Abstract
Two results, proved synthetically in plane Euclidean geometry by Chisini in 1924—stating that: (i) if MAB is an isosceles triangle, with MA≡MB, inscribed in a circle C, P1 and P2 are two points on C such that {B, Pi} separates {A, M} for i∈ {1 , 2} , and {B, P2} separates {M, P1}, then AP1+ BP1< AP2+ BP2, and (ii) of all triangles inscribed in a given circle the equilateral triangle has the greatest perimeter—are proved inside Hilbert’s absolute geometry.
Original language | English (US) |
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Pages (from-to) | 265-270 |
Number of pages | 6 |
Journal | Journal of Geometry |
Volume | 108 |
Issue number | 1 |
DOIs | |
State | Published - Apr 1 2017 |
Keywords
- Absolute plane geometry
- Primary 51F05
- Secondary 51M16
- optimization
ASJC Scopus subject areas
- Geometry and Topology