Oxford University Press, 1993 - 307 sider
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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Axioms for geometry
Coordinates and equations
Conics and other curves
algebra angle axiom basis calculate called centre Chapter circle complex concept conic consider constant construct contains coordinate coordinate system corresponding curvature curve defined definition denote derivative Desargues determinant differential dimensions direction distance dot product ellipse equal equation Euclidean example expression fact Figure fixed follows formula four function geometry given gives idea integral intersection isometry length linear matrix means meet multiple Notice numbers obtained oriented origin orthogonal orthogonal matrix parallel parallelogram parameter parameterized perpendicular plane polygonal position vector possible problem projective Proof properties Proposition prove rational region regular relative represented result roots rotation rule ruler scalar Show sides similar space sphere square straight line Suppose surface symmetric matrix tangent theorem theory transformation triangle unique unit vector zero