On Fuhrmann's Theorem in Abstract Spaces

Yıl 2019, Cilt: 23 Sayı: 5, 788 - 791, 01.10.2019

Nilgün Sönmez

https://doi.org/10.16984/saufenbilder.518403

Öz

We prove that Fuhrmann's Theorem holds on
every Ptolemaean space.

Anahtar Kelimeler

Fuhrmann's theorem, Ptolemaean theorem

Kaynakça

• Referans 1 H. S. M. Coxeter and S. L. Greitzer, “Geometry Revisited,” Washington, DC:Math. Assoc. Amer., pp. 42–43, 1967.Referans 2 W. Fuhrmann, “Synthetische Beweise Planimetrischer Sa ̈tze,” Berlin, pp. 61, 1890. Referans 3 R.A. Johnson, “Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle,” Boston, MA: Houghton Mifflin, pp. 65-66, 1929.Referans 4 I. D. Platis, “Cross-ratios and the Ptolemaean inequality in boundaries of symmetric spaces of Rank 1,” Geometriae Dedicata, vol. 169, pp. 187–208, 2014.Referans 5 I. D. Platis and V. Schroeder, “Möbius Rigidity of Invariant Metrics in Boundaries of Symmetric Spaces of Rank 1,” Monatshefte für Mathematic, vol. 183, no. 2, pp. 357–373, 2017.