Methods for Euclidean Geometry

Methods for Euclidean Geometry

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Methods for Euclidean Geometry explores one of the oldest and most beautiful of mathematical subjects. The book begins with a thorough presentation of classical solution methods for plane geometry problems, but its distinguishing feature is the subsequent collection of methods which have appeared since 1600. For example, the coordinate method, which is a central part of the book, has been part of mathematics for four centuries. However, it has rarely served as a tool that students consider using when faced with geometry problems. The same holds true regarding the use of trigonometry, vectors, complex numbers, and transformations. The book presents each of these as self-contained topics, providing examples of their applications to geometry problems. Both strengths and weaknesses of various methods, as well as the ranges of their effective applications, are discussed. Importance is placed on the problems and their solutions. The book contains numerous problems of varying difficulty; over a third of its contents are devoted to problem statements, hints, and complete solutions. The book can be used as a textbook for geometry courses; as a source book for geometry and other mathematics courses; for capstone, problem-solving, and enrichment courses; and for independent study courses.The chord containing both foci is called the major axis of the ellipse, and the chord joining the other two vertices, which is perpendicular to the major axis, ... We leave several other properties of ellipses as problems, and devote the end of this section to four examples. ... Solution: The equation is equivalent to 9x2 aˆ’ 18x + y2 + 4y + 4 = 0. ... (Recall that we explored a similar question with the parabola. )anbsp;...

Title:Methods for Euclidean Geometry
Author:Owen Byer, Felix Lazebnik, Deirdre L. Smeltzer
Publisher:MAA - 2010-09-02


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