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Engineering Calculus Notes 129

Engineering Calculus Notes 129 - their solution • planar...

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2 Curves and Vector-Valued Functions of One Variable 2.1 Conic Sections We begin this chapter by looking at the conic sections , which were regarded by the Greeks as the simplest curves after the straight line and circle. A major source of information about classical Greek mathematics is Pappus of Alexandria ( ca. 300 AD ), a formidable geometer of the late third century AD . 1 In his Mathematical Collection 2 he surveyed the work of his predecessors; many of these works have been lost. He classified mathematical problems according to the kinds of loci (curves) required for
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Unformatted text preview: their solution: • planar problems can be solved using circles and straight lines, or planar loci . These are often called compass and straightedge constructions ; • solid problems involve the intersection of a plane with a cone ( solid loci , or conic sections ); 1 The work of Pappus is sometimes taken to mark the end of the classical Greek tradition in mathematics. 2 Parts of this survive in a twelfth-century copy. 117...
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