Synopsis
Master poles, polars, and quadric transformations in projective geometry.
A clear, structured introduction shows how polarities in a plane give rise to powerful transformations and the role of conics in these mappings. Learn how degeneracy, perspective, and inversions intertwine to shape geometric relationships. This edition explains the core ideas of poles and polars, fundamental lines and points, and how a quadric transformation connects lines to conics. It also covers inversions with respect to a circle, circular transformations, and the birational and involutoric properties that govern these maps, all with concrete descriptions and historical context.
- How two polarities create quadric transformations and when such maps are degenerate or non-degenerate.
- The concept of inversion with respect to a circle and how centers, radii, and polarity interact.
- What makes circular transformations birational and, in some cases, involutoric.
- Key exercises and historical notes that illuminate the development of these ideas.
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Projective Geometry (Classic Reprint)
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Paperback. Condition: New. Print on Demand. Journey through the realm of projective geometry, an intricate mathematical framework that transcends traditional Euclidean concepts. This book invites you to envision a world where points and lines form a harmonious dance, governed by principles that transcend our intuitive understanding of shapes and sizes. The author, a skilled guide, unravels the mysteries of duality, correlation, and perspective, revealing the hidden symmetries that connect seemingly disparate geometric figures. Dive into harmonic ranges and pencils, where points and rays align in captivating patterns, embodying the essence of mathematical beauty. This book unveils a world beyond the boundaries of ordinary geometry, expanding your perception of space and shape, offering a deeper appreciation for the intricacies that shape our visual world. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781451000696_0
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Projective Geometry Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781451000696
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Projective Geometry Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781451000696
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Projective Geometry (Classic Reprint)
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Paperback. Condition: Brand New. 232 pages. 9.00x6.00x0.53 inches. This item is printed on demand. Seller Inventory # zk1451000693
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