Mathematics - Geometry 1

This book атом essentially from two sources: a course called ''Maihe-maliques Element aires Approfondies'', taught in 1972-1973 and 1973-1974 at the University of Paris VII; and the author's fifteen years of experience in preparing the geometry part of the orals in the Agrigation de Mathemaliquee. a competition lo select the best high school teachers in France.The main objectives pursued in this book, more precisely, in the framework of elementary geometry, are the following:— to emphasise the vbual, or ''artistic'', aspect of geometry, by using figures in abundance;— to accompany each nrw notion with as interesting a result as possible, preferably one with a simple statement but a non-obvious proof;— finally, to show ibal this simple-looking mathematics does not belong in a museum, that it is an everyday tool in advanced mathematical research, and that occasionally one encounters unsolved problems at even the most elementary level.Here are some particularities of this book that derive from the general principles above. Main definitions are, whenever possible, followed by non-trivial (and sometimes new) examples. Figures abound: at the beginning, especially, each geometric reasoning is illustrated by a diagram. (Such was the general practice fifty years ago, but pictures have all but disappeared from modern geometry books. One reason seems to be that authors think that readers keep pencil and paper next to them and draw figures as they go along, or else draw mental pictures. But the author's experience from university examinations shows that students aren't likely to draw pictures, either on paper or in their heads. Thus one of the aims of this book is to teach the reader to make systematic use of figures as he reads.)Notes are also common, referring to both the historical development and (he current, often very advanced, applications of the ideas introduced. This is meant to convey to the reader a feeling that the elementary mathematics that he is studying is an integral part of the living, continuing corpus of mathematical knowledge. The notes are backed by an extensive bibliography. This is the first part of the 2-volume textbook "Geometry" which provides a very readable and lively presentation of large parts of geometry in the classical sense. An attractive characteristic of the book is that it appeals systematically to the reader's intuition and vision, and illustrates the mathematical text with many figures. For each topic the author presents a theorem that is esthetically pleasing and easily stated - although the proof of the same theorem may be quite hard and concealed. Many open problems and references to modern literature are given. Yet another strong trait of the book is that it provides a comprehensive and unified reference source for the field of geometry in the full breadth of its subfields and ramifications

Volume I of this 2-volume textbook provides a lively and readable presentation of large parts of classical geometry. For each topic the author presents an esthetically pleasing and easily stated theorem - although the proof may be difficult and concealed. The mathematical text is illustrated with figures, open problems and references to modern literature, providing a unified reference to geometry in the full breadth of its subfields and ramifications.