03826nam a22004215a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001500168072001700183084003600200245011100236260008200347300003400429336002600463337002600489338003600515347002400551490008300575505156700658506006602225520076002291650002403051650003103075650004403106650001803150650003803168650003103206700003103237700003703268856003203305856006703337243-190219CH-001817-320190219233004.0a fot ||| 0|cr nn mmmmamaa190219e20190227sz fot ||| 0|eng d a978303719696070a10.4171/1962doi ach0018173 7aPB2bicssc 7aPBCD2bicssc a03-xxa51-xxa52-xxa53-xx2msc10aEighteen Essays in Non-Euclidean Geometryh[electronic resource] /cVincent Alberge, Athanase Papadopoulos3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2019 a1 online resource (475 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v2900tArea in non-Euclidean geometry /rNorbert A’Campo, Athanase Papadopoulos --tThe area formula for hyperbolic triangles /rElena Frenkel, Weixu Su --tOn a problem of Schubert in hyperbolic geometry /rVincent Alberge, Elena Frenkel --tOn a theorem of Lambert: medians in spherical and hyperbolic geometries /rHimalaya Senapati --tInscribing a triangle in a circle in spherical geometry /rHimalaya Senapati --tMonotonicity in spherical and hyperbolic triangles /rHimalaya Senapati --tDe Tilly’s mechanical view on hyperbolic and spherical geometries /rDmitriy Slutskiy --tThe Gauss–Bonnet theorem and the geometry of surfaces /rSon Lam Ho --tOn the non-existence of a perfect map from the 2-sphere to the Euclidean plane /rCharalampos Charitos, Ioannis Papadoperakis --tArea preserving maps from the sphere to the Euclidean plane /rCharalampos Charitos --tArea and volume in non-Euclidean geometry /rNikolay Abrosimov, Alexander Mednykh --tStatics and kinematics of frameworks in Euclidean and non-Euclidean geometry /rIvan Izmestiev --tContributions to non-Euclidean geometry I /rEduard Study --tNotes on Eduard Study’s paper “Contributions to non-Euclidean geometry I” /rAnnette A’Campo-Neuen, Athanase Papadopoulos --tSpherical and hyperbolic conics /rIvan Izmestiev --tSpherical, hyperbolic, and other projective geometries: convexity, duality, transitions /rFrançois Fillastre, Andrea Seppi --tHermitian trigonometry /rBoumediene Et-Taoui --tA theorem on equiareal triangles with a fixed base /rVictor Pambuccian.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis 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.07aMathematics2bicssc07aMathematical logic2bicssc07aMathematical logic and foundations2msc07aGeometry2msc07aConvex and discrete geometry2msc07aDifferential geometry2msc1 aAlberge, Vincent,eeditor.1 aPapadopoulos, Athanase,eeditor.40uhttps://doi.org/10.4171/196423cover imageuhttps://www.ems-ph.org/img/books/alberge_mini.jpg