TY - BOOK ID - 216132 TI - Classical geometries in modern contexts : geometry of real inner product spaces PY - 2007 SN - 1281140635 9786611140632 3764385413 3764385405 PB - Basel ; Boston : Birkhauser, DB - UniCat KW - Functional equations. KW - Conformal geometry. KW - Lie algebras. KW - Special relativity (Physics) KW - Complexes. KW - Linear complexes KW - Algebras, Linear KW - Coordinates KW - Geometry KW - Line geometry KW - Transformations (Mathematics) KW - Ether drift KW - Mass energy relations KW - Relativity theory, Special KW - Restricted theory of relativity KW - Special theory of relativity KW - Relativity (Physics) KW - Algebras, Lie KW - Algebra, Abstract KW - Lie groups KW - Circular geometry KW - Geometry of inverse radii KW - Inverse radii, Geometry of KW - Inversion geometry KW - Möbius geometry KW - Equations, Functional KW - Functional analysis KW - Geometry. KW - Mathematical physics. KW - Mathematical Methods in Physics. KW - Physical mathematics KW - Physics KW - Mathematics KW - Euclid's Elements KW - Physics. KW - Natural philosophy KW - Philosophy, Natural KW - Physical sciences KW - Dynamics UR - https://www.unicat.be/uniCat?func=search&query=sysid:216132 AB - 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. ER -