Plane and Solid Geometry (Universitext)

About this book

Nature and the world around us that we ourselves design furnish and build contain many geometric patterns and structures. This is one of the reasons that geometry should be studied at school. At ?rst the study of geometry is experimental. Results are taught and used in numerous examples. Only later do proofs come into play. But are these proofs truly necessary or can we do without them? A natural answer is that every statement must be provided with a proof because we want to know whether it is true. However it is clear that the less experienced student may become frustrated by the pr- ence of too many proofs. Only later will the student understand that proofs not only show the correctness of a statement but also provide better insight into the relationsamong various propertiesof the objects that arebeing st- ied. Learning statements without proofs you risk not being able to see the forest for the trees. For this reason we will pay much attention to a careful presentation of proofs in this book. In the development of the theory of plane geometry there are however many tricky questions especially at the beg- ning. The presentation of proofs at that stage is in general more concealing than revealing. My ?rst objective in writing this book has been to give an accessible - position of the most common notions and properties of elementary Euclidean geometry in dimensions two and three.