Journal of Geometry

, 109:8 | Cite as

Euler’s inequality in absolute geometry

  • Victor Pambuccian
  • Celia Schacht


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 \(R\ge 2r\)).


Absolute plane geometry Euler’s inequality Area Optimization 

Mathematics Subject Classification

Primary 51F05 Secondary 51M16 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical and Natural Sciences (MC 2352)Arizona State University - West CampusPhoenixUSA

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