This more or less quarterly Math e-Newsletter is sent out mainly in Southern Africa, but has information that may be of interest to others from different parts of the world. Please e-mail me at profmd@mweb.co.za if you'd like to be on the mailing list. (Also please say if you specifically want it sent to you as an e-mail or whether you prefer downloading/reading it from my homepage and just receiving a notification).


For the PREVIOUS two e-Newsletters go to:


and the one before that from:







(To unsubscribe from this e-Newsletter, please reply with the word 'remove' in the subject box of the email.)

(If you prefer to just receive a notice with a URL link to this newsletter online, please reply with the word 'internet read' in the subject box of the e-mail)




Dear Colleagues & friends


Happy Madiba day, 18 July! Hope you all spent a little time in service to others in recognition of the great man. This newsletter is my own modest contribution.




My homepage at http://mysite.mweb.co.za/residents/profmd/homepage4.html has been updated with the following new items:

1)      "Equi-angled cyclic and equilateral circumscribed polygons", PDF (2011)

2)      2010 "Reflections on Van Hiele" paper now available in Portuguese & Croatian

3)      mathematical/mathematics education quote

4)      mathematics/science cartoon.


My dynamic geometry sketches Link at http://math.kennesaw.edu/~mdevilli/JavaGSPLinks.htm has been updated with the following (new & revised) sketches:

             1) Fermat-Torricelli point generalizations (updated)

             2) Semi-regular angle-gons and side-gons (new)

             3) Some parallelo-hexagon areas (updated)

             4) Some unproved conjectures (updated)


and the Student Explorations section  with:

             1) Collinear conjecture (new)

             2) Gielis Super-shape formula (new)

             3) Napoleon variation problem (new)

             4) Paul Yiu's problem and a generalization (new)


Please REFRESH pages if they don't load properly the first time.




Tinkerplots 2, the innovative data handling software for younger learners (and quite adequate for Math Literacy in the South African Curriculum) not only has some great new features, but is now available as a download. Hence, it is available at a lower cost than before, e.g. currently at about R150 for a student license and about R370 for a Single User (and even lower for bulk orders). For more information and to download a free demo go to http://www.keypress.com/x5715.xml Please contact dynamiclearn@mweb.co.za for more information and to order.





The books below might be valuable additions to add to your university, school or personal libraries.


a) Exploring Number and Operations in Grades 3–5 with Sketchpad 5

b) Exploring Geometry and Measurement in Grades 3–5 with Sketchpad 5

c) Exploring Ratio, Proportion, and Probability in Grades 6–8 with Sketchpad 5

(For more info about the above 3 books or to order please contact dynamiclearn@mweb.co.za )


d) The Preparation of Teachers of Mathematics: Considerations and Challenges, download FREE PDF from http://www.nap.edu/catalog.php?record_id=10055


e) Statistics for People Who (Think they) Hate Statistics, 2nd Edition Excel 2007 Edition by Neil J Salkind from University of Kansas, SAGE publishers. 2010.


f) Sweet Reason: A field guide to modern logic. 1995, By Thomas Tymoczko, James M. Henle. (For more info or to order please contact dynamiclearn@mweb.co.za )


g) AMESA (Assoc. Math. Ed. of South Africa) Congress 2011 Proceedings are now available online at http://www.amesa.org.za/amesa2011/Proceedings.htm )





a) Useful free book for Math Competition & Olympiad Enthusiasts on "Elementary Number Theory" at http://www.scribd.com/doc/26455476/Math-Elementary-Number-Theory  


b) View a video clip or read the transcript of Conrad Wolfram's 2010 talk "Stop teaching calculating; start teaching math" at http://www.computerbasedmath.org/resources/reforming-math-curriculum-with-computers.html


c) Free Interactive Math Crossword Puzzles Online at http://www.mathgoodies.com/puzzles/crosswords/icircle1.html  


d) PROJECT MATHEMATICS by Tom Apostel at http://www.projectmathematics.com/ has several wonderful short video clips on topics for classroom use such as Similarity, Pythagoras, Pi, Sine and Cosine, History of Math, Polynomials, etc.


e) SAGE- Viable free open source alternative to Magma, Maple, Mathematica, and Matlab Sage is free open source math software that supports research and teaching in algebra, geometry, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, and exact linear algebra. Download for Win, Linux and Mac at http://www.sagemath.org/  


f) The Community for Undergraduate Learning in the Mathematical Sciences Newsletter is available online at www.math.auckland.ac.nz/CULMS/newsletters  


g) International lists of Mathematics Educations journals are available at http://mathedjournals.wikispaces.com/ and http://www.crme.soton.ac.uk/links/journals.html  


h) Download a number  of great articles for free from NCTM's three journals, "Teaching Children Mathematics", "Mathematics Teaching in the Middle School" and "Mathematics Teacher" at http://iem.nctm.org/display.php?M=1333613&C=e1230c7d7a5c78229b97f9bb794d9c51&S=955&L=36&N=963


i) Curriki is an online environment created to support the development and free distribution of world-class educational materials to anyone who  needs them. It is a great place to find and post classroom activities and course curriculum. Go to http://www.curriki.org/xwiki/bin/view/Main/WebHome


j) A list of articles and their abstracts from the Far East Journal of Mathematical Education, May 2011, is available at http://pphmj.com/journals/articles/761.htm





a) BRIDGES 2011 Conference: Connections between Mathematics, Music, Art, Architecture, Culture, Univ of Coimbra, Portugal, July 27-31, 2011. URL: http://bridgesmathart.org/bridges-2011/


b) 11th International Conference of The Mathematics Education into the 21st Century Project: 'Turning Dreams into Reality: Transformations and Paradigm Shifts in Mathematics Education', 10-16 September 2011, Rhodes University, Grahamstown, South Africa. Download the First Announcement and Call for Papers at: http://math.unipa.it/~grim/21project.htm E-mail, Alan Rogerson, Programme Chair at alan@rogerson.pol.pl


c) The ATCM and Chinese Association of Mathematics Education is launching the ATCM-China chapter (http://atcm.mathandtech.org/China ) and its first meeting is to be held at Xi'an, China during August 3-6, 2011.  The ATCM local chapter is meant to promote the exchanges of students-centered projects where technological tools are being implemented creatively in solving real-life problems.


d) The 16th Asian Technology Conference in Mathematics (ATCM 2011 http://atcm.mathandtech.org), which is going to be hosted by the Abantzzet Baysal University, Bolu, Turkey at the beautiful five star BŸyŸk Abant hotel, September 19-23 of 2011.


e) ICMI Study 21 entitled "Mathematics Education and Language diversity". The two co-chairs are Mamokgethi Setati, University of South Africa, and Maria Do Carmo Domite, Universidade de Sao Paulo, Brazil.  The Discussion Document may be found at the study website at http://www.icmi-21.com/index.php?page_id=140 and the Study Conference will be held on 16 - 20 September 2011 in Sao Paulo, Brazil.


f) The 2011 International Conference on School Mathematics Textbooks (ICSMT 2011) will be held during October 12-14, 2011 in Shanghai, China and hosted by East China Normal University (ECNU). The theme of ICSMT 2011 is to explore trends and characteristics of school mathematics textbooks around the world. Official website of ICSMT 2011 at: http://math.ecnu.edu.cn/academia/icsmt/mainpage.html


g) The ISTE International Conference on Mathematics, Science and Technology Education, Kruger Park, South Africa, 17-20 October 2011. Theme: "Towards Effective Teaching and Meaningful Learning in Mathematics, Science and Technology Education". URL: http://www.unisa.ac.za/iste-conference


h) CARN Conference 2011 (Collaborative Action Research Network) at http://ius.uni-klu.ac.at/misc/carn/

Bringing a different world into existence: Action research as a trigger for innovations, 4th - 6th November, 2011



i) 1st Computer-Based Math Education Summit. Organised by http://computerbasedmath.org in association with Wolfram Research at The Royal Institution, London, 10-11 November 2011. Visit:



j) Volcanic Delta 2011, the Eighth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics, will be held in Rotorua, NZ from 27th November to 2nd December 2011. To express your interest in the conference or find further information please visit www.delta2011.co.nz


k) Joint Mathematics Meeting of the South African Mathematical Society (SAMS) and the American Mathematical Society (AMS) at Nelson Mandela Metropolitan University, Port Elizabeth, 29 November – 3 December 2011 at http://www.nmmu.ac.za/sams-ams2011/ssprop.htm


l) The annual meeting of the Southern African Association for Research in Mathematics, Science & Technology Education (SAARMSTE), 16-19 January 2012, University of Malawi. Theme: "Mathematics, Science & Technology Education : A key to sustainable development". Go to: 1st Announcement


m) The didactics of mathematics: approaches and issues. International colloquium in honour of Michele Artigue (Professor UniversitŽ Paris Diderot, ex-president of ICMI), Paris 31 May – 2 June 2012. First Announcement with a description of Scientific Activities of Plenary Lectures, Panels, Workshops, Poster Session is available in French, English and Spanish at http://www.lar.univ-paris-diderot.fr/colloque/artigue


n) 12th International Congress on Mathematics Education, ICME-12, July 8-15, 2012, Seoul, Korea. The 2nd Announcement has been uploaded on the ICME-12 website (http://www.icme12.org ). Calls for papers for different topic groups have also been posted.





"Moreover, there is a growing consensus that human minds are fundamentally not very good at mathematics, and must be trained ... Given this fact, the computer can be seen as a perfect complement to humans - we can intuit but not reliably calculate or manipulate; computers are not yet very good at intuition, but are great at calculations and manipulations."        – Dave Baily in e-mail discussion with experimental mathematician Jonathan Borwein (during 2010)


"The art is not in the 'truth' but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity— to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs — you deny them mathematics itself. "    - Paul Lockhart in A Mathematician's Lament


"Often the key to answering a mathematical riddle is not to focus on fine details, but to look at broad details. Less can mean more. When it works, this trick is spectacular ..." - Ian Stewart in Taming the Infinite, Quercus Publishing, 2008, p. 236.





Martin's Law of Committees: "A committee is a group of people who, individually, can do nothing, but collectively can meet and decide that nothing can be done."


"Photons have mass? I didn't even know they were Catholic." - Woody Allen


A wife asks her husband, "Could you please go shopping for me and buy one carton of milk, and if they have eggs, get 6." A short time later the husband comes back with 6 cartons of milk. The wife asks him, "Why the hell did you buy 6 cartons of milk?" He replied, "They had eggs."





Solve the problem at: http://math.kennesaw.edu/~mdevilli/paul-yiu-theorem.html  

(Use a free, Java enabled web browser like Firefox or Safari or download & install Java for Internet Explorer).





I'm always grateful for any feedback I receive. Humberto Bortolossi from Brazil kindly wrote to point out that

the video clip mentioned in the previous e-newsletter "Fibonacci Numbers - The Fingerprint of God" at www.youtube.com/watch?v=e9MwNm0gXd8&feature=player_embedded has some popular misconceptions.


The following article by George Markowsky. "Misconceptions About The Golden Ratio". College Mathematics Journal, vol. 23, n. 1, pp. 2-19, 1992 at http://www.umcs.maine.edu/~markov/GoldenRatio.pdf discusses this and other misconceptions.


Humberto has also implemented a Java Applet (in Portuguese) where it's possible to experiment and to see that the shape of the nautilus shell is actually not well described by a golden spiral as often popularly claimed: http://www.uff.br/cdme/rza/rza-html/rza-spirals-br.html


Geometrically yours




"With the aid of dynamic geometry, my ability to discover new conjectures exceeds the available time to prove them and sometimes even my mathematical background and ability."


Prof Michael de Villiers

(Dynamic Math Learning)

8 Cameron Rd

3615 SARNIA (Pinetown)

South Africa

Tel: 027-(0)31-7083709 (h)

Fax: 0866726536 (w): Cell: 0836561396

Skype: michaeldevilliersksu

Homepage: http://mysite.mweb.co.za/residents/profmd/homepage.html

Dynamic Geometry Sketches: http://math.kennesaw.edu/~mdevilli/JavaGSPLinks.htm


Official SA Supplier of Key Curriculum Press at http://www.keypress.com


Visit the SA Mathematics Olympiad at http://www.samf.ac.za/Default2.aspx