Abstract
The approximation of arbitrary points on the unit circle by so-called Pythagorean points will be considered where Pythagorean points are points of the form (x/z, y/z), withx, y, z integers satisfyingx 2+y 2=z 2. An analogue of the approximation theorem of Hurwitz will be derived with a best possible approximation constant. Further, the set of all points will be characterized for which this constant cannot be improved; also an improvement of this constant for the remaining points will be given.
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Kopetzky, H.G. Rationale Approximationen am Einheitskreis. Monatshefte für Mathematik 89, 293–300 (1980). https://doi.org/10.1007/BF01659493
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DOI: https://doi.org/10.1007/BF01659493