Eighteen Essays in Non-Euclidean Geometry


Book details

Area in non-Euclidean geometry
Norbert A’Campo and Athanase Papadopoulos
pp. 3–25
Abstract | Full-Text PDF (589 KB)

The area formula for hyperbolic triangles
Elena Frenkel and Weixu Su
pp. 27–46
Abstract | Full-Text PDF (200 KB)

On a problem of Schubert in hyperbolic geometry
Vincent Alberge and Elena Frenkel
pp. 47–56
Abstract | Full-Text PDF (202 KB)

On a theorem of Lambert: medians in spherical and hyperbolic geometries
Himalaya Senapati
pp. 57–65
Abstract | Full-Text PDF (171 KB)

Inscribing a triangle in a circle in spherical geometry
Himalaya Senapati
pp. 67–79
Abstract | Full-Text PDF (240 KB)

Monotonicity in spherical and hyperbolic triangles
Himalaya Senapati
pp. 81–91
Abstract | Full-Text PDF (178 KB)

De Tilly’s mechanical view on hyperbolic and spherical geometries
Dmitriy Slutskiy
pp. 93–111
Abstract | Full-Text PDF (199 KB)

The Gauss–Bonnet theorem and the geometry of surfaces
Son Lam Ho
pp. 113–123
Abstract | Full-Text PDF (207 KB)

On the non-existence of a perfect map from the 2-sphere to the Euclidean plane
Charalampos Charitos and Ioannis Papadoperakis
pp. 125–134
Abstract | Full-Text PDF (147 KB)

Area preserving maps from the sphere to the Euclidean plane
Charalampos Charitos
pp. 135–150
Abstract | Full-Text PDF (180 KB)

Area and volume in non-Euclidean geometry
Nikolay Abrosimov and Alexander Mednykh
pp. 151–189
Abstract | Full-Text PDF (496 KB)

Statics and kinematics of frameworks in Euclidean and non-Euclidean geometry
Ivan Izmestiev
pp. 191–233
Abstract | Full-Text PDF (526 KB)

Contributions to non-Euclidean geometry I
Eduard Study
pp. 237–251
Abstract | Full-Text PDF (410 KB)

Notes on Eduard Study’s paper “Contributions to non-Euclidean geometry I”
Annette A’Campo-Neuen and Athanase Papadopoulos
pp. 253–262
Abstract | Full-Text PDF (147 KB)

Spherical and hyperbolic conics
Ivan Izmestiev
pp. 262–320
Abstract | Full-Text PDF (1629 KB)

Spherical, hyperbolic, and other projective geometries: convexity, duality, transitions
François Fillastre and Andrea Seppi
pp. 321–409
Abstract | Full-Text PDF (922 KB)

Hermitian trigonometry
Boumediene Et-Taoui
pp. 413–425
Abstract | Full-Text PDF (152 KB)

A theorem on equiareal triangles with a fixed base
Victor Pambuccian
pp. 427–437
Abstract | Full-Text PDF (238 KB)

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