Euler’s inequality in absolute geometry
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Two results are proved synthetically in Hilbert’s absolute geometry: (i) of all triangles inscribed in a circle, the equilateral one has the greatest area; (ii) of all triangles inscribed in a circle, the equilateral one has the greatest radius of the inscribed circle (which amounts, in the Euclidean case, to Euler’s inequality \(R\ge 2r\)).
KeywordsAbsolute plane geometry Euler’s inequality Area Optimization
Mathematics Subject ClassificationPrimary 51F05 Secondary 51M16
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