Projective Transformations
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| Author | : P. S. Modenov |
| Publisher | : Academic Press |
| Total Pages | : 149 |
| Release | : 2014-05-12 |
| Genre | : Mathematics |
| ISBN | : 1483261492 |
Geometric Transformations, Volume 2: Projective Transformations focuses on collinearity-preserving transformations of the projective plane. The book first offers information on projective transformations, as well as the concept of a projective plane, definition of a projective mapping, fundamental theorems on projective transformations, cross ratio, and harmonic sets. Examples of projective transformations, projective transformations in coordinates, quadratic curves in the projective plane, and projective transformations of space are also discussed. The text then examines inversion, including the power of a point with respect to a circle, definition and properties of inversion, and circle transformations and the fundamental theorem. The manuscript elaborates on the principle of duality. The manuscript is designed for use in geometry seminars in universities and teacher-training colleges. The text can also be used as supplementary reading by high school teachers who want to extend their range of knowledge on projective transformations.
| Author | : Henry Byron Newson |
| Publisher | : |
| Total Pages | : 64 |
| Release | : 1895 |
| Genre | : History |
| ISBN | : |
| Author | : Henry Byron Newson |
| Publisher | : |
| Total Pages | : 26 |
| Release | : 1895 |
| Genre | : Collineation |
| ISBN | : |
| Author | : Petr Sergeevich Modenov |
| Publisher | : |
| Total Pages | : 152 |
| Release | : 1966 |
| Genre | : Geometry, Algebraic |
| ISBN | : |
| Author | : Elisabetta Fortuna |
| Publisher | : Springer |
| Total Pages | : 275 |
| Release | : 2016-12-17 |
| Genre | : Mathematics |
| ISBN | : 3319428241 |
This book starts with a concise but rigorous overview of the basic notions of projective geometry, using straightforward and modern language. The goal is not only to establish the notation and terminology used, but also to offer the reader a quick survey of the subject matter. In the second part, the book presents more than 200 solved problems, for many of which several alternative solutions are provided. The level of difficulty of the exercises varies considerably: they range from computations to harder problems of a more theoretical nature, up to some actual complements of the theory. The structure of the text allows the reader to use the solutions of the exercises both to master the basic notions and techniques and to further their knowledge of the subject, thus learning some classical results not covered in the first part of the book. The book addresses the needs of undergraduate and graduate students in the theoretical and applied sciences, and will especially benefit those readers with a solid grasp of elementary Linear Algebra.
| Author | : Olive Whicher |
| Publisher | : Rudolf Steiner Press |
| Total Pages | : 294 |
| Release | : 2013 |
| Genre | : Mathematics |
| ISBN | : 185584379X |
Whicher explores the concepts of polarity and movement in modern projective geometry as a discipline of thought that transcends the limited and rigid space and forms of Euclid, and the corresponding material forces conceived in classical mechanics. Rudolf Steiner underlined the importance of projective geometry as, "a method of training the imaginative faculties of thinking, so that they become an instrument of cognition no less conscious and exact than mathematical reasoning." This seminal approach allows for precise scientific understanding of the concept of creative fields of formative (etheric) forces at work in nature--in plants, animals and in the human being. Olive Whicher's groundbreaking book presents an accessible--non-mathematician's--approach to projective geometry. Profusely illustrated, and written with fire and intuitive genius, this work will be of interest to anyone wishing to cultivate the power of inner visualization in a realm of structural beauty.
| Author | : Reinhold Baer |
| Publisher | : Courier Corporation |
| Total Pages | : 338 |
| Release | : 2012-06-11 |
| Genre | : Mathematics |
| ISBN | : 0486154661 |
Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. 1952 edition.
| Author | : John Wesley Young |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 185 |
| Release | : 1930-12-31 |
| Genre | : Geometry, Projective |
| ISBN | : 1614440042 |
John Wesley Young co-authored with Oswald Veblen the first monograph on projective geometry in English. That careful and thorough axiomatic treatment remains read today. This volume is Young's attempt to write an accessible and intuitive treatment for non-specialists. The first five chapters are a careful and elementary treatment of the subject culminating in the theorems of Pascal and Brianchon and the polar system of a conic. Later chapters pull metric consequences from projective results and consider the Kleinian classification of geometries by their groups of transformations. This book, nearly a century after its initial publication, remains a very approachable and understandable treatment of the subject.
| Author | : Norman W. Johnson |
| Publisher | : Cambridge University Press |
| Total Pages | : 455 |
| Release | : 2018-06-07 |
| Genre | : Mathematics |
| ISBN | : 1107103401 |
A readable exposition of how Euclidean and other geometries can be distinguished using linear algebra and transformation groups.
| Author | : Henry Byron Newson |
| Publisher | : |
| Total Pages | : 346 |
| Release | : 1911 |
| Genre | : Collineation |
| ISBN | : |
