Exploring Advanced Euclidean Geometry with GeoGebra

Gerard A. Venema

doi:10.5948/9781614441113

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Fiangga, S Azizah, M A N Rini, R N K and Hidayanti, A N 2018. Introducing Nine-Point Circle to Junior High School Students. Journal of Physics: Conference Series, Vol. 947, Issue. , p. 012075.

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DEMİRAY, Esra IŞIKSAL-BOSTAN, Mine and SAYGI, Elif 2022. Types of Global Argumentation Structures in Conjecture-Generation Activities Regarding Geometry. International Journal of Science and Mathematics Education, Vol. 20, Issue. 4, p. 839.

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Maryono, I. Kusumah, Y. S. and Dahlan, J. A. 2023. Geometric construction using compass and straightedge on GeoGebra. Vol. 2646, Issue. , p. 040014.

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Gerard A. Venema, Calvin College

Publisher:: Mathematical Association of America
Online publication date:: August 2013
Print publication year:: 2013
Online ISBN:: 9781614441113
DOI:: https://doi.org/10.5948/9781614441113

Subjects:: Mathematics, Geometry and Topology
Series:: Classroom Resource Materials

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Exploring Advanced Euclidean Geometry with GeoGebra provides an inquiry-based introduction to advanced Euclidean geometry. It utilizes dynamic geometry software, specifically GeoGebra, to explore the statements and proofs of many of the most interesting theorems in the subject. Topics covered include triangle centers, inscribed, circumscribed, and escribed circles, medial and orthic triangles, the nine-point circle, duality, and the theorems of Ceva and Menelaus, as well as numerous applications of those theorems. The final chapter explores constructions in the Poincaré disk model for hyperbolic geometry. The book can be used either as a computer laboratory manual to supplement an undergraduate course in geometry or as a standalone introduction to advanced topics in Euclidean geometry.

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Exploring Advanced Euclidean Geometry with GeoGebra

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Frontmatter
pp i-vi

Preface
pp vii-xii

Contents
pp xiii-xvi

0 - A Quick Review of Elementary Euclidean Geometry
pp 1-12

1 - The Elements of GeoGebra
pp 13-22

2 - The Classical Triangle Centers
pp 23-30

3 - Advanced Techniques in GeoGebra
pp 31-38

4 - Circumscribed, Inscribed, and Escribed Circles
pp 39-46

5 - The Medial and Orthic Triangles
pp 47-52

6 - Quadrilaterals
pp 53-56

7 - The Nine-Point Circle
pp 57-62

8 - Ceva's Theorem
pp 63-76

9 - The Theorem of Menelaus
pp 77-80

10 - Circles and Lines
pp 81-84

11 - Applications of the Theorem of Menelaus
pp 85-98

12 - Additional Topics in Triangle Geometry
pp 99-104

13 - Inversions in Circles
pp 105-110

14 - The Poincaré Disk
pp 111-120

References
pp 121-122

Index
pp 123-127

About the Author
pp 128-129

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Exploring Advanced Euclidean Geometry with GeoGebra

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