Geometry of Conics (Mathematical World) by A. V. Akopyan (PDF)

Description

The book is devoted to 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, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confocal ellipses. The book demonstrates the advantage of purely geometric methods of studying conics. It contains over 50 exercises and problems aimed at advancing geometric intuition of the reader. The book also contains more than 100 carefully prepared figures, which will help the reader to better understand the material presented

User’s Reviews

Editorial Reviews: Review “The book is well written and contains a lot of figures illustrating the theorems and their proofs.” —- MAA Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Traditional geometric approach. Pretty easy to read. Would have liked a slightly more modern, algebraic approach, but it has what I needed.

⭐I became acquainted with Dandelin’s device for obtaining properties of conic sections many years ago (in a lecture) and was moved by its elegance, simplicity and naturalness. Yet, Conic Sections are entirely absent from school textbooks nowadays. The circle, the parabola and the hyperbola (but not the ellipse) are covered superficially and only from a utilitarian algebraic perspective. It is far better to have a unified geometric treatment. To be sure, you will find conics and Dandelin Spheres mentioned in Courant and Robbins’s “What is Mathematics?”, Ogilvy’s “Through the Mathescope” and “Excursions in Geometry” and, of course, in Hilbert and Cohn-Vossen’s “Geometry and the Imagination” but these books have no place in mathematics classrooms of the present day. So this new book devoted entirely to the Geometry of the Conic Sections is very welcome indeed.

⭐There is a definite dearth of modern books dealing with geometrical conics, that is to say using the methods of classical euclidean and projective geometry to derive their properties. In this respect Akopyan’s book should be warmly welcomed.A few other points pertaining to what used to be called Modern Geometry, such as cevians, symmedians, Lemoine and Brocard points, Simson lines, and some of their properties are also presented to new generations of readers.Much of this stuff used to be taught in this way in the 19th and early 20th century (cfr. C. V. Durell’s delightful books), but later fell out of fashion. Fortunately a revival of interest in this classical way of teaching geometry can be perceived these days.I’ve only read part of the book so far, but I must admit it is a lovely book.However I find the book a bit beyond “… the reach of high school students”, as the pace is rather brisk. Particularly projective geometry definitely deserves a longer and more detailed introduction.There is a mistake in the definition of parabola in the last paragraph of page 2 (line 3 from bottom), where “equal” should be substituted for “constant”.

⭐A fantastic treatment of conic sections with as little analytical geometry as possible.

⭐

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