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Exploring Advanced Euclidean Geometry with GeoGebra

Exploring Advanced Euclidean Geometry with GeoGebra


Part of Classroom Resource Materials

  • Date Published: October 2013
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
  • format: Hardback
  • isbn: 9780883857847

£ 32.99

This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
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About the Authors
  • This book provides an enquiry-based introduction to advanced Euclidean geometry. It utilises the dynamic geometry program GeoGebra to explore many of the most interesting theorems in the subject. Topics covered include triangle centres, inscribed, circumscribed and escribed circles, medial and orthic triangles, the nine-point circle, the theorems of Ceva and Menelaus, and many applications. 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 or as a stand-alone introduction to advanced topics in Euclidean geometry. The exposition consists almost entirely of exercises (with hints) that guide students as they discover the geometric relationships for themselves. The ideas are first explored at the computer and then assembled into a proof of the result under investigation, allowing readers to experience the joy of discovery and develop a deeper appreciation for the subject.

    • An enquiry-based guide to advanced Euclidean geometry
    • Also functions as a guide to the dynamic geometry program GeoGebra
    • Takes the reader from the basics through to advanced constructions in hyperbolic geometry
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    Product details

    • Date Published: October 2013
    • format: Hardback
    • isbn: 9780883857847
    • length: 186 pages
    • dimensions: 260 x 182 x 13 mm
    • weight: 0.42kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
  • Table of Contents

    A quick review of elementary Euclidean geometry
    1. The elements of GeoGebra
    2. The classical triangle centers
    3. Advanced techniques in GeoGebra
    4. Circumscribed, inscribed, and escribed circles
    5. The medial and orthic triangles
    6. Quadrilaterals
    7. The nine-point circle
    8. Ceva's theorem
    9. The theorem of Menelaus
    10. Circles and lines
    11. Applications of the theorem of Menelaus
    12. Additional topics in triangle geometry
    13. Inversions in circles
    14. The Poincaré disk.

  • Author

    Gerard A. Venema, Calvin College, Michigan
    Gerard A. Venema is a Professor of Mathematics at Calvin College, Michigan. He is a member of the American Mathematical Society and the Mathematical Association of America. In addition, he served for ten years as an Associate Editor of American Mathematical Monthly and currently sits on the editorial board of MAA FOCUS. Venema has served the Michigan Section of the MAA as chair and is the 2013 recipient of the section's distinguished service award.

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