Dynamic Geometry Sketches
(Interactive dynamic geometry sketches with JavaSketchpad, Cabri 3D , Cinderella , GeoGebra & GEONexT)
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.
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Michael de Villiers
Dept of Mathematics & Computer Science Education
University of KwaZulu-Natal, South Africa
(Last Update: 9 April 2013)
Visit p. 4 of my homepage for downloadable articles Downloadable articles on Math & Math Ed
Circumcyclicquad
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
JavaScript
Kit
20% Discount until 14 December 2012 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.
Explorations for
Students
Affine Equivalence of Cubic Polynomials
Area Ratios of Octagons/Parallelograms: IMTS problem
Balancing Quadrilaterals Theorem
An application of centroids (centres of mass)
British Mathematics Olympiad Problem and its Dual
An application of perpendicular and angle bisectors of a triangle
Circumcentres (or Perpendicular Bisectors) of Circumscribed Quadrilateral Theorem
Clough's Theorem (a variation of Viviani) and some Generalizations (New!)
Concurrency and Euler line locus result
Cyclic Quadrilateral Incentre-Rectangle (Updated)
Cyclic Quadrilateral Rectangle Result
De Villiers points and hyperbola of a triangle
Du Plooy's generalization of the Theorem of Pythagoras
Fermat-Torricelli Point Generalizations
Feynman's Triangle and some generalizations
Generalizations of
Cross's (Vecten's) Theorem
Generalization of Euclid Book III, proposition 22 (cyclic quadrilateral theorem), and its dual
A generalization of
Neuberg's Theorem and the Simson line
2D Generalizations of
Viviani's Theorem
3D Generalizations of
Viviani's Theorem (New*)
2D Generalizations of a theorem of Sylvester
Sylvester's theorem for a tetrahedron (New!)
Generalizing the Nagel line to Circumscribed Polygons by Analogy & Constructive Defining
A generalization of a Parallelogram Theorem to Parallelo-hexagons, and Douglas' Theorem (New!*)
Haruki's Theorem (Three Overlapping Circles)
Hierarchical Quadrilateral Tree (*Updated!)
Interior Angle Sum of Polygons (incl. Crossed): a General Formula
Locus Problem (fixed chords in circle)
Napoleon's Theorem and some Generalizations & Variations
Nine-point (or Euler) centre & Maltitudes of Cyclic Quadrilateral
Nine-point conic and
Euler line generalization
Octagon
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
Quadrilateral Similar-Triangles Collinearity Theorem
Semi-regular Angle-gons and Side-gons
A generalization of rectangles and rhombi
Some Parallelo-hexagon Area Ratios
Spieker conic and Nagel line generalization
Van Aubel's Theorem and some Generalizations (Updated!*)
Some unproved conjectures (Updated)
Other Activities and Links
Cut-the-Knot - Interactive Mathematics Miscellany and Puzzles
Dynamically Explore Elliptic (Spherical) Geometry
Dynamically Explore Hyperbolic Geometry
Mathematics Archives - Topics in Mathematics - Geometry
The Importance of Geometric Literacy in Engineering & Design
Wolfram Alpha Online Computational Knowledge Engine
By Michael de Villiers at: prof md @ mweb .co.za (use without spaces in between)
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