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The section on bisecting an angle with Euclidean compass and straight edge contains errors.
First, you may not draw a circle with an arbitrary radius ("any radius you like"). The only thing you can do with a Euclidean compass is to draw a circle with the center at a known point, and the circumference containing a known point. You cannot just "pick a point," you must construct it. This problem can be avoided by instead drawing the circle with center at the vertex of the angle, and through one of the other two points that are given to define the angle. Restatement: given angle ABC (B the vertex), draw the circle with center B and radius the length of segment AB.
Second, when you lift a Euclidean compass off the paper, it collapses. You cannot just move the compass and keep it set at the same radius.
Mike Ochs
B.A. Mathematics, Univ of Colorado