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This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. The topics covered are: a history of Euclidean geometry, Voronoi diagrams, randomized geometric algorithms, computational algebra; triangulations, machine proofs, topological designs finite-element mesh, computer-aided geometric designs and steiner trees. Each chapter is written by a specialist in the field and together they are intended to provide a clear picture of what computational Euclidean geometry is and the direction in which research is going.