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This book is based on real inner product spaces X of arbitrary (finite or infinite) dimension greater than or equal to 2. With natural properties of (general) translations and general distances of X, euclidean and hyperbolic geometries are characterized. For these spaces X also the sphere geometries of Möbius and Lie are studied (besides euclidean and hyperbolic geometry), as well as geometries where Lorentz transformations play the key role. The geometrical notions of this book are based on general spaces X as described. This implies that also mathematicians who have not so far been especially interested in geometry may study and understand great ideas of classical geometries in modern and general contexts. Proofs of newer theorems, characterizing isometries and Lorentz transformations under mild hypotheses are included, like for instance infinite dimensional versions of famous theorems of A.D. Alexandrov on Lorentz transformations. A real benefit is the dimension-free approach to important geometrical theories. Only prerequisites are basic linear algebra and basic 2- and 3-dimensional real geometry.

Functional equations. --- Conformal geometry. --- Lie algebras. --- Special relativity (Physics) --- Complexes. --- Linear complexes --- Algebras, Linear --- Coordinates --- Geometry --- Line geometry --- Transformations (Mathematics) --- Ether drift --- Mass energy relations --- Relativity theory, Special --- Restricted theory of relativity --- Special theory of relativity --- Relativity (Physics) --- Algebras, Lie --- Algebra, Abstract --- Lie groups --- Circular geometry --- Geometry of inverse radii --- Inverse radii, Geometry of --- Inversion geometry --- Möbius geometry --- Equations, Functional --- Functional analysis --- Geometry. --- Mathematical physics. --- Mathematical Methods in Physics. --- Physical mathematics --- Physics --- Mathematics --- Euclid's Elements --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

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This book is based on real inner product spaces X of arbitrary (finite or infinite) dimension greater than or equal to 2. With natural properties of (general) translations and general distances of X, euclidean and hyperbolic geometries are characterized. For these spaces X also the sphere geometries of Möbius and Lie are studied (besides euclidean and hyperbolic geometry), as well as geometries where Lorentz transformations play the key role. The geometrical notions of this book are based on general spaces X as described. This implies that also mathematicians who have not so far been especially interested in geometry may study and understand great ideas of classical geometries in modern and general contexts. Proofs of newer theorems, characterizing isometries and Lorentz transformations under mild hypotheses are included, like for instance infinite dimensional versions of famous theorems of A.D. Alexandrov on Lorentz transformations. A real benefit is the dimension-free approach to important geometrical theories. Only prerequisites are basic linear algebra and basic 2- and 3-dimensional real geometry.

Functional equations. --- Conformal geometry. --- Lie algebras. --- General relativity (Physics) --- Equations fonctionnelles --- Géométrie conforme --- Algèbres de Lie --- Relativité générale (Physique) --- Complexes. --- General relativity (Physics). --- Geometry. --- Mathematical physics. --- Functional equations --- Conformal geometry --- Lie algebras --- Complexes --- Mathematics --- Civil & Environmental Engineering --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Operations Research --- Geometry --- Géométrie conforme --- Algèbres de Lie --- Relativité générale (Physique) --- EPUB-LIV-FT LIVMATHE SPRINGER-B --- Relativistic theory of gravitation --- Relativity theory, General --- Linear complexes --- Algebras, Lie --- Circular geometry --- Geometry of inverse radii --- Inverse radii, Geometry of --- Inversion geometry --- Möbius geometry --- Equations, Functional --- Mathematics. --- Physics. --- Mathematical Methods in Physics. --- Gravitation --- Physics --- Relativity (Physics) --- Algebras, Linear --- Coordinates --- Line geometry --- Transformations (Mathematics) --- Algebra, Abstract --- Lie groups --- Functional analysis --- Physical mathematics --- Euclid's Elements --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

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Geometry.

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Geometry --- Mathematical physics --- wiskunde --- fysica --- geometrie

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Geometry --- Mathematical physics --- wiskunde --- geometrie