The geometry of two and three dimensional space has long been studied for its own sake, but its results also underlie modern developments in fields as diverse as linear algebra, quantum physics, and number theory. This text is a careful introduction to Euclidean geometry that emphasizes its connections with other subjects. Glimpses of more advanced topics in pure mathematics are balanced by a straightforward treatment of the geometry needed for mechanics and classical applied mathematics. The exposition is based on vector methods; an introductory chapter relates these methods to the more classical axiomatic approach. The text is suitable for undergraduate courses in geometry and will be useful supplementary reading for students of mechanics and mathematical methods.
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Coordinates and equations
Conies and other curves
ABCD affine space algebra arc length axis calculate called Cartesian Cavalieri's principle centre Ceva's theorem Chapter circle collinear complex numbers congruent conic constant coordinate system corresponding curvature defined definition denote Desargues differential dimensions distance dot product eigenvalue eigenvectors ellipse equal equation Euclid's Euclidean plane Euclidean space example fact Figure formula four points function fundamental form given hyperbola inequality integral isometry Lemma line segment linear linearly independent mathematics meet midpoint Mobius transformation multiple nonzero obtained oriented angle oriented Euclidean origin orthogonal matrix orthonormal basis parabola parallel axiom parallelogram parameter parameterized perpendicular points of intersection polar coordinates polygonal region position vector Proof properties Proposition prove quadric quaternion radius real numbers regular curve represented result roots rotation ruler Show sides similarity axiom sphere straight line subset subspace Suppose tangent line theorem triangle ABC unique unit vector vector field vector space zero