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At last: geometry in an exemplary, accessible and attractive form! The authors emphasise both the intellectually stimulating parts of geometry and routine arguments or computations in concrete or classical cases, as well as practical and physical applications. They also show students the fundamental concepts and the difference between important results and minor technical routines. Altogether, the text presents a coherent high school curriculum for the geometry course, naturally backed by numerous examples and exercises.
Introduction. 1: Distance and Algebra. 2: Coordinates. 3: Area and the Pythagoras Theorem. 4: The Distance Formula. 5: Some Applications of Right Triangles. 6: Polygons. 7: Congruent Triangles. 8: Dilations and Similarities. 9: Volumes. 10: Vectors and Dot Product. 11: Transformations. 12: Isometries. Index.
Posted October 4, 2005
Most high school geometry texts are based on the presentation in Euclid's Elements. They state his postulates (axioms) and common notions in modern language, then proceed to develop the subject along the lines Euclid did (no pun intended). The authors of this text opted not to do that. They introduce their own postulates, from which they develop the material they cover. They omit some of the material that appears in other texts, such as inequalites, theorems about circles, and the concurrence theorems. Instead they include material on dilations, vectors, the dot product, transformations, and isometries. They introduce coordinate geometry early in the text, allowing them to use algebraic arguments throughout. Also, proofs are presented in the paragraph form used by mathematicians rather than the two-column format favored by geometry teachers for pedagogical reasons. The text covers distance and angles, coordinates, area, the Pythagorean Theorem, the distance formula, right triangles, polygons, congruent triangles, dilations and similarities, volumes, vectors and the dot product, transformations, and isometries. The material at the end of the text, which concludes with a proof that any isometry can be expressed as the composition of at most three reflections, is fascinating. The problems are interesting and, for the most part, tractable. A couple problems, one involving the use of similar triangles and the other based on the Side-Angle-Side congruence postulate for triangles, are introduced before the relevant topics are. There are no answers in the text, but a solution manual written by Philip Carlson is available separately. There are some errors in the text, including a triangle whose three vertices are collinear. Some of the terminology and notation used in the text is idiosyncratic, limiting its usefulness as a reference. I recommend using this text as a supplement after working through a standard text so that you can build on what you have already learned and are familiar with standard terminology and notation.
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Posted October 27, 2008
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