## rational trigonometry site

These pages will attempt to provide an overview of Rational Trigonometry and how it allows us to reformulate spherical and elliptic geometries, hyperbolic geometry, and inversive geometry, and leads to the new theory of chromogeometry, along with many practical applications.

**Reference**

The main reference is the book

*Divine Proportions: Rational Trigonometry to Universal Geometry*

by N J Wildberger, ISBN 0-9757492-0-X (hardcover), Wild Egg Books, Sydney 2005 available here at http://wildegg.com and also at amazon.com.

Here are free downloads of sections of this book (all in pdf format)

- Preface -- a one page outline of the book
- Contents -- table of contents
- Introduction -- a detailed description of the book
- Chapter1 -- an overview of rational trigonometry and justification
- Chapter27 -- polar and spherical coordinates done rationally

**YouTube Videos**

I have posted a series of YouTube videos on rational trigonometry and geometry in the WildTrig series under user name njwildberger. These videos are meant for a general audience with an interest in geometry, and are packed with information about rational trigonometry and its applications, and about geometry more generally.

Elementary papers about RT (by N J Wildberger)

The following papers are meant for an academic audience, meaning mathematicians, university math majors, and enthusiastic high school teachers. You may download as pdf.

- The Wrong Trigonometry -- Facing up to the true difficulties of classical trigonometry, usually hidden behind the power of calculators.
- A Rational Approach to Trigonometry-- Statements and brief proofs of the 5 main laws of rational trigonometry, together with illustrative examples.
- Survivor: the Trigonometry Challenge -- Classical or rational trigonometry---which is superior? This paper poses some geometrical challenges to both.
- Pythagoras, Euclid, Archimedes and a new Trigonometry --How the basic laws of rational trigonometry follow naturally from the work of the ancient Greeks.

Additional Papers and Resources (by others)

To post your comments/papers/developments involving Rational trigonometry here, send them to me at n.wildberger (at) unsw (dot) edu (dot) au

- The Impossibility of Trisecting an Angle with Straightedge and Compass: An Approach Using Rational Trigonometry by David Poole, Trent University
- Samuel's blog on Rational Trigonometry (2005)
- Print a rational protractor by M. Ossmann (2005)

- Rational Trigonometry: Computational Viewpoint by Olga Koshaleva
- Euler Math Toolbox by Rene Grothmann
- Why does Rational Trigonometry not work over a field of characteristic two? Stack Exchange 2013
- New trigonometry is a sign of the times: Phys Org
- A rational trigonometry calculator by Peter Bollhorn 2016
- Rational Trigonometry applied to Robotics by Joao Pequito Almeida
- Rational Trigonometry applied to Robotics slideshow by Joao Pequito Almeida
- Rational Trigonometry blog by Dextre Zebre
- Pentagons with Rational Trigonometry by Tim Leslie
- Planar Universal Geometry by Tim Leslie (UNSW Master's thesis done under my supervision: this is very good)
- Euler's Rational Trigonometry by E Sandiner (OK this is not our RT, but a nice description of some of Euler's thinking in roughly parallel directions. It would be fun for someone to reframe this in terms of our RT)
- A fast algorithm for coordinate rotation without using transcendental functions by J. REsa, D. Cortes and D. Navarro in Int'l Conference Scientific Computing / CSC 2015 (This is a nice paper which applies RT to the important computational problem of rotating frames of reference).
- Rational Trigonometry and the simple pendulum an internet discussion

**Links, news and reviews**

Here are links to various places on the internet where you can read about Rational Trigonometry.

- Wikipedia
- ABC Online News
- Slashdot.com
- Phys.org
- EE Times
- Book Review for Proc. Edinburgh Math. Soc. by L. Wiswell
- Book Review for Journal of Australian Math. Soc. by R. Gover

- M. Ossman (print a protractor)
- Michael Hardy (Amazon book review)
- Jim Sogi (book review)
- Book Review for Mathematical Intelligencer by James Franklin
- Book review for Solstice: An Electronic Journal for Geography and Mathematics by S. L. Arlinghaus
- Intro to Rational Trig at Cut The Knot (a great site for geometry)