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Textbook
Advanced Euclidean Geometry: Excursions for Secondary Teachers and StudentsISBN: 978-0-470-41256-5
Paperback
264 pages
June 2008, ©2002
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Introduction.
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.
Introduction.
Ceva's Theorem.
Applications of Ceva's Theorem.
The Gergonne Point.
Chapter 3: 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.
Chapter 4: Some Symmetric Points in a Triangle.
Introduction.
Equiangular Point.
A Property of Equilateral Triangles.
A Minimum Distance Point.
Chapter 5: More Triangle Properties.
Introduction.
Angle Bisectors.
Stewart's Theorem.
Miquel's Theorem.
Medians.
Chapter 6: Quadrilaterals.
Centers of a Quadrilateral.
Cyclic Quadrilaterals.
Ptolemy's Theorem.
Applications of Ptolemy's Theorem.
Chapter 7: Equicircles.
Points of Tangency.
Equiradii.
Chapter 8: The Nine-Point Circle.
Introduction to the Nine-Point Circle.
Altitudes.
The Nine-Point Circle Revisited.
Chapter 9: Triangle Constructions.
Introduction.
Selected Constructions.
Chapter 10: Circle Constructions.
Introduction.
The Problem of Apollonius.
Chapter 11: 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.
Related Titles
Geometry & Topology
Resources for
Instructors
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