Conics
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| Author | : Arseny V. Akopyan |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 148 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : 9780821884324 |
"Geometry Of Conics deals with the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, this book moves to less trivial results, both classical and contemporary. It demonstrates the advantage of purely geometric methods of studying conics."--Publisher's website.
| Author | : Georg Glaeser |
| Publisher | : Springer |
| Total Pages | : 496 |
| Release | : 2016-03-22 |
| Genre | : Mathematics |
| ISBN | : 3662454505 |
This text presents the classical theory of conics in a modern form. It includes many novel results that are not easily accessible elsewhere. The approach combines synthetic and analytic methods to derive projective, affine and metrical properties, covering both Euclidean and non-Euclidean geometries. With more than two thousand years of history, conic sections play a fundamental role in numerous fields of mathematics and physics, with applications to mechanical engineering, architecture, astronomy, design and computer graphics. This text will be invaluable to undergraduate mathematics students, those in adjacent fields of study, and anyone with an interest in classical geometry. Augmented with more than three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises.
| Author | : Apollonius (of Perga.) |
| Publisher | : |
| Total Pages | : 444 |
| Release | : 1896 |
| Genre | : Conic sections |
| ISBN | : |
| Author | : Barry Spain |
| Publisher | : Courier Corporation |
| Total Pages | : 164 |
| Release | : 2007-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486457737 |
This concise text introduces students to analytical geometry, covering basic ideas and methods. Readily intelligible to any student with a sound mathematical background, it is designed both for undergraduates and for math majors. It will prove particularly valuable in preparing readers for more advanced treatments. The text begins with an overview of the analytical geometry of the straight line, circle, and the conics in their standard forms. It proceeds to discussions of translations and rotations of axes, and of the general equation of the second degree. The concept of the line at infinity is introduced, and the main properties of conics and pencils of conics are derived from the general equation. The fundamentals of cross-ratio, homographic correspondence, and line-coordinates are explored, including applications of the latter to focal properties. The final chapter provides a compact account of generalized homogeneous coordinates, and a helpful appendix presents solutions to many of the examples.
| Author | : Keith Kendig |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 428 |
| Release | : 2020-07-29 |
| Genre | : Mathematics |
| ISBN | : 1470456834 |
This book engages the reader in a journey of discovery through a spirited discussion among three characters: philosopher, teacher, and student. Throughout the book, philosopher pursues his dream of a unified theory of conics, where exceptions are banished. With a helpful teacher and examplehungry student, the trio soon finds that conics reveal much of their beauty when viewed over the complex numbers. It is profusely illustrated with pictures, workedout examples, and a CD containing 36 applets. Conics is written in an easy, conversational style, and many historical tidbits and other points of interest are scattered throughout the text. Many students can selfstudy the book without outside help. This book is ideal for anyone having a little exposure to linear algebra and complex numbers.
| Author | : Michael N. Fried |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 134 |
| Release | : 2011-09-03 |
| Genre | : Mathematics |
| ISBN | : 1461401461 |
Apollonius’s Conics was one of the greatest works of advanced mathematics in antiquity. The work comprised eight books, of which four have come down to us in their original Greek and three in Arabic. By the time the Arabic translations were produced, the eighth book had already been lost. In 1710, Edmond Halley, then Savilian Professor of Geometry at Oxford, produced an edition of the Greek text of the Conics of Books I-IV, a translation into Latin from the Arabic versions of Books V-VII, and a reconstruction of Book VIII. The present work provides the first complete English translation of Halley’s reconstruction of Book VIII with supplementary notes on the text. It also contains 1) an introduction discussing aspects of Apollonius’s Conics 2) an investigation of Edmond Halley's understanding of the nature of his venture into ancient mathematics, and 3) an appendices giving a brief account of Apollonius’s approach to conic sections and his mathematical techniques. This book will be of interest to students and researchers interested in the history of ancient Greek mathematics and mathematics in the early modern period.
| Author | : Gerald J. Toomer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 978 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461389852 |
With the publication of this book I discharge a debt which our era has long owed to the memory of a great mathematician of antiquity: to pub lish the /llost books" of the Conics of Apollonius in the form which is the closest we have to the original, the Arabic version of the Banu Musil. Un til now this has been accessible only in Halley's Latin translation of 1710 (and translations into other languages entirely dependent on that). While I yield to none in my admiration for Halley's edition of the Conics, it is far from satisfying the requirements of modern scholarship. In particular, it does not contain the Arabic text. I hope that the present edition will not only remedy those deficiencies, but will also serve as a foundation for the study of the influence of the Conics in the medieval Islamic world. I acknowledge with gratitude the help of a number of institutions and people. The John Simon Guggenheim Memorial Foundation, by the award of one of its Fellowships for 1985-86, enabled me to devote an unbroken year to this project, and to consult essential material in the Bodleian Li brary, Oxford, and the Bibliotheque Nationale, Paris. Corpus Christi Col lege, Cambridge, appointed me to a Visiting Fellowship in Trinity Term, 1988, which allowed me to make good use of the rich resources of both the University Library, Cambridge, and the Bodleian Library.
| Author | : Robert Bix |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 356 |
| Release | : 2006-11-22 |
| Genre | : Mathematics |
| ISBN | : 0387392734 |
Conics and Cubics offers an accessible and well illustrated introduction to algebraic curves. By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves. It includes a simple proof of Bezout’s Theorem on the number of intersections of two curves. The subject area is described by means of concrete and accessible examples. The book is a text for a one-semester course.
| Author | : J. W. Downs |
| Publisher | : Courier Corporation |
| Total Pages | : 116 |
| Release | : 2012-10-16 |
| Genre | : Mathematics |
| ISBN | : 0486148882 |
Using examples from everyday life, this text studies ellipses, parabolas, and hyperbolas. Explores their ancient origins and describes the reflective properties and roles of curves in design applications. 1993 edition. Includes 98 figures.
| Author | : Christopher Baltus |
| Publisher | : Springer Nature |
| Total Pages | : 190 |
| Release | : 2020-09-01 |
| Genre | : Mathematics |
| ISBN | : 3030462870 |
This volume combines an introduction to central collineations with an introduction to projective geometry, set in its historical context and aiming to provide the reader with a general history through the middle of the nineteenth century. Topics covered include but are not limited to: The Projective Plane and Central Collineations The Geometry of Euclid's Elements Conic Sections in Early Modern Europe Applications of Conics in History With rare exception, the only prior knowledge required is a background in high school geometry. As a proof-based treatment, this monograph will be of interest to those who enjoy logical thinking, and could also be used in a geometry course that emphasizes projective geometry.
