Advanced euclidean geometry: excursions for secondary teachers and students

INDICE: Preface. 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 aTriangle. 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. TheGolden Rectangle Revisited. The Golden Triangle. Index.

• ISBN: 978-0-470-41256-5
• Editorial: John Wiley & Sons
• Encuadernacion: Rústica
• Páginas: 254
• Fecha Publicación: 19/09/2008
• Nº Volúmenes: 1
• Idioma: Inglés