Advanced Euclidean Geometry : Excursions for Secondary Teachers and Students - With CD / Edition 1

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More About This Textbook


State curriculum standards are mandating more coverage of geometry,as are the curricula for pre-service mathematics education andin-service teaching. Yet many secondary teachers know just enoughgeometry to stay one chapter ahead of their students! What's more,most college-level geometry texts don't address their specificneeds.

Advanced Euclidean Geometry fills this void by providing a thoroughreview of the essentials of the high school geometry course andthen expanding those concepts to advanced Euclidean geometry, togive teachers more confidence in guiding student explorations andquestions. The text contains hundreds of illustrations created inThe Geometer's Sketchpad Dynamic Geometry? software, and it ispackaged with a CD-ROM (for Windows?/Macintosh? formats) containingover 100 interactive sketches using Sketchpad(TM) (assumes that theuser has access to the program).

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Product Details

  • ISBN-13: 9780470412565
  • Publisher: Wiley
  • Publication date: 6/16/2008
  • Series: Key Curriculum Press Series
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 264
  • Product dimensions: 8.01 (w) x 9.94 (h) x 0.56 (d)

Table of Contents



About the Author.

Chapter 1: Elementary Euclidean Geometry Revisited.

Review of Basic Concepts of Geometry.

Learning from Geometric Fallacies.

Common Nomenclature.

Chapter 2: Concurrency of Lines in a Triangle.


Ceva's Theorem.

Applications of Ceva's Theorem.

The Gergonne Point.

Chapter 3: Collinearity of Points.


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.

Chapter 4: Some Symmetric Points in a Triangle.


Equiangular Point.

A Property of Equilateral Triangles.

A Minimum Distance Point.

Chapter 5: More Triangle Properties.


Angle Bisectors.

Stewart's Theorem.

Miquel's Theorem.


Chapter 6: Quadrilaterals.

Centers of a Quadrilateral.

Cyclic Quadrilaterals.

Ptolemy's Theorem.

Applications of Ptolemy's Theorem.

Chapter 7: Equicircles.

Points of Tangency.


Chapter 8: The Nine-Point Circle.

Introduction to the Nine-Point Circle.


The Nine-Point Circle Revisited.

Chapter 9: Triangle Constructions.


Selected Constructions.

Chapter 10: Circle Constructions.


The Problem of Apollonius.

Chapter 11: The Golden Section and FibonacciNumbers.

The Golden Ratio.

Fibonacci Numbers.

Lucas Numbers.

Fibonacci Numbers and Lucas Numbers in Geometry.

The Golden Rectangle Revisited.

The Golden Triangle.


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