Unexpectedly Intriguing!
21 September 2005

Tired of trigonometry? Having trouble keeping track of all those sines, cosines, tangents, cotangents, et cetera, so on and so forth?

Norman Wildberger of the University of New South Wales in Sydney, Australia may have done away with all of those in rewriting the Euclidean geometry that we've all come to know and dread in high school math classes. Here's the scoop from the UNSW's news release announcing the publication of his book Divine Proportions: Rational Trigonometry to Universal Geometry, now available from Wild Egg Books:

This text introduces a new and simplified approach to trigonometry and a major restructuring of Euclidean geometry. It replaces cos, sin, tan and all those other transcendental trig functions with rational functions and elementary arithmetic. It develops a complete theory of planar Euclidean geometry over a general field without any reliance on 'axioms'. And it shows how to apply this new theory to a wide range of practical problems from engineering, physics, surveying and calculus.

The news release spells out the potential impact for math students:

Trigonometry has for centuries been difficult for students to learn. Part of the reason is that the foundations of the subject are problematic, relying on vague pictorial definitions of the key concepts of angles and trigonometric functions. That means students rarely come to grips with the logical structure of the theory. Rational trigonometry is much simpler, relying on the fundamental quadratic notions of quadrance and spread, and with basic laws that can be derived completely rigorously using only elementary algebra.

As it happens, quadrance is equal to the square of the distance between two points and spread is equal to the square of the sine of an angle. Here are some extracts from the text that provide more detail of the scope of Wildberger's rewriting of the rules of trigonometry:

Sigh. Where was this guy when I was in school....

Labels:

About Political Calculations

Welcome to the blogosphere's toolchest! Here, unlike other blogs dedicated to analyzing current events, we create easy-to-use, simple tools to do the math related to them so you can get in on the action too! If you would like to learn more about these tools, or if you would like to contribute ideas to develop for this blog, please e-mail us at:

ironman at politicalcalculations

Thanks in advance!

Recent Posts

Indices, Futures, and Bonds

Closing values for previous trading day.

Most Popular Posts
Quick Index

Site Data

This site is primarily powered by:

This page is powered by Blogger. Isn't yours?

CSS Validation

Valid CSS!

RSS Site Feed

AddThis Feed Button

JavaScript

The tools on this site are built using JavaScript. If you would like to learn more, one of the best free resources on the web is available at W3Schools.com.

Other Cool Resources

Blog Roll

Market Links

Useful Election Data
Charities We Support
Shopping Guides
Recommended Reading
Recently Shopped

Seeking Alpha Certified

Archives