PLANE GEOMETRY
CONTENTS I A?NE GEOMETRY 1 A?NE SPACES 2 A?NE MAPPINGS 3 USING A?NE MAPPINGS: THREE THEOREMS IN PLANE GEOMETRY 4 APPENDIX: A FEW WORDS ON BARYCENTERS 5 APPENDIX: THE NOTION OF CONVEXITY 6 APPENDIX: CARTESIAN COORDINATES IN A?NE GEOMETRY EXERCISES AND PROBLEMS II EUCLIDEAN GEOMETRY, GENERALITIES 1 EUCLIDEAN VECTOR SPACES, EUCLIDEAN A?NE SPACES 2 THE STRUCTURE OF ISOMETRIES 3 THE GROUP OF LINEAR ISOMETRIES III EUCLIDEAN GEOMETRY IN THE PLANE 1 ANGLES 2 ISOMETRIES AND RIGID MOTIONS IN THE PLANE 3 PLANE SIMILARITIES 4 INVERSIONS AND PENCILS OF CIRCLES IV EUCLIDEAN GEOMETRY IN SPACE 1 ISOMETRIES AND RIGID MOTIONS IN SPACE 2 THE VECTOR PRODUCT, WITH AREA COMPUTATIONS 3 SPHERES, SPHERICAL TRIANGLES 4 POLYHEDRA, EULER FORMULA 5 REGULAR POLYHEDRA V PROJECTIVE GEOMETRY 1 PROJECTIVE SPACES 2 PROJECTIVE SUBSPACES 3 A?NE VS PROJECTIVE 4 PROJECTIVE DUALITY 5 PROJECTIVE TRANSFORMATIONS 6 THE CROSS-RATIO 7 THE COMPLEX PROJECTIVE LINE AND THE CIRCULAR GROUP VI CONICS AND QUADRICS 1 A?NE QUADRICS AND CONICS, GENERALITIES 2 CLASSI?CATION AND PROPERTIES OF A?NE CONICS 3 PROJECTIVE QUADRICS AND CONICS 4 THE CROSS-RATIO OF FOUR POINTS ON A CONIC AND PASCAL’S THEOREM 5 A?NE QUADRICS, VIA PROJECTIVE GEOMETRY 6 EUCLIDEAN CONICS, VIA PROJECTIVE GEOMETRY 7 CIRCLES, INVERSIONS, PENCILS OF CIRCLES 8 APPENDIX: A SUMMARY OF QUADRATIC FORMS VII CURVES, ENVELOPES, EVOLUTES 1 THE ENVELOPE OF A FAMILY OF LINES IN THE PLANE 2 THE CURVATURE OF A PLANE CURVE 3 EVOLUTES 4 APPENDIX: A FEW WORDS ON PARAMETRIZED CURVES VIII SURFACES IN 3-DIMENSIONAL SPACE 1 EXAMPLES OF SURFACES IN 3-DIMENSIONAL SPACE 2 DI?ERENTIAL GEOMETRY OF SURFACES IN SPACE 3 METRIC PROPERTIES OF SURFACES IN THE EUCLIDEAN SPACE 4 APPENDIX: A FEW FORMULAS