Advanced Plane Geometry
by: Patrick D. Barry (Author)
Publication Date: 2019/11/23
Language: English
Print Length: 514 pages
ISBN-10: 0244838224
ISBN-13: 9780244838225
Book Description
This book begins at the point where Professor Barry’s text ‘Geometry with Trigonometry’ leaves off, and develops advanced elements of plane geometry. It culminates in an account of the geometry of conics in the complex projective plane. Along the way it considers invariants of affine, projective, and complex-affine plane geometry under the various appropriate group actions. The ideas and progressive generalisations are introduced in a gradual way, and thoroughly explored at each stage. Some of these ideas go back to difficult and little-read works from the nineteenth century, and are here rescued and made more accessible. Included are many gems of plane geometry that originated with masters such as Newton, Pascal, Caot, Simson, and Desargues, and unexpected variations on classical Greek results such as Pythagoras’ Theorem. The material is almost all accessible to anyone who understands elementary plane geometry.
About the Author
This book begins at the point where Professor Barry’s text ‘Geometry with Trigonometry’ leaves off, and develops advanced elements of plane geometry. It culminates in an account of the geometry of conics in the complex projective plane. Along the way it considers invariants of affine, projective, and complex-affine plane geometry under the various appropriate group actions. The ideas and progressive generalisations are introduced in a gradual way, and thoroughly explored at each stage. Some of these ideas go back to difficult and little-read works from the nineteenth century, and are here rescued and made more accessible. Included are many gems of plane geometry that originated with masters such as Newton, Pascal, Caot, Simson, and Desargues, and unexpected variations on classical Greek results such as Pythagoras’ Theorem. The material is almost all accessible to anyone who understands elementary plane geometry.
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