104 number theory problems. From the training of the USA IMO team
104 number theory problems. From the training of the USA IMO team By Titu Andreescu; D Andrica; Zuming Feng
2007 | 214 Pages | ISBN: 0817645276 | PDF | 1 MB
2007 | 214 Pages | ISBN: 0817645276 | PDF | 1 MB
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