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Guggenheimer H.W. — Plane geometry and its groups
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Название: Plane geometry and its groupsАвтор: Guggenheimer H.W. Аннотация: In this book the main theorems of plane euclidean geometry are proved on a university level. In the opinion of the writer, a reasonable training of high-school teachers must present them with a good working knowledge of geometry before starting to speak about foundations, i.e., about geometry.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1967Количество страниц: 297Добавлена в каталог: 26.07.2013Операции: Положить на полку |
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Absolute, of hyperbolic geometry 225 Absolute, theorem 228 Addition points 106 Addition ratios 116 Addition vectors 42 Addition, of lengths 50 Addition, oriented angles 31 Addition, power series 260 Altitude 23 Anallagmatic 207 Angle bisector 9 33 263 Angle Bisector, external 16 Angle of analytic geometry 32 Angle of circles 149 Angle of pair of elliptic points 258 Angle of trigonometry 32 71 Angle Sum, hyperbolic 236 Angle, acute 20 Angle, alternating 37 Angle, center 89 Angle, elementary 9 Angle, obtuse 20 Angle, oriented 68 29 30 Angle, oriented, hyperbolic 231 Angle, right 20 Angle, straight 18 Angle, subtended at circumference 91 Angle, vertical 36 Antipodal point 251 Archimedes, axiom of 51 Archimedes, method of 197 Area function 107 Area Function of parallelogram 112 Area Function of rectangle 111 Area Function of triangle 112 124 Area Function, hyperbolic 237 Area Function, oriented 118 Artin, E. 266 Associative law 7 31 111 Asystatic 71 72 Automorphism of group 64 Automorphism of ordered field 199 Automorphism, of archimedean field 199 Axiom I Axis of symmetry 40 Axis, radical 148 Bachmann, F. v 266 Bankoff, L. 277 Barrow, D.F. 186 Base 20 Bernstein, L. 277 BETWEEN 3 226 Blumenthal, L. 266 Boltyanskii, V.G. 121 266 267 Burckhardt, J.J. 266 Cantor, G. 285 Carlitz, L. 277 Center, of circle 85 Center, of group 64 Center, of homothety 152 Center, of hyperbolic circle 231 Center, of nine-point circle 165 Center, of rotation 29 Central 87 Centroid 48 Chord 89 circle 85 Circle of Appolonius 130 Circle of similitude 162 Circle, hyperbolic 231 Circle, M- 204 Circle, nine-point 165 Circumcenter 23 circumcircle 87 Circumradius 135 Closure, of plane 205 Collinear 4 Commutative law 31 43 61 111 Commutator subgroup 71 Commuting maps 12 Comparison theorems 19 199 Comparison, of angles 18 Comparison, of segments 17 Completeness 70 Concentric 89 concurrent 2 Concyclic 93 Congruence 10 Convex 4 Coordinates of hyperbolic line 247 Coordinates, homogeneous hyperbolic 247 Coordinates, in analytic geometry 262 Coset 65 Court, N.A. 266 Covering map 252 Coxeter, H.S.M. 266 Cross ratio 119 239 248 Curve of Constant Distance 233 De Comberousse, C. 267 Decagon, regular 137 Diameter 85 Disjoint 2 Distance 86 Distributive law 111 Duplication, of Cube 34 Edge, of polygon 44 Edge, of triangle 4 Element 2 END 229 Endpoint 3 Entity, elliptic 251 Entity, hyperbolic 225 Epimorphism 63 Equation of Line, normal 263 Equiangular Triangles 128 Equidistant 20 Equivalence, relation of 11 Erdoes, P. 186 Ergodic 184 Euclid 122 Euclidean algorithm 74 Euler line 50 165 Eves, H. 266 Excenter 88 Excircle 87 Exponential 63 Exponential of segment 248 Factor group 67 Faithful 71 Fejes Toth, L. 77 266 Field 116 Field of geometry 132 Field, non-Archimedean 136 262 Field, ordered 116 Field, Pythagorean 132 Field, uniquely ordered 136 Foot, of altitude 23 Forder, H. 266 Formal power series 260 Freudenthal, H. v 266 Fundamental domain 73 Gauss plane 205 Geometry, analytic 116 Gerretsen, J.C.H. 266 Glide reflection 53 Glide Reflection, hyperbolic 233 Gnomon 107 Golden section 136 Gonseth, F. 266 Group 59 Group, abelian 61 Group, crystallographic 73 Group, crystallographic, hyperbolic 238 Group, cyclic 62 Group, cyclic, infinite 62 Group, GL(2, F) 248 Group, special linear 244 Hadamard, J. v 266 Halfplane 3 262 Halfplane, hyperbolic 226 Harmonic range 129 Hart's Linkage 207 Heptagon 84 Hexagon, Pappus 99 Hexagon, Pascal 104 Hilbert Plane 260 Hilbert, D. 266 Hjelmslev's Midline 235 Hjelmslev, J. 10 Homogeneous space 66 Homomorphism 62 Homothety 152 Homothety of ratio one 153 Horocycle 233 Hypotenuse 24 Hypothesis 1 identity map 8 Incenter 24 incircle 87 Indeterminate 260 Inequality of L'Huilier 191 Inequality, arithmetic-geometric mean 187 Inequality, isoperimetric 194 195 Infinity, neighborhood of 205 Infinity, point at 205 Interior of convex set 86 Interior of polygon 72 Interior of triangle 5 Interior, of angle 18 Intersection 2 Inverse 10 59 inversion 200 Involution 8 Isogonal 28 95 143 Isometry 22 Isomorphism, of group 63 Isomorphism, of structure 224 Isoperimetric Polygons 189 Isotomic Map 40 Isotropy group 68 Jeger, M. 267 Kazarinoff, N.D. 267 Kernel, of map 71 Kernel, of set 7 Klein, F. 267 L'Huilier's Inequality 191 Lattice 73 Lattice group 73 Lattice, hexagonal 82 Lattice, parallelogram 79 Lattice, rectangular 80 Lattice, rhombic 80 Lattice, square 81 Leg, of angle 9 Leg, of isosceles triangle 20 Leg, of right triangle 24 Length of segment 50 Length, in real hyperbolic plane 240 Leuenberger, F. 275 277 Line 2 262 Line of support 85 Line, elliptic 252 Line, hyperbolic 225 Logarithmic function 63 Lune 257 M'Clelland, W.J. 267 MAP 7 Map, fractional linear 244 Matrix 244 Matrix, product 244 Median 23 Method, axiomatic 1 Midline 9 264 Midline, Hjelmslev's 235 midpoint 9 Midpoint of edge 44 45 Midpoint of hyperbolic lines 234 Mitrinovic, D.S. 277 Model, of a geometry 224 Moebius Circle 204 Moise, E.E. 267 Monomorphism 63 Mordell, L.J. 186 Moser, W.O. 266 Motion, euclidean 10 60 Motion, horocyclic 233 Motion, proper 60 Multiplication, of lengths 111 Multiplication, of oriented segments 114 Multiplication, of points 106 Multiplication, of power series 260 Multiplication, of ratios 116 Nairizi, An 121 Nowacki, W. 77 Null set 2 Numbers, mod n 61 Numbers, real 61 Order, of cyclic group 62 Origin, of coordinates 116 Ornament 72 Ornament, ribbon 84 orthocenter 47 Pappus, problem of 197 Pappus, theorem 138 Pappus, theorem, affine 100 parallel 2 Parallel, angle 240 248 Parallel, polygon, inner 191 Parallelogram 38 Parallelogram law 43 Parallelogram, complementary 107 Pascal line 104 145 Path, regular 182 Peaucellier's cell 207 Pedoe, D. 277 Pencil, maximal 26 Pencil, of circles 148 Pencil, of lines 26 Pencil, of M-circles 209 Pentagon, regular 136 Perpendicular 9 Perpendicular bisector 9 263 Perspective 101 Plane, elliptic 252 Plane, Gauss 205 Plane, Hilbert 260 Plane, hyperbolic 225 Point 2 66 Point at infinity 26 205 Point, antipodal 251 Point, diagonal 100 Point, elliptic 251 Point, Feuerbach 169 Point, ideal 26 Point, invariable 163 Point, negative Brocard 170 Point, positive Brocard 170 Point, symmedian 169 polar 207 Polar of elliptic point 255
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