Contributor
Alberge, Vincent, editor.
ImprintZürich, Switzerland : European Mathematical Society Publishing House, [2019]
Imprint2019
Descriptionxxvii, 447 pages : illustrations ; 25 cm
Note:Area in non-Euclidean geometry / Norbert A'Campo, Athanase Papadopoulos -- The area formula for hyperbolic triangles / Elena Frenkel, Weixu Su -- On a problem of Schubert in hyperbolic geometry / Vincent Alberge, Elena Frenkel -- On a theorem of Lambert: medians in spherical and hyperbolic geometries / Himalaya Senapati -- Inscribing a triangle in a circle in spherical geometry / Himalaya Senapati -- Monotonicity in spherical and hyperbolic triangles / Himalaya Senapati -- De Tilly's mechanical view on hyperbolic and spherical geometries / Dmitriy Slutskiy -- The Gauss-Bonnet theorem and the geometry of surfaces / Son Lam Ho -- On the non-existence of a perfect map from the 2-sphere to the Euclidean plane / Charalampos Charitos, Ioannis Papadoperakis -- Area preserving maps from the sphere to the Euclidean plane / Charalampos Charitos -- Area and volume in non-Euclidean geometry / Nikolay Abrosimov, Alexander Mednykh -- Statics and kinematics of frameworks in Euclidean and non-Euclidean geometry / Ivan Izmestiev -- Contributions to non-Euclidean geometry I / Eduard Study -- Notes on Eduard Study's paper "Contributions to non-Euclidean geometry I" / Annette A'Campo-Neuen, Athanase Papadopoulos -- Spherical and hyperbolic conics / Ivan Izmestiev -- Spherical, hyperbolic, and other projective geometries: convexity, duality, transitions / François Fillastre, Andrea Seppi -- Hermitian trigonometry / Boumediene Et-Taoui -- A theorem on equiareal triangles with a fixed base / Victor Pambuccian.
Bibliography Note:Includes bibliographical references and index.
Note:This book consists of a series of self-contained essays in non-Euclidean geometry in a broad sense, including the classical geometries of constant curvature (spherical and hyperbolic), de Sitter, anti-de Sitter, co-Euclidean, co-Minkowski, Hermitian geometries, and some axiomatically defined geometries. Some of these essays deal with very classical questions and others address problems that are at the heart of present day research, but all of them are concerned with fundamental topics. All the essays are self-contained and most of them can be understood by the general educated mathematician. They should be useful to researchers and to students of non-Euclidean geometry, and they are intended to be references for the various topics they present.
