Compass Ruler
August 27th, 2010 | 
Author: Compass Ruler
Is it possible to draw an angle of 20 degrees using just a ruler and a pair of compass?
I would change "draw" to "construct". This means the standard Euclidean construction using only an unmarked straightedge and a pair of compasses (usually, these days just called a compass):
Then the statement is correct, but far from obvious. The trisection of certain angles (e.g. of a 90 degree angle) is possible to construct. But there is a famous problem, called "trisection of an angle", where given any angle one tries to construct an angle 1/3 as big, i.e. trisect the angle. The ancient Greeks attempted this problem with ruler an compass but never found a way (except by using other tools also). It was finally proved in 1837 that ruler and compass alone are inadequate tools to trisect an arbitrary angle. In particular, it can be proved that ruler and compass cannot trisect a 60 degree angle, so one cannot construct, with ruler and compass, a 20 degree angle.
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US $24.00
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