32 citations · 162 across the 72 of their papers we have counts for
8 papers · 1 filter
On three early papers by Herbert Busemann
Athanase Papadopoulos, Marc Troyanov
This paper is a commentary and a reading guide to three papers by Herbert Busemann, Über die Geometrien, in denen die "Kreise mit unendlichem Radius" die kürzesten Linien sind." (O…
Hyperbolic geometry in the work of Johann Heinrich Lambert
Athanase Papadopoulos, Guillaume Théret
The memoir Theorie der Parallellinien (1766) by Johann Heinrich Lambert is one of the founding texts of hyperbolic geometry, even though its author's aim was, like many of his pre-…
On hyperbolic analogues of some classical theorems in spherical geometry
Athanase Papadopoulos, Weixu Su
We provide hyperbolic analogues of some classical theorems in spherical geometry due to Menelaus, Euler, Lexell, Ceva and Lambert. Some of the spherical results are also made more…
On Klein's So-called Non-Euclidean geometry
Norbert A'Campo, Athanase Papadopoulos
In two papers titled "On the so-called non-Euclidean geometry", I and II, Felix Klein proposed a construction of the spaces of constant curvature -1, 0 and and 1 (that is, hyperbol…
From Funk to Hilbert Geometry
Athanase Papadopoulos, Marc Troyanov
We survey some basic geometric properties of the Funk metric of a convex set in . In particular, we study its geodesics, its topology, its metric balls, its convexity…
A Remark on the Projective Geometry of Constant Curvature Spaces
Athanase Papadopoulos, Sumio Yamada
We highlight the relation between the projective geometries of -dimensional Euclidean, spherical and hyperbolic spaces through the projective models of these spaces in the …