Modern geometries: non-Euclidean, projective, and discrete
Engaging, accessible, and extensively illustrated, this brief, but solid introduction to modern geometry describes geometry as it is understood and used by contemporary mathematicians and theoretical scientists. Basically non-Euclidean in approach, it relates geometry to familiar ideas from analytic geometry, staying firmly in the Cartesian plane. It uses the principle geometric concept of congruence or geometric transformation--introducing and using the Erlanger Program explicitly throughout. It features significant modern applications of geometry--e.g., the geometry of relativity, symmetry, art and crystallography, finite geometry and computation. Covers a full range of topics from plane geometry, projective geometry, solid geometry, discrete geometry, and axiom systems. For anyone interested in an introduction to geometry used by contemporary mathematicians and theoretical scientists.
47 pages matching hyperbolic straight line in this book
Results 1-3 of 47
What people are saying - Write a review
We haven't found any reviews in the usual places.
13 other sections not shown
absolute geometry algebraic angle Apqr axiom system axis Bachmann's bundles called Chapter clines complex numbers complex plane congruent coordinates cross ratio curve cut set cycle deﬁned Deﬁnition Let dimensional dimensions distance edges elements elliptic geometry equation Erlanger Programm Euclid Euclidean geometry Euclidean plane Euclidean transformation example Exercise ﬁgure ﬁnd ﬁnite ﬁxed point ﬂats formula frieze groups fundamental theorem glide reﬂection graph Hilbert's axioms Hint homothetic transformation horocycle hyperbolic geometry hyperbolic plane hyperbolic straight line ideal point identiﬁed inﬁnite intersect invariant inversion involutions lattice line segment mathematics matroid metric absolute geometry Mobius geometry Mobius transformation motions multiplication non-Euclidean geometry perpendicular polar form postulate projective geometry projective plane proof properties Prove quatemions real numbers reﬂection reﬂection planes satisﬁes Show single elliptic geometry space Steiner circles stereographic projection subgeometries subset symmetry groups three-dimensional transformation group translational geometry translational symmetry triangle unit circle unit disk vector vertex x-axis