Rational Angled Hyperbolic Polygons
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math.GN
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angledhyperbolicrationalsidelengthsalgebraiceveryexist
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We prove that every rational angled hyperbolic triangle has transcendental side lengths and that every rational angled hyperbolic quadrilateral has at least one transcendental side length. Thus, there does not exist a rational angled hyperbolic triangle or quadrilateral with algebraic side lengths. We conjecture that there does not exist a rational angled hyperbolic polygon with algebraic side lengths.
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