A survey of geometry 2

Cover......Page 1 Title page......Page 3 IX. ANALYTIC GEOMETRY I......Page 17 9.1 ANALYTIC GEOMETRY VERSUS SYNTHETIC GEOMETRY......Page 21 9.2 ABRIDGED NOTATION......Page 32 9.3 SOLVABILITY AND INSOLVABILITY WITH EUCLIDEAN TOOLS......Page 46 9.4 THE FUNDAMENTAL THEOREM OF LINEAR PROGRAMMING......Page 55 9.5 COORDINATE SYSTEMS; PLÜCKER'S DIMENSION THEORY......Page 64 9.6 REPRESENTATIONAL GEOMETRY......Page 75 10.1 HOMOGENEOUS COORDINATES AND INFINITE ELEMENTS......Page 85 10.2 LINE COORDINATES AND THE PRINCIPLE OF DUALITY......Page 92 10.3 IMAGINARY ELEMENTS AND THE CIRCULAR POINTS AT INFINITY......Page 96 10.4 PROJECTIVE COORDINATES IN A PLANE......Page 109 10.5 THE CONSISTENCY OF PLANE EUCLIDEAN GEOMETRY......Page 118 10.6 A CLASSIFICATION OF SOME ASSOCIATED GEOMETRIES......Page 123 10.7 MULTIPLE ALGEBRA AND VECTOR GEOMETRY......Page 129 XI. GEOMETRY AND THE THEORY OF GROUPS......Page 149 11.1 THE NOTION OF GROUP......Page 150 11.2 THE ERLANGER PROGRAMM......Page 159 11.3 ANALYTICAL ASPECT OF KLEINIAN GEOMETRIES......Page 165 11.4 PLANE AFFINE GEOMETRY......Page 173 11.5 CONCLUSION......Page 178 XII. GEOMETRY OF COMPLEX NUMBERS......Page 185 12.1 FUNDAMENTAL CONCEPTS AND OPERATIONS......Page 186 12.2 SOME ELEMENTARY GEOMETRY OF THE GAUSS PLANE......Page 192 12.3 ELEMENTARY TRANSFORMATIONS......Page 204 12.4 SOME GEOMETRY OF THE TRIANGLE......Page 211 12.5 CIRCULAR TRANSFORMATIONS......Page 216 12.6 CROSS RATIO......Page 227 XIII. LIMIT OPERATIONS IN GEOMETRY......Page 235 13.1 THE LIMIT CONCEPT IN ELEMENTARY GEOMETRY......Page 236 13.2 SOME GEOMETRICAL APPLICATIONS OF THE LIMIT CONCEPT......Page 243 13.3 SOME GEOMETRICAL APPLICATIONS OF THE CONTINUITY CONCEPT......Page 255 13.4 PATHOLOGICAL CURVES AND SURFACES......Page 266 XIV. DIFFERENTIAL GEOMETRY......Page 281 14.1 PLANE CURVES......Page 283 14.2 SPACE CURVES......Page 295 14.3 SURF ACES......Page 302 14.4 ANALYTICAL TREATMENT OF SPACE CURVES......Page 313 14.5 ANALYTICAL TREATMENT OF SURFACES......Page 330 14.6 CURVATURE OF SURFACES......Page 344 14.7 RIEMANNIAN GEOMETRY......Page 356 XV. COMBINATORIAL TOPOLOGY......Page 361 15.1 STANDARD SURFACES......Page 364 15.2 THE 2-MANIFOLDS......Page 375 15.3 CANONICAL FORMS AND THE CLASSIFICATION OF 2-MANIFOLDS......Page 383 15.4 ORIENTABLE AND NONORIENTABLE 2-MANIFOLDS, ONE-SIDED AND TWO-SIDED 2-MANIFOLDS......Page 391 15.5 EULER CHARACTERISTIC OF 2-MANIFOLDS......Page 398 15.6 RETICULATIONS ON 2-MANIFOLDS......Page 405 15.7 MAP-COLORING ON 2-MANIFOLDS......Page 410 15.8 VECTOR FIELDS......Page 421 16.1 n-DIMENSIONAL GEOMETRY......Page 431 16.2 METRIC SPACES......Page 438 16.3 HAUSDORFF AND TOPOLOGICAL SPACES......Page 448 16.4 CONTINUOUS MAPPINGS......Page 454 16.5 WHAT IS GEOMETRY?......Page 458 SUGGESTIONS FOR SOLUTIONS OF SOME OF THE PROBLEMS......Page 465 INDEX......Page 495