Dynamic Geometry Sketches
(Interactive dynamic geometry sketches with JavaSketchpad, 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.
Michael de Villiers
Dept of Mathematics & Computer Science Education
University of KwaZulu-Natal, South Africa
(Last Update: 23 April 2012)
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 18 May 2012 Downloadable PDF papers/books on Geometry, Mathematics & Mathematics Education for sale
Explorations for
Students
Affine Equivalence of Cubic Polynomials
Area Ratios of Octagons/Parallelograms: IMTS problem
Balancing Quadrilaterals Theorem
British Mathematics Olympiad Problem and its Dual
Circumscribed Quadrilateral Perpendicular-Bisectors Theorem
Concurrency and Euler line locus result
Cyclic Quadrilateral Incentre-Rectangle
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 (*New)
A generalization of
Neuberg's Theorem and the Simson line
Generalizations of
Viviani's Theorem (New)
Generalizing the Nagel line to Circumscribed Polygons by Analogy & Constructive Defining
Haruki's Theorem (Three Overlapping Circles)
Hierarchical Quadrilateral Tree
Interior Angle Sum of Polygons: a General Formula
Locus Problem (fixed chords in circle)
Napoleon's Theorem and some Generalizations & Variations
Nickalls' Conic Theorem (*New)
Nine-point (or Euler) centre & Maltitudes of Cyclic Quadrilateral
Nine-point conic and
Euler line generalization
Octagon
Centroids forming Parallelo-octagon & Generalization
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 (Updated*)
A generalization of rectangles and rhombi
Some Parallelo-hexagon Area Ratios
Spieker conic and Nagel line generalization
Van Aubel's Theorem and some Generalizations
Other Activities and Links
Cut-the-Knot - Interactive Mathematics Miscellany and Puzzles
Linear Equations Solver
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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