C. G. Gibson

Elementary Euclidean Geometry (eBook, PDF)

An Introduction

• Format: PDF

Produktbeschreibung

This book, first published in 2004, is a genuine introduction to the geometry of lines and conics in the Euclidean plane. Lines and circles provide the starting point, with the classical invariants of general conics introduced at an early stage, yielding a broad subdivision into types, a prelude to the congruence classification. A recurring theme is the way in which lines intersect conics. From single lines one proceeds to parallel pencils, leading to midpoint loci, axes and asymptotic directions. Likewise, intersections with general pencils of lines lead to the central concepts of tangent, normal, pole and polar. The treatment is example based and self contained, assuming only a basic grounding in linear algebra. With numerous illustrations and several hundred worked examples and exercises, this book is ideal for use with undergraduate courses in mathematics, or for postgraduates in the engineering and physical sciences.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 25. März 2004
• Englisch
• ISBN-13: 9780511189425
• Artikelnr.: 38189246

Autorenporträt

Chris Gibson received an honours degree in Mathematics from St Andrews University in 1963, and later the degrees of Drs Math and Dr Math from the University of Amsterdam, returning to England in 1967 to begin his 35 year mathematics career at the University of Liverpool. His interests turned towards the geometric areas, and he was a founder member of the Liverpool Singularities Group until his retirement in 2002 as Reader in Pure Mathematics, with over 60 published papers in that area. In 1974 he co-authored the significant 'Topological Stability of Smooth Mappings' (published by Springer Verlag) presenting the first detailed proof of Thom's Topological Stability Theorem. In addition to purely theoretical work in singularity theory, he jointly applied singular methods to specific questions about caustics arising in the physical sciences. His later interests lay largely in the applications to theoretical kinematics, and to problems arising in theoretical robotics. This interest gave rise to a substantial collaboration with Professor K. H. Hunt in the Universities of Monash and Melbourne, and produced a formal classification of screw systems. At the teaching level his major contribution was to pioneer the re-introduction of undergraduate geometry teaching. The practical experience of many years of undergraduate teaching was distilled into three undergraduate texts published by Cambridge University Press, now widely adopted internationally for undergraduate (and graduate) teaching.

Inhaltsangabe

1. Points and lines
2. The Euclidean plane
3. Circles
4. General conics
5. Centres of general conics
6. Degenerate conics
7. Axes and asymptotes
8. Focus and directrix
9. Tangents and normals
10. The parabola
11. The ellipse
12. The hyperbola
13. Pole and polar
14. Congruences
15. Classifying conics
16. Distinguishing conics
17. Uniqueness and invariance.