GEOMETRIC TRANSFORMATIONS: EUCLIDEAN AND AFFINE TRANSFORMATIONS
CONTENTS PART I CIRCLE MEASUREMENT, TRANSFORMATIONS, SPACE GEOMETRY, CONIC SECTIONS CIRCLE MEASUREMENT THE DIFFICULTIES, THE LIMIT DEFINITION OF THE PERIMETER OF THE CIRCLE THE NUMBER ? ARC LENGTH OF A CIRCLE, RADIANS DEFINITION OF THE AREA OF THE CIRCLE THE AREA OF A CIRCULAR SECTOR THE ISOPERIMETRIC INEQUALITY ANTHYPHAIRESIS COMMENTS AND EXERCISES FOR THE CHAPTER REFERENCES TRANSFORMATIONS OF THE PLANE TRANSFORMATIONS, ISOMETRIES REFLECTIONS AND POINT SYMMETRIES TRANSLATIONS ROTATIONS CONGRUENCY OR ISOMETRY OR EQUALITY HOMOTHETIES SIMILARITIES INVERSIONS THE HYPERBOLIC PLANE 2 10 ARCHIMEDEAN TILINGS 2 11 COMMENTS AND EXERCISES FOR THE CHAPTER LINES AND PLANES IN SPACE AXIOMS FOR SPACE PARALLEL PLANES ANGLES IN SPACE SKEW LINES LINE ORTHOGONAL TO PLANE ANGLE BETWEEN LINE AND PLANE THEOREM OF THALES IN SPACE SOLIDS DIHEDRAL ANGLES TRIHEDRAL ANGLES PYRAMIDS, POLYHEDRAL ANGLES TETRAHEDRA REGULAR PYRAMIDS POLYHEDRA, PLATONIC SOLIDS PRISMS CYLINDER CONE, CONICAL SURFACE 4 10 TRUNCATED CONE, CONE UNFOLDING 4 11 SPHERE 4 12 SPHERICAL AND CIRCUMSCRIBED POLYHEDRA 4 13 SPHERICAL LUNE, ANGLE OF GREAT CIRCLES 4 14 SPHERICAL TRIANGLES 4 15 THE SUPPLEMENTARY TRIHEDRAL 4 16 AXONOMETRIC PROJECTION, AFFINITIES 4 17 PERSPECTIVE PROJECTION 4 18 COMMENTS AND EXERCISES FOR THE CHAPTER AREAS IN SPACE, VOLUMES AREAS IN SPACE AREA OF THE SPHERE AREA OF SPHERICAL POLYGONS EULER CHARACTERISTIC VOLUMES VOLUME OF PRISMS VOLUME OF PYRAMIDS VOLUME OF CYLINDERS VOLUME OF CONES 5 10 VOLUME OF SPHERES 5 11 COMMENTS AND EXERCISES FOR THE CHAPTER CONIC SECTIONS DANDELIN’S SPHERES DIRECTRICES GENERAL CHARACTERISTICS OF CONICS THE PARABOLA THE ELLIPSE THE HYPERBOLA TRANSFORMATIONS IN SPACE ISOMETRIES IN SPACE REFLECTIONS IN SPACE TRANSLATIONS IN SPACE ROTATIONS IN SPACE CONGRUENCE OR ISOMETRY IN SPACE HOMOTHETIES IN SPACE SIMILARITIES IN SPACE ARCHIMEDEAN SOLIDS EPILOGUE