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.), 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.
| 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.
In: Journal of Geometry, 28.06.2016, p. 1-6.Research output: Contribution to journal › Article
}
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 -