TREATISE OF PLANE GEOMETRY THROUGH GEOMETRIC ALGEBRA

By SUSAN MARTIN

FIRST PART: THE VECTOR PLANE AND THE COMPLEX NUMBERS 1 THE VECTORS AND THEIR OPERATIONS 2 A BASE OF VECTORS FOR THE PLANE 3 THE COMPLEX NUMBERS 4 TRANSFORMATIONS OF VECTORS SECOND PART: THE GEOMETRY OF THE EUCLIDEAN PLANE 5 POINTS AND STRAIGHT LINES 6 ANGLES AND ELEMENTAL TRIGONOMETRY 7 SIMILARITIES AND SINGLE RATIO 8 PROPERTIES OF TRIANGLES 9 CIRCLES 10 CROSS RATIOS AND RELATED TRANSFORMATIONS 11 CONICS THIRD PART: PSEUDO-EUCLIDEAN GEOMETRY 12 MATRIX REPRESENTATION AND HYPERBOLIC NUMBERS 13 THE HYPERBOLIC OR PSEUDO-EUCLIDEAN PLANE CONTENTS FOURTH PART: PLANE PROJECTIONS OF TRIDIMENSIONAL SPACES 14 SPHERICAL GEOMETRY IN THE EUCLIDEAN SPACE 15 HYPERBOLOIDAL GEOMETRY IN THE PSEUDO-EUCLIDEAN SPACE (LOBACHEVSKY'S GEOMETRY) 16 SOLUTIONS OF THE PROPOSED EXERCISES