Abstract
A subset E of the plane is said to be a configuration with rational angles (CRA) if the angle determined by any three points of E is rational when measured in degrees. We prove that there is a constant C such that whenever a CRA has more than C points, then it can be covered either by a circle and its center or by a pair of points and their bisecting line. The proof is based on the description of all rational solutions of the equation $$ \sin \pi p_1 \cdot \sin \pi p_2 \cdot \sin \pi p_3 \cdot = \sin \pi q_1 \cdot \sin \pi q_2 \cdot \sin \pi q_3 . $$ KeywordsSingular PointRegular PointRational SolutionArithmetical ProgressionRational MultipleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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