Survivor the Trigonometry Challenge

Survivor the Trigonometry ChallengeShort Description
and explain that trigonometry is the study of the measurement of triangles. I propose to demonstrate the theory just for this particular triangle, to keep …

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Content
Survivor: the Trigonometry Challenge
N. J. Wildberger
School of Mathematics UNSW
November 23, 2005
Abstract
A mathematical drama involves marooned students, a triangle, and a
tense competition between classical and rational trigonometry.
1 Threeguysmakeatriangle
We’ve been marooned on a desert island for a month with plenty of food, pens
and paper, but little entertainment. As a diversion from lying in the sun and
eating tinned sardines, the red haired guy suggests we explain trigonometry to
him, which he never understood in high school, despite being a fan of geometry.
The tall skinny guy and I have just finished the standard first year university
mathematics courses, so we agree this is a splendid idea to pass some time.
Unfortunately we have no trig tables, calculators or computers with us, but
we should be able to explain most everything with just pen and paper. After all,
if you really grasp a mathematical subject, simple examples should be accessible
by hand. Especially if its as basic as high school trigonometry.
So I get out a big piece of graph paper, randomly pick the three points
A1 = [4, 1] A2 = [1, 2] A3 = [2, 4]
and explain that…

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