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
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"The book is well written and contains a lot of figures illustrating the theorems and their proofs." ---- MAA Reviews
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20 of 20 people found the following review helpful:
5.0 out of 5 stars
A lovely book !!,
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This review is from: Geometry of Conics (Mathematical World) (Paperback)
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".
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If you stake a goat, it will graze the grass inside the circle that is centered at the stake and has radius the length of the rope. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
polar correspondence with respect, isotomic conjugation, isogonal conjugation, unique conic tangent, trilinear polar, equilateral hyperbola passing, isogonal conjugate, pedal triangle, pedal circles, conics theorem, ellipse confocal, conic passing, midpoint perpendicular, radical axis, degenerate curve, radical axes, complete quadrilateral, tangency points, polar transformation, parabola tangent, equilateral hyperbolas, projective transformation, given conic, polar curve, given ellipse Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
If you stake a goat, it will graze the grass inside the circle that is centered at the stake and has radius the length of the rope. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
polar correspondence with respect, isotomic conjugation, isogonal conjugation, unique conic tangent, trilinear polar, equilateral hyperbola passing, isogonal conjugate, pedal triangle, pedal circles, conics theorem, ellipse confocal, conic passing, midpoint perpendicular, radical axis, degenerate curve, radical axes, complete quadrilateral, tangency points, polar transformation, parabola tangent, equilateral hyperbolas, projective transformation, given conic, polar curve, given ellipse Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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