Euclidean Geometry and Transformations"A good textbook." ― Mathematical Gazette. This introduction to Euclidean geometry emphasizes both the theory and the practical application of isometries and similarities to geometric transformations. Each chapter begins with an optional commentary on the history of geometry. Contents include modern elementary geometry, isometries and similarities in the plane, vectors and complex numbers in geometry, inversion, and isometries in space. Numerous exercises appear throughout the text, many of which have corresponding answers and hints at the back of the book. Prerequisites for this text, which is suitable for undergraduate courses, include high school algebra, geometry, and elementary trigonometry. 1972 edition. |
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ABCD accompanying figure algebra altitude analytic representation apply bilinear transformation bisector of angle bisects central inversion centroid Ceva’s theorem Cevians chord circumcenter circumcircle commute complex numbers construct defined Definition denote diagonals diameter direct isometry Draw circle equal equation Euclidean Euclidean geometry Exercise Set Figure find first fixed point Gauss plane given circle given point given triangle glide-reflection halfturn Hence homothety hypotenuse ideal point intersection involutoric isogonal conjugate isosceles triangle length maps triangle mathematics medial triangle medians meet Menelaus midpoint mirror Modern Elementary Geometry multiplication ninepoint circle Numbers in Geometry opposite isometry orthic triangle orthocenter orthocentric quadrangle orthogonal parallel parallelogram perpendicular bisector Problem product of reflections proof of Theorem Prove Corollary Prove Theorem radius ratio real numbers reflections in planes right triangle rotation Show side BC square tangent theorem follows trapezoid triangle ABC Vectors and Complex vertex vertices