Dynamic Geometry Sketches
(Interactive dynamic geometry sketches with JavaSketchpad, Cabri 3D, Cinderella, GeoGebra & GEONexT)
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This site has interactive Java sketches which demonstrate several famous and beautiful theorems in mathematics such as Napoleon, Viviani, nine-point circle, Euler line, Neuberg, Van Aubel, Spieker circle, Fermat-Torricelli points, etc., as well as further generalizations of many of these. It also includes Student Explorations which contain mostly geometric problems, challenges, explorations, and classroom material of interest hopefully to both students and teachers of mathematics in school as well as undergraduate level at university such as the hierarchical classification of quadrilaterals, interior angle sum of polygons, etc. Some of the explorations are directly related to the school math curriculum such as the "classifying, exploring and defining quadrilaterals" activity, while others such as "Bottema's theorem" are intended as challenges to extend students and teachers a little beyond the usual confines of the school. Some challenges are more suitable for training of enthusiasts of mathematical competitions.
Michael de Villiers
Prof Extraordinaire, Research Unit for Mathematics Education (RUMEUS)
University of Stellenbosch, South Africa
[Retired, Dept of Mathematics & Computer Science Education
University of KwaZulu-Natal, South Africa]
(Last Update: 17 June 2017)
Visit p. 4 of my homepage for downloadable articles Downloadable articles on Math & Math Ed
A proof of the result above, a generalization as well as an interesting dual, and much more,
can be found in my book, available in bound form or downloadable PDF Some Adventures in Euclidean Geometry
Free Java applets provided by
Get 10% off print books + free mail till 6 Nov 2017 Downloadable PDF papers/books on Geometry, Mathematics & Mathematics Education for sale
NEW! Problem solving and logical thinking games for young children Contact dynamic learn @mweb. co. za (without the spaces) to order.
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Explorations for Students (Updated)
Balancing Quadrilaterals Theorem: A 'Van Aubel-like' result
(An application of centroids - centres of mass)
British Mathematics Olympiad Problem and its Dual
(An application of perpendicular and angle bisectors of a triangle)
A Hierarchical Classification of Quadrilaterals
(Inclusive Classification of Quadrilaterals)
Centroids forming Parallelo-octagon: A Varignon Generalization
(A generalization of Varignon's Theorem to 2D and 3D)
Para-Hexagon Concurrency Theorem
(A generalization of concurrency of triangle medians) (Updated!)
Semi-regular Angle-gons and Side-gons
(A generalization of rectangles and rhombi)
Spieker conic and Nagel line generalization (Updated!)
Other Activities and Links
By Michael de Villiers at: prof md @ mweb .co.za (use without spaces in between)
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