Advanced Euclidean Geometry Excursions for Secondary Teachers and Students

by Posamentier, Alfred S.

• ISBN13: 9780470412565
• ISBN10: 0470412569
• Edition: 1st
• Format: Paperback
• Copyright: 2008-06-16
• Publisher: Wiley

Summary

State curriculum standards are mandating more coverage of geometry, as are the curricula for pre-service mathematics education and in-service teaching. Yet many secondary teachers know just enough geometry to stay one chapter ahead of their students! What's more, most college-level geometry texts don't address their specific needs. Advanced Euclidean Geometry fills this void by providing a thorough review of the essentials of the high school geometry course and then expanding those concepts to advanced Euclidean geometry, to give teachers more confidence in guiding student explorations and questions. The text contains hundreds of illustrations created in The Geometer's Sketchpad Dynamic Geometry? software, and it is packaged with a CD-ROM (for Windows?/Macintosh? formats) containing over 100 interactive sketches using Sketchpad(TM) (assumes that the user has access to the program).

Author Biography

Alfred S. Posamentier: Dean, City College of New York School of Education, 1999 - present; Professor of Mathematics Education, 1970 - present; Director, European Exchange Programs at the City College, (with Argentina, Austria, Czech Republic, Germany, Great Britain, Hungary, Poland) since 1983; Director, CCNY Extension Center at Rockland County Teacher's Center, since 1984.

Table of Contents

Preface

Introduction

About the Author

Elementary

Euclidean Geometry Revisited

Review of Basic Concepts of Geometry

Learning from Geometric Fallacies

Common Nomenclature

Concurrency of Lines in a Triangle

Introduction

Ceva's Theorem

Applications of Ceva's Theorem

The Gergonne Point

Collinearity of Points

Duality

Menelaus's Theorem

Applications of Menelaus's Theorem

Desargues's Theorem

Pascal's Theorem

Brianchon's Theorem

Pappus's Theorem

The Simson Line

Radical Axes

Some Symmetric Points in a Triangle

Introduction

Equiangular Point

A Property of Equilateral Triangles

A Minimum Distance Point

More Triangle Properties

Introduction

Angle Bisectors

Stewart's Theorem

Miquel's Theorem

Medians

Quadrilaterals

Centers of a Quadrilateral

Cyclic Quadrilaterals

Ptolemy's Theorem

Applications of Ptolemy's Theorem

Equicircles

Equiradii

The Nine-Point Circle

Introduction to the Nine-Point Circle

Altitudes

The Nine-Point Circle Revisited

Triangle Constructions

Selected Constructions

Circle Constructions

Introduction

The Problem of Apollonius

The Golden

Section and Fibonacci Numbers

The Golden Ratio

Fibonacci Numbers

Lucas Numbers

Fibonacci Numbers and Lucas Numbers in Geometry

The Golden Rectangle Revisited

The Golden Triangle

Index

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