[extropy-chat] Rational Trigonometry

Emlyn emlynoregan at gmail.com
Thu Sep 29 03:11:12 UTC 2005


On 24/09/05, kevinfreels.com <kevin at kevinfreels.com> wrote:
>
> I read a report the other day about Norman Wildberger's "Rational
> Trigonometry" which supposedly does away with sines, cosines, and tangents
> and allows for using algebra and simple arithmetic. It is also supposedly
> more accurate. I hadn;t seen anyone here comment on this and I was wondering
> if anyone has had a chance to review his work.

It's explained in wikipedia:

http://en.wikipedia.org/wiki/Rational_trigonometry

"From Wikipedia, the free encyclopedia.
Rational trigonometry is a modern envisioning of trigonometry by Dr.
Norman Wildberger of The University of New South Wales, explained in
his book Divine Proportions: Rational Trigonometry to Universal
Geometry.

Instead of distance and angle, it uses as its fundamental units
quadrance (square of distance) and spread (square of sine of angle).
This choice of variables enables calculations without square roots and
trigonometric functions that generate irrational numbers - hence the
name. For distinction, he refers to the traditional trigonometry as
classical trigonometry.

It is otherwise broadly based on Cartesian analytic geometry, with a
point defined as an ordered pair (x,y) and a line as a general linear
equation Ax + By + C = 0."

(find more detail on wikipedia itself)

---

It looks kind of cool. I get the feeling that it would feel weird to
use his approach for someone trained in "classical" trigonometry (his
term), until you grok it, then it would be really smooth.

--
Emlyn

http://emlynoregan.com   * blogs * music * software *



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