Sketchpad 3 Sketches

Michael de Villiers


1. To view and dynamically manipulate these Sketchpad 3 sketches, requires a copy of Sketchpad 3 or the demonstration copy of Sketchpad 3, which can be downloaded for free from:

2. The sketches have all been zipped in BinHex 4.0 and requires WinZip or similar programme to unzip. (A free unzipping programme Stuffit Expander can be downloaded from or use WinZip from - also available for free at many other sites). After unzipping, and Sketchpad or Sketchpad Demo has been installed, the sketches can be opened from the File menu in the programme or by double clicking.

For ordering a full version of Sketchpad in Southern Africa, consult:

Some of the sketches below can be used as investigations while others are intended as mere demonstrations. Note that the sketches have been prepared on a Macintosh Powerbook, hence the screen-size and outlay may differ a little for IBM compatibles and other Macintoshes. If you experience any downloading problems, please let me know.

A. SOME SAMPLE SKETCHES FROM MY BOOK "Rethinking Proof with Sketchpad 3", Key Curriculum Press, USA.

There are 17 Sketchpad sketches included in this sample (zipped to 92 K). They have been slightly adapted to be somewhat independent from the worksheets in the book, and a few have been extended a little. Four additional sketches not in the book have been included as extensions to the Parallelogram Squares activity (parmsq.gsp). Go to page 2 of my Homepage for more information on my book.

B. SOME SAMPLE SKETCHES FROM "Let's Talk Mathematics!", a Grade 9 Textbook by E. Makae, M. Nhlapo, M. de Villiers, H. Glover, M. Shembe & M. Masimela. (2001). (Available from Gariep Publishers, PO Box 26605, Hout Bay 7872. Tel: 021-6743321;

This book follows a problem-centered approach, in the sense, that problems are used to motivate and develop mathematical content from. There are 7 Sketchpad sketches related to Module 9: Water Supply which introduce the concepts perpendicular bisector, circumcircle, proof as a means of explanation, and maximisation and minimisation. These can be downloaded from:

There are 9 Sketchpad sketches related to Module 10: Best Positions & Shortest Routes which introduce the concepts angle bisector, incircle, proof as a means of explanation, conjecturing and generalisation. These can be downloaded from:


The Sketchpad sketches below refer to articles of mine, which can be downloaded from:

1. Generalizing Van Aubel using Duality

2. Place Kicking Locus in Rugby

3. Mathematical Treasure Hunting

4. Overlapping Circles

5. A Dual, and Generalizations, of a Sharp result

6. An Interesting Duality in Geometry

7. A Sketchpad discovery involving triangles and quadrilaterals

8. Conjecture and Proof with Sketchpad: A Case Study

9. A Generalization of an IMTS problem

(Sketches illustrating the area preservation property of shearing are included, and reference is made to its use in proving certain types of results by suitable specialisation. Related additional problems involving area ratios that might be suitable for a high school project are also included).

10. All parabola similar? Never!

(This sketch uses enlargements to illustrate the similarity of all parabola; i.e. that they all have exactly the same shape.)


The Sketchpad sketches below refer to other articles of mine, which have either been published or submitted/accepted for publication.

1. From nested Miquel triangles to Miquel distances and lines. (Article to appear in The Mathematical Gazette, Nov 2002, Website:

(Includes sketches of generalisations of Neuberg's theorem and the Simson-Wallace line, and related results).


1. Napoleon's theorem (named after the famous French Emperor) and several generalizations.