PROJECTIVE GEOMETRY

By CHARLES CLARK

CONTENTS 1 PAPPOS’S THEOREM: NINE PROOFS AND THREE VARIATIONS PART I PROJECTIVE GEOMETRY 2 PROJECTIVE PLANES 3 HOMOGENEOUS COORDINATES 4 LINES AND CROSS-RATIOS 5 CALCULATING WITH POINTS ON LINES 6 DETERMINANTS 7 MORE ON BRACKET ALGEBRA PART II WORKING AND PLAYING WITH GEOMETRY 8 QUADRILATERAL SETS AND LIFTINGS 9 CONICS AND THEIR DUALS 10 CONICS AND PERSPECTIVITY 11 CALCULATING WITH CONICS 12 PROJECTIVE D-SPACE 13 DIAGRAM TECHNIQUES 14 WORKING WITH DIAGRAMS 15 CONFIGURATIONS, THEOREMS, AND BRACKET EXPRESSIONS PART III MEASUREMENTS 16 COMPLEX NUMBERS: A PRIMER 17 THE COMPLEX PROJECTIVE LINE 18 EUCLIDEAN GEOMETRY 19 EUCLIDEAN STRUCTURES FROM A PROJECTIVE PERSPECTIVE 20 CAYLEY-KLEIN GEOMETRIES 21 MEASUREMENTS AND TRANSFORMATIONS 22 CAYLEY-KLEIN GEOMETRIES AT WORK 23 CIRCLES AND CYCLES 24 NON-EUCLIDEAN GEOMETRY: A HISTORICAL INTERLUDE 25 HYPERBOLIC GEOMETRY 26 SELECTED TOPICS IN HYPERBOLIC GEOMETRY 27 WHAT WE DID NOT TOUCH REFERENCES