Pamfilos P. Lectures on Euclidean Geometry Vol 2...of Circle...,Conics 2024

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Pamfilos P. Lectures on Euclidean Geometry Vol 2...of Circle...,Conics 2024

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Textbook in PDF format This is a comprehensive two-volumes text on plane and space geometry, transformations and conics, using a synthetic approach. The first volume focuses on Euclidean Geometry of the plane, and the second volume on Circle measurement, Transformations, Space geometry, Conics. The book is based on lecture notes from more than 30 courses which have been taught over the last 25 years. Using a synthetic approach, it discusses topics in Euclidean geometry ranging from the elementary (axioms and their first consequences), to the complex (the famous theorems of Pappus, Ptolemy, Euler, Steiner, Fermat, Morley, etc.). Through its coverage of a wealth of general and specialized subjects, it provides a comprehensive account of the theory, with chapters devoted to basic properties of simple planar and spatial shapes, transformations of the plane and space, and conic sections. As a result of repeated exposure of the material to students, it answers many frequently asked questions. Particular attention has been given to the didactic method; the text is accompanied by a plethora of figures (more than 2000) and exercises (more than 1400), most of them with solutions or expanded hints. Each chapter also includes numerous references to alternative approaches and specialized literature. The book is mainly addressed to students in mathematics, physics, engineering, school teachers in these areas, as well as, amateurs and lovers of geometry. Offering a sound and self-sufficient basis for the study of any possible problem in Euclidean geometry, the book can be used to support lectures to the most advanced level, or for self-study. Preface Symbol index Circle measurement Transformations Space Geometry Conic sections Circle measurement The difficulties the limit Definition of the perimeter of the circle The number π Arc length of a circle radians Definition of the area of the circle The area of a circular sector The isoperimetric inequality Anthyphairesis Comments and exercises for the References Transformations of the plane Transformations isometries Reflections and point symmetries Translations Rotations Congruency or isometry or equality Homotheties Similarities Inversions The hyperbolic plane Archimedean tilings Comments and exercises for the References Lines and planes in space Axioms for space Parallel planes Angles in space Skew lines Line orthogonal to plane Angle between line and plane Theorem of Thales in space Comments and exercises for the Solids Dihedral angles Trihedral angles Pyramids polyhedral angles Tetrahedra Regular pyramids Polyhedra Platonic solids Prisms Cylinder Cone conical surface Truncated cone cone unfolding Sphere Spherical and circumscribed polyhedra Spherical lune angle of great circles Spherical triangles The supplementary trihedral Axonometric projection affinities Perspective projection Comments and exercises for the References Areas in space volumes Areas in space Area of the sphere Area of spherical polygons Euler Characteristic Volumes Volume of prisms Volume of pyramids Volume of cylinders Volume of cones Volume of spheres Comments and exercises for the References Conic sections Conic sections Dandelin’s spheres Directrices General characteristics of conics The parabola The ellipse The hyperbola Comments and exercises for the References Transformations in space Isometries in space Reflections in space Translations in space Rotations in space Congruence or isometry in space Homotheties in space Similarities in space Archimedean solids Epilogue References Index