Essentially, with a few measured EKG leads and the appropriate algorithm, could one provide accurate, estimated coverage across the entire thorax? This would seem to provide much broader and more refined capture of electrical heart/cardiovascular signals and, as a result, much “higher-resolution” of disease indicators.

J

Yes Tyrone, trigonometry is simultaneously weird and hard and easy (but only occasionally!)

this is so weird and hard but sometimes easy