### Abstract

Two results, proved synthetically in plane Euclidean geometry by Chisini in 1924—stating that: (i) if MAB is an isosceles triangle, with (Formula presented.), inscribed in a circle (Formula presented.), P_{1} and P_{2} are two points on (Formula presented.) such that {B, P_{i}} separates {A, M} for (Formula presented.), and {B, P_{2}} separates {M, P_{1}}, then (Formula presented.), 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) |
---|---|

Pages (from-to) | 1-6 |

Number of pages | 6 |

Journal | Journal of Geometry |

DOIs | |

State | Accepted/In press - Jun 28 2016 |

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### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

**Absolute geometry proofs of two geometric inequalities of Chisini.** / Pambuccian, Victor.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Absolute geometry proofs of two geometric inequalities of Chisini

AU - Pambuccian, Victor

PY - 2016/6/28

Y1 - 2016/6/28

N2 - Two results, proved synthetically in plane Euclidean geometry by Chisini in 1924—stating that: (i) if MAB is an isosceles triangle, with (Formula presented.), inscribed in a circle (Formula presented.), P1 and P2 are two points on (Formula presented.) such that {B, Pi} separates {A, M} for (Formula presented.), and {B, P2} separates {M, P1}, then (Formula presented.), and (ii) of all triangles inscribed in a given circle the equilateral triangle has the greatest perimeter—are proved inside Hilbert’s absolute geometry.

AB - Two results, proved synthetically in plane Euclidean geometry by Chisini in 1924—stating that: (i) if MAB is an isosceles triangle, with (Formula presented.), inscribed in a circle (Formula presented.), P1 and P2 are two points on (Formula presented.) such that {B, Pi} separates {A, M} for (Formula presented.), and {B, P2} separates {M, P1}, then (Formula presented.), and (ii) of all triangles inscribed in a given circle the equilateral triangle has the greatest perimeter—are proved inside Hilbert’s absolute geometry.

UR - http://www.scopus.com/inward/record.url?scp=84976351861&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84976351861&partnerID=8YFLogxK

U2 - 10.1007/s00022-016-0339-x

DO - 10.1007/s00022-016-0339-x

M3 - Article

AN - SCOPUS:84976351861

SP - 1

EP - 6

JO - Journal of Geometry

JF - Journal of Geometry

SN - 0047-2468

ER -