Pamfilos P. Lectures on Euclidean Geometry Vol 1...of the Plane 2024

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Pamfilos P. Lectures on Euclidean Geometry Vol 1...of the Plane 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 Euclidean Geometry of the plane The basic notions Undefined terms, axioms Line and line segment Length, distance Angles Angle kinds Triangles Congruence, the equality of shapes Isosceles and right triangle Triangle congruence criteria Triangle’s sides and angles relations The triangle inequality The orthogonal to a line The parallel from a point The sum of triangle’s angles The axiom of parallels Symmetries Ratios, harmonic quadruples Comments and exercises for the References Circle and polygons The circle, the diameter, the chord Circle and line Two circles Constructions using ruler and compass Parallelograms Quadrilaterals The middles of sides The triangle’s medians The rectangle and the square Other kinds of quadrilaterals Polygons, regular polygons Arcs, central angles Inscribed angles Inscriptible or cyclic quadrilaterals Circumscribed quadrilaterals Geometric loci Comments and exercises for the References Areas, Thales, Pythagoras, Pappus Area of polygons The area of the rectangle Area of parallelogram and triangle Pythagoras and Pappus Similar right triangles The trigonometric functions The theorem of Thales Pencils of lines Similar triangles Similar polygons Triangle’s sine and cosine rules Stewart, medians, bisectors, altitudes Antiparallels, symmedians Comments and exercises for the References The power of the circle Power with respect to a circle Golden section and regular pentagon Radical axis, radical center Apollonian circles Circle pencils Orthogonal circles and pencils Similarity centers of two circles Inversion Polar and pole Comments and exercises for the References From the classical theorems Escribed circles and excenters Heron’s formula Euler’s circle Feuerbach’s Theorem Euler’s theorem Tangent circles of Apollonius Theorems of Ptolemy and Brahmagupta Simson’s and Steiner’s lines Miquel point, pedal triangle Arbelos Sangaku Fermat’s and Fagnano’s theorems Morley’s theorem Signed ratio and distance Cross ratio, harmonic pencils Theorems of Menelaus and Ceva The complete quadrilateral Desargues’ theorem Pappus’ theorem Pascal’s and Brianchon’s theorems Castillon’s problem, homographic relations Malfatti’s problem Calabi’s triangle Comments and exercises for the References Index