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Field name	Details
Title	Eighteen Essays in Non-Euclidean Geometry ([EBook] /) / Vincent Alberge, Athanase Papadopoulos
Added Personal Name	Alberge, Vincent
Added Personal Name	Papadopoulos, Athanase
Publication	Zuerich, Switzerland : : European Mathematical Society Publishing House, , 2019
Physical Details	1 online resource (475 pages)
Series	IRMA Lectures in Mathematics and Theoretical Physics (IRMA) 2523-5133 ; ; 29
ISBN	9783037196960
Summary 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.:
Contents note	Area in non-Euclidean geometry /: The area formula for hyperbolic triangles /: On a problem of Schubert in hyperbolic geometry /: On a theorem of Lambert: medians in spherical and hyperbolic geometries /: Inscribing a triangle in a circle in spherical geometry /: Monotonicity in spherical and hyperbolic triangles /: De Tilly’s mechanical view on hyperbolic and spherical geometries /: The Gauss–Bonnet theorem and the geometry of surfaces /: On the non-existence of a perfect map from the 2-sphere to the Euclidean plane /: Area preserving maps from the sphere to the Euclidean plane /: Area and volume in non-Euclidean geometry /: Statics and kinematics of frameworks in Euclidean and non-Euclidean geometry /: Contributions to non-Euclidean geometry I /: Notes on Eduard Study’s paper “Contributions to non-Euclidean geometry I” /: Spherical and hyperbolic conics /: Spherical, hyperbolic, and other projective geometries: convexity, duality, transitions /: Hermitian trigonometry /: A theorem on equiareal triangles with a fixed base /:
Mode of acces to digital resource	Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.4171/196
See Also	https://www.ems-ph.org/img/books/alberge_mini.jpg
Links to Related Works	Subject References: Convex and Discrete Geometry . Differential Geometry . Geometry . Mathematical logic . Mathematical Logic and Foundations . Mathematics . Authors: Alberge, Vincent . editor . Papadopoulos, Athanase . Series: IRMA Lectures in Mathematics and Theoretical Physics (IRMA) .

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Eighteen Essays in Non-Euclidean Geometry

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