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In his "Géométrie" of 1637 Descartes achieved a monumental innovation of mathematical techniques by introducing what is now called analytic geometry. Yet the key question of the book was foundational rather than technical: When are geometrical objects known with such clarity and distinctness as befits the exact science of geometry? Classically, the answer was sought in procedures of geometrical construction, in particular by ruler and compass, but the introduction of new algebraic techniques made these procedures insufficient. In this detailed study, spanning essentially the period from the first printed edition of Pappus' "Collection" (1588, in Latin translation) and Descartes' death in 1650, Bos explores the current ideas about construction and geometrical exactness, noting that by the time Descartes entered the field the incursion of algebraic techniques, combined with an increasing uncertainty about the proper means of geometrical problem solving, had produced a certain impasse. He then analyses how Descartes transformed geometry by a redefinition of exactness and by a demarcation of geometry's proper subject and procedures in such a way as to incorporate the use of algebraic methods without destroying the true nature of geometry. Although mathematicians later essentially discarded Descartes' methodological convictions, his influence was profound and pervasive. Bos' insistence on the foundational aspects of the "Géométrie" provides new insights both in the genesis of Descartes' masterpiece and in its significance for the development of the conceptions of mathematical exactness.

Geometrical constructions --- Geometry --- History --- Mathematics --- Euclid's Elements --- Constructions, Geometric --- Constructions, Geometrical --- Geometric constructions --- Descartes, René, --- Descartes, Renatus --- Cartesius, Renatus --- Descartes, René --- Descartes, René --- Geometry.

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Academic collection --- 512.54 --- Discrete groups --- Geometrical constructions --- Constructions, Geometric --- Constructions, Geometrical --- Geometric constructions --- Geometry --- Groups, Discrete --- Infinite groups --- Groups. Group theory --- Conferences - Meetings --- 512.54 Groups. Group theory --- Discrete mathematics --- Discrete groups - Congresses --- Geometrical constructions - Congresses

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Geometrical constructions --- -Constructions, Geometric --- Constructions, Geometrical --- Geometric constructions --- Geometry --- Early works to 1800 --- -Early works to 1800 --- Constructions, Geometric --- Euclides. Elementen. Vertaling (Engelse) door Joseph Moxon. --- Mohr (Georg). Vertaling (Nederlandse) van de Elementen van Euclides. --- Moxon (Joseph). Vertaling (Engelse) van de Elementen van Euclides. --- Euclide. Eléments. Traduction néerlandaise par Georg Mohr. --- Euclide. Eléments. Traduction anglaise par Joseph Moxon. --- Moxon (Joseph). Traduction anglaise des Eléments d'Euclide. --- Mohr (Georg). Traduction néerlandaise des Eléments d'Euclide. --- Euclides. Elementen. Vertaling (Nederlandse) door Georg Mohr. --- Operation cesarienne

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Icons of mathematics are certain geometric diagrams that play a crucial role in visualizing mathematical proofs, and in the book the authors present 20 of them and explore the mathematics that lies within and that can be created. The authors devote a chapter to each icon, illustrating its presence in real life, its primary mathematical characteristics and how it plays a central role in visual proofs of a wide range of mathematical facts. Among these are classical results from plane geometry, properties of the integers, means and inequalities, trigonometric identities, theorems from calculus, and puzzles from recreational mathematics.

Geometry --- Geometrical constructions. --- Generation of geometric forms. --- Proof theory. --- Mathematical notation. --- Geometrical drawing. --- Geometry, Plane. --- Visualization. --- Visualisation --- Imagination --- Visual perception --- Imagery (Psychology) --- Plane geometry --- Mathematical drawing --- Plans --- Drawing --- Mechanical drawing --- Projection --- Mathematical symbols --- Mathematics --- Notation, Mathematical --- Logic, Symbolic and mathematical --- Geometric forms, Generation of --- Geometrical drawing --- Geometry, Descriptive --- Constructions, Geometric --- Constructions, Geometrical --- Geometric constructions --- Famous problems in geometry --- Problems, Famous, in geometry --- Famous problems. --- Symbols --- Problems, Famous

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Arrangements of curves constitute fundamental structures that have been intensively studied in computational geometry. Arrangements have numerous applications in a wide range of areas – examples include geographic information systems, robot motion planning, statistics, computer-assisted surgery and molecular biology. Implementing robust algorithms for arrangements is a notoriously difficult task, and the CGAL arrangements package is the first robust, comprehensive, generic and efficient implementation of data structures and algorithms for arrangements of curves.   This book is about how to use CGAL two-dimensional arrangements to solve problems. The authors first demonstrate the features of the arrangement package and related packages using small example programs. They then describe applications, i.e., complete standalone programs written on top of CGAL arrangements used to solve meaningful problems – for example, finding the minimum-area triangle defined by a set of points, planning the motion of a polygon translating among polygons in the plane, computing the offset polygon, finding the largest common point sets under approximate congruence, constructing the farthest-point Voronoi diagram, coordinating the motion of two discs moving among obstacles in the plane, and performing Boolean operations on curved polygons.   The book contains comprehensive explanations of the solution programs, many illustrations, and detailed notes on further reading, and it is supported by a website that contains downloadable software and exercises. It will be suitable for graduate students and researchers involved in applied research in computational geometry, and for professionals who require worked-out solutions to real-life geometric problems. It is assumed that the reader is familiar with the C++ programming-language and with the basics of the generic-programming paradigm.

Algorithms. --- Combinatorial geometry -- Data processing. --- Geometrical constructions -- Data processing. --- Geometry -- Data processing. --- Geometry --- Geometrical constructions --- Combinatorial geometry --- Algorithms --- Mathematics --- Engineering & Applied Sciences --- Electrical & Computer Engineering --- Physical Sciences & Mathematics --- Applied Physics --- Electrical Engineering --- Technology - General --- Data processing --- Data processing. --- Constructions, Geometric --- Constructions, Geometrical --- Geometric constructions --- Geometric combinatorics --- Geometrical combinatorics --- Algorism --- Computer science. --- Computer graphics. --- Geometry. --- Applied mathematics. --- Engineering mathematics. --- Computer Science. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Appl.Mathematics/Computational Methods of Engineering. --- Combinatorial analysis --- Discrete geometry --- Algebra --- Arithmetic --- Foundations --- Computer vision. --- Mathematical and Computational Engineering. --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Euclid's Elements --- Engineering --- Engineering analysis --- Mathematical analysis --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Optical equipment