Proceedings ...: Geometric transformation groups and other topics; lectures by H. S. M. Coxeter and othersLincoln K. Durst Committee on the Undergraduate Program in Mathematics, Mathematical Association of America, 1967 - Geometry |
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Page 135
... mathematical system nor denies the logical criterion it must satisfy . On the other hand , the relation of the two subjects explains the motivation for the way in which the mathematical system is constructed . Also , it keeps the ...
... mathematical system nor denies the logical criterion it must satisfy . On the other hand , the relation of the two subjects explains the motivation for the way in which the mathematical system is constructed . Also , it keeps the ...
Page 137
... mathematical set that is planar , non - linear , and bounded ( contained in the interior of some circle ) . Restrict- ing the physical " cut - out , " we can use convexity to express the " oneness " or connectedness of the corresponding ...
... mathematical set that is planar , non - linear , and bounded ( contained in the interior of some circle ) . Restrict- ing the physical " cut - out , " we can use convexity to express the " oneness " or connectedness of the corresponding ...
Page 139
... mathematical and scientific systems , to mathematical proof and disproof , to the processes of analogy and generalization , and to the creative aspect of making definitions . It initiates topological ideas , notions related to functions ...
... mathematical and scientific systems , to mathematical proof and disproof , to the processes of analogy and generalization , and to the creative aspect of making definitions . It initiates topological ideas , notions related to functions ...
Contents
TRANSFORMATION GROUPS FROM THE GEOMETRIC | 1 |
TWO APPLICATIONS OF GEOMETRY | 73 |
SOME COMPUTATIONAL ILLUSTRATIONS OF GEOMETRICAL | 107 |
Copyright | |
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Common terms and phrases
ABCD affine geometry affine reflections affinely regular angle axioms axis called circle centered coaxal circles collinear complete quadrangle conic connected sets consider convex body convex set coordinates corresponding course Coxeter curve defined definition denote dilatation dilative rotation direct isometry distinct points ellipse equiaffinity Euclidean geometry Euclidean plane example Figure given Gleason glide reflection H. S. M. Coxeter half-turn homographies hyperbolic geometry hyperbolic space idea inequality integral geometry invariant point inversive distance inversive geometry inversive invariant inversive plane lattice point lecture mappings mathematical metric mid-circle midpoint mirrors Möbius involution normal subgroup notation operation orthogonal pair perpendicular perspectivity point of intersection polar polygon Prenowitz problem projective collineation projective geometry projective plane proof quadric ratio real numbers result segment semispace similarity sphere subsets symmetric tangent theorem three reflections tion topology transformation translation triangle ABC ultraparallel unique vertex vertices Wallace separation