Date: Jan 27, 2013 5:52 AM
Author: Michael de Villiers
Subject: Math Homepage Updated

My 'Downloadable Articles' Homepage at has been updated with the following new items:
1) "An Example of the Explanatory and Discovery Functions of Proof". My ICME 12 Regular Lecture, published in Pythagoras, Dec 2012. Deals with a variation of Viviani's theorem and some generalizations.
2) "An Alternative Approach to Proof in Dynamic Geometry". Chapter from 1998 book Designing Learning Environments for developing Understanding of Geometry and Space edited by Lehrer and Chazan.
3) Jan 2013 Math e-Newsletter with info about new books, journals, conferences, websites, math quotes & humour.
4) mathematical/mathematics education quote
5) mathematics/science cartoon.

My 'Dynamic Geometry Sketches' site available at: has been updated with the following:
1) Clough's theorem - a variation of Viviani, and some generalizations. (New)
2) Cyclic Quadrilateral Incentre-Rectangle. (Updated)
3) Sylvester's Theorem for a Tetrahedron. (New)
4) A generalization of Varignon's theorem to 2n-gons (Updated to 3D)

and the 'Student Explorations' section with:
1) Anele's Method: Constructing an equilateral triangle (New)
2) Clough's Conjecture (New)
3) Finding the median and centroid of a triangle by experimentation (Updated)

Hope some here find some of the material useful.