Dynamic Geometry Sketches
(Interactive dynamic geometry sketches with JavaSketchpad, Cabri 3D, Cinderella, GeoGebra & GEONexT)
My website, dynamicmathematicslearning.com, is completely SECURE and SAFE - see note below for Java settings to enable the dynamic applets.
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. 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
Dept of Mathematics & Computer Science Education
University of KwaZulu-Natal, South Africa
(Last Update: 2 April 2014)
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
20% Discount until 10 March 2014 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.
NOTE: Please WAIT while the applets at the links below load. If a security pop-up menu appears in your browser, please choose RUN/ALLOW to let the applets run properly. It is completely safe & can be trusted. If you have the very latest Java on your PC or Apple Mac, and experience problems with the applets loading, please go here for additional information on Java settings that should resolve the issue.
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
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
Semi-regular Angle-gons and Side-gons
A generalization of rectangles and rhombi
Van Aubel's Theorem and some Generalizations (Updated!)
Some unproved conjectures (Updated!)
Other Activities and Links
By Michael de Villiers at: prof md @ mweb .co.za (use without spaces in between)
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