Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Projective geometry, and the Cayley-Klein geometries embedded into it, were originated in the 19th century. It is one of the foundations of algebraic geometry and has many applications to differential geometry. The book presents a systematic introduction to projective geometry as based on the notion of vector space, which is the central topic of the first chapter. The second chapter covers the most important classical geometries which are systematically developed following the principle founded by Cayley and Klein, which rely on distinguishing an absolute and then studying the resulting invariants of geometric objects. An appendix collects brief accounts of some fundamental notions from algebra and topology with corresponding references to the literature. This self-contained introduction is a must for students, lecturers and researchers interested in projective geometry. .

Geometry, Projective. --- Geometry, Modern. --- Modern geometry --- Sphere --- Projective geometry --- Geometry, Modern --- Geometry. --- Mathematics --- Euclid's Elements

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The familiar plane geometry of high school - figures composed of lines and circles - takes on a new life when viewed as the study of properties that are preserved by special groups of transformations. No longer is there a single, universal geometry: different sets of transformations of the plane correspond to intriguing, disparate geometries. This book is the concluding Part IV of Geometric Transformations, but it can be studied independently of Parts I, II, and III, which appeared in this series as Volumes 8, 21, and 24. Part I treats the geometry of rigid motions of the plane (isometries); Part II treats the geometry of shape-preserving transformations of the plane (similarities); Part III treats the geometry of transformations of the plane that map lines to lines (affine and projective transformations) and introduces the Klein model of non-Euclidean geometry. The present Part IV develops the geometry of transformations of the plane that map circles to circles (conformal or anallagmatic geometry). The notion of inversion, or reflection in a circle, is the key tool employed. Applications include ruler-and-compass constructions and the Poincaré model of hyperbolic geometry. The straightforward, direct presentation assumes only some background in high-school geometry and trigonometry. Numerous exercises lead the reader to a mastery of the methods and concepts. The second half of the book contains detailed solutions of all the problems.

Inversions (Geometry) --- Geometry, Modern. --- Modern geometry --- Sphere --- Inversion geometry --- Circle --- Geometry, Modern --- Transformations (Mathematics)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Almost everyone is acquainted with plane Euclidean geometry as it is usually taught in high school. This book introduces the reader to a completely different way of looking at familiar geometrical facts. It is concerned with transformations of the plane that do not alter the shapes and sized of geometric figures. Such transformations (called isometries) play a fundamental role in the group-theoretic approach to geometry. The treatment is direct and simple, The reader is introduced to new ideas and then is urged to solve problems using these ideas. The problems form an essential part of this book and the solutions are given in detail in the second half of the book.

Inversions (Geometry) --- Geometry, Modern. --- Modern geometry --- Sphere --- Inversion geometry --- Circle --- Geometry, Modern --- Transformations (Mathematics) --- Geometry --- Algorithms --- Differential invariants --- Geometry, Differential

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book is the sequel to Geometric Transformations I and II, volumes 8 and 21 in this series, but can be studies independently. It is devoted to the treatment of affine and projective transformations of the plane these transformations include the congruencies and similarities investigated in the previous volumes. The simple text and the many problems are designed mainly to show how the principles of affine and projective geometry may be used to furnish relatively simple solutions of large classes of problems in elementary geometry, including some straight edge construction problems. In the Supplement, the reader is introduced to hyperbolic geometry. The latter part of the book consists of detailed solutions of the problems posed throughout the text.

Inversions (Geometry) --- Geometry, Modern. --- Modern geometry --- Sphere --- Inversion geometry --- Circle --- Geometry, Modern --- Transformations (Mathematics) --- Geometry --- Plane. --- Algorithms --- Differential invariants --- Geometry, Differential

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Geometry, Modern. --- Geometry, Modern --- Géométrie moderne --- 514.12 --- Euclidean and pseudo-Euclidean geometries. Analytic geometry --- 514.12 Euclidean and pseudo-Euclidean geometries. Analytic geometry --- Géométrie moderne --- #KVIV:BB --- Modern geometry --- Sphere --- Geometry