Dynamic Geometry Sketches
(Interactive dynamic geometry sketches with JavaSketchpad, Cabri 3D, Cinderella, GeoGebra & GEONexT)
Some internet security programs are set to detect Java applets and will automatically give cautionaries when you visit here. Please rest assured that my website is completely SECURE and SAFE. Also see note further down for downloading a bookmarklet or specific Javasettings to enable the dynamic applets if they are not running in your browser.
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
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: 16 June 2016)
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 20% off print books till 18 July 2016 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.
|site search by freefind||advanced|
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 experience problems with the applets loading, please go here for additional information 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)
Hierarchical Quadrilateral Classification or Tree
(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)
Pirate Treasure Hunt and a Generalization (Updated!*)
Semi-regular Angle-gons and Side-gons
(A generalization of rectangles and rhombi)
Some unproved conjectures (Updated!)
Other Activities and Links
Logic, Strategy & Geometry Games (Updated!)
By Michael de Villiers at: prof md @ mweb .co.za (use without spaces in between)
Please kindly consider making donations to help update & maintain this site.