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Birkhäuser - Birkhäuser Mathematics | Methods of Solving Complex Geometry Problems

Methods of Solving Complex Geometry Problems

Grigorieva, Ellina

2013, XVI, 234 p. 201 illus., 191 illus. in color.

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  • Contains over 160 complex problems with answers, hints, and detailed solutions
  • Serves as the bridge to more advanced texts in problem-solving 
  • Serves as a self-study or extra resource in the classroom

This book is a unique collection of challenging geometry problems and detailed solutions that will build students’ confidence in mathematics. By proposing several methods to approach each problem and emphasizing geometry’s connections with different fields of mathematics, Methods of Solving Complex Geometry Problems serves as a bridge to more advanced problem solving.  Written by an accomplished female mathematician who struggled with geometry as a child, it does not intimidate, but instead fosters the reader’s ability to solve math problems through the direct application of theorems.

 

Containing over 160 complex problems with hints and detailed solutions, Methods of Solving Complex Geometry Problems can be used as a self-study guide for mathematics competitions and for improving problem-solving skills in courses on plane geometry or the history of mathematics. It contains important and sometimes overlooked topics on triangles, quadrilaterals, and circles such as the Menelaus-Ceva theorem, Simson’s line, Heron’s formula, and the theorems of the three altitudes and medians. It can also be used by professors as a resource to stimulate the abstract thinking required to transcend the tedious and routine, bringing forth the original thought of which their students are capable.

 

Methods of Solving Complex Geometry Problems will interest high school and college students needing to prepare for exams and competitions, as well as anyone who enjoys an intellectual challenge and has a special love of geometry. It will also appeal to instructors of geometry, history of mathematics, and math education courses.

Content Level » Lower undergraduate

Keywords » Geometry Problem Solving - History of Mathematics - Math Competition - Plane Geometry - Pythagorean Theorem - Quadrilateral

Related subjects » Birkhäuser History of Science - Birkhäuser Mathematics

Table of contents 

1 Problems Involving Triangles.- 2 Quadrilaterals and other Polygons.- 3 Problems Involving Circles.- 4 Problems on Construction.- Appendix A Ratios and Proportion.- Appendix B My 9th Grade Notebook Page.- Appendix C My Pictures.- References.- Index.

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