Re: Survivor: the trig challenge


"Ian Johnston" <ian.groups@xxxxxxxxxxxxxx> wrote in message
news:cCUlhtvFIYkV-pn2-4477yzVGC4Ri@xxxxxxxxxxxx
> On Sat, 26 Nov 2005 20:12:26 UTC, "Norman Wildberger"
> <wildberger@xxxxxxxxxxxxxx> wrote:
>
> : These short papers, meant for a high school audience, discuss a
> : simpler form of trigonometry that students can learn in a fraction of
> the
> : time required for the usual trig.
>
> Do you do complex numbers in terms of spread and quadrance as well?
>
> Ian
>
> --
Yes, the idea is to dispense with the usual (cos theta, sin theta)
description of the unit circle in favour of the rational parametrization
((1-t^2)/(1+t^2),2t/(1+t^2)). In fact it turns out that not only polar
coordinates, but 3d spherical coordinates also can be replaced by purely
algebraic rational coordinates involving quadrance and spreads.

Many classical volume, surface area, moment of inertia problems involving
spherical symmetry can be done this way. See the download of Chapter 27 at
wildegg.com.

Norman


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