Sketchpad 3 Sketches

Michael de Villiers

http://mzone.mweb.co.za/residents/profmd/homepage.html

**IMPORTANT**:

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 www.aladdinsys.com/expander or use WinZip from http://www.winzip.com/ - 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:

http://mzone.mweb.co.za/residents/profmd/homepage3.html

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. **www.keypress.com

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.

http://mzone.mweb.co.za/residents/profmd/rethink.zip

**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; gariep@mweb.co.za).

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:

http://mzone.mweb.co.za/residents/profmd/talk.zip

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:

http://mzone.mweb.co.za/residents/profmd/talk2.zip

C. SKETCHES RELATED TO DOWNLOADABLE ARTICLES

The *Sketchpad* sketches below refer to articles of mine, which can be downloaded from: http://mzone.mweb.co.za/residents/profmd/homepage4.html

1. Generalizing Van Aubel using Duality

http://mzone.mweb.co.za/residents/profmd/aubel.zip

2. Place Kicking Locus in Rugby

http://mzone.mweb.co.za/residents/profmd/rugby.zip

3. Mathematical Treasure Hunting

http://mzone.mweb.co.za/residents/profmd/hunt.zip

4. Overlapping Circles

http://mzone.mweb.co.za/residents/profmd/overlap.zip

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

http://mzone.mweb.co.za/residents/profmd/sharp.zip

6. An Interesting Duality in Geometry

http://mzone.mweb.co.za/residents/profmd/amesa96.zip

7. A Sketchpad discovery involving triangles and quadrilaterals

http://mzone.mweb.co.za/residents/profmd/areas1.zip

8. Conjecture and Proof with Sketchpad: A Case Study

http://mzone.mweb.co.za/residents/profmd/conject.zip

9. A Generalization of an IMTS problem

http://mzone.mweb.co.za/residents/profmd/imts.zip

(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!

http://mzone.mweb.co.za/residents/profmd/simpara.zip

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

**D.** **SKETCHES RELATED TO OTHER ARTICLES**

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: http://www.m-a.org.uk).

http://mzone.mweb.co.za/residents/profmd/miquel.zip

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

E. OTHER SKETCHES

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