Most of you are already busy or almost in final year-end examination mode. So hang in there, the summer holidays are just around the corner (for those of us in the Southern Hemisphere), and time to kick back & relax a bit, preferably at the beach!

1.

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

1) AMESA (2009) paper "From the Fermat points to the De Villiers points of a triangle"

2) SA Tydskrif vir Wet & Tegnologie (2010) "Vanaf die Fermat punte na die De Villiers punte van 'n driehoek"

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) Affine invariance of conics

2) British Mathematics Olympiad problem & its dual

3) De Villiers points & Hyperbola of a triangle (updated)

4) Pirate Treasure Hunt and some generalizations

5) Some unproved conjectures (updated)

and the Student Explorations sections with:

1) Bride's Chair Concurrency and locus (updated)

2) British Mathematics Olympiad Concurrency Problems

3) Cosine-Sine Angle Rule (updated)

4) Desargues' theorem

5) Links to 'SA Math Olympiad Questions and Problems' and 'Cut the Knot'

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

2.

**SOUTH AFRICAN MATHEMATICS OLYMPIAD**About 50000 learners participated in this year's competition. The dates for next year√ïs Olympiad are:

Closing date for entries: 4 Feb

1st round: 16 March

2nd round: 17 May

3rd round: 7 Sep

For more info about entering this prestige competition, past papers and answers, go to:

Download the free e-Book, "Geometry Unbound" at http://www.scribd.com/doc/18935265/Geometry-Unbound

It provides great training and reference for students to prepare for the Senior 3rd Round of SA Mathematics Olympiad (SAMO) and the International Mathematical Olympiad (IMO)

3.

**NEW BOOKS**Due to some past Math e-newsletters that people did not receive the following is reposted. The books below might be valuable additions to add to your university, school or personal libraries.

a)

**Explanation and Proof in Mathematics**Philosophical and Educational Perspectives by Hanna, Gila; Jahnke, Hans Niels; Pulte, Helmut (Eds.) 2010, VIII, 296 p., Hardcover, ISBN: 978-1-4419-0575-8 URL: http://www.springer.com/education/mathematics+education/book/978-1-4419-0575-8

b)

**Some Adventures in Euclidean Geometry**Christmas holiday season special: this book in bound form is discounted by 15%. For more info go tohttp://www.lulu.com/content/7622884

c) The book

**TINHLELO, Interweaving Art and Mathematics**: Colourful Basket Trays from the South of Mozambique exhibits and analyses coloured circular winnowing baskets collected since the end of the 1970s (Lulu, 2010, 132 pp. colour). Available from http://stores.lulu.com/pgerdes**4. OBITUARIES**

Benoit Mandelbrot, who developed the field of fractal geometry and applied it to physics, biology, finance and many other fields, died on 14 Oct 2010 in Cambridge, Mass. He was 85. For more info, see: http://www.nytimes.com/2010/10/17/us/17mandelbrot.html?_r=2

5.

**WEBSITES**a) Free Webinars on

*Discovering Algebra*,*Discovering Geometry*,*Sketchpad*and other Key Curriculum Press products are available at: www.keypress.com/pd Click on the webinar link to find a list of past webinars, each of which has a link for the recording of the webinar itself and a link to the materials.b) The November 2010 issue of the ATM's

*Mathematics Teaching*journal is available online at: http://www.atm.org.uk/journal/c) Go to http://mathonline.missouri.edu for free online testing and evaluation components in Algebra, Geometry, Trigonometry, Calculus readiness, and Calculus I and III with links to other sites with Online Drills and Quizzes.

d) Read the

*Math Forum Internet Weekly Newsletter*at http://mathforum.org/electronic.newsletter/mf.intnews15.43.html with latest news, links, etc.Past issues of the Newsletter are archived at http://mathforum.org/electronic.newsletter/

*The Math Forum*is also home to Ask Dr. Math, Problems of the Week, MathTools, Teacher2Teacher, the Internet Math Library, Math Discussion groups, and over 1,000,000 pages of mathematics information and discussions (links are at the bottom of the page).e) Be dazzled, perplexed and amazed by the

*Optical Illusions*at http://videogames.yahoo.com/events/brain-teasers/brain-teasers-and-optical-illusions/1400154f) Visit the Dynamic Geometry Gallery Geometrikon at http://www.math.uoc.gr/~pamfilos/eGallery/Gallery.html for a fascinating alphabetically arranged collection of Topics in Geometry and geometric examples from Geometry: Euclidean, Affine, and Projective.

g) Download one of the opening lectures at the Faulkes Institute for Geometry, University of Cambridge, 2002, 'Why study geometry?' at http://www.dpmms.cam.ac.uk/~piers/F-I-G_opening_ppr.pdf

h) MATH PLACE is a new on-line on-demand distributor of mathematics e-books and software, MATH PLACE, influenced by the thinking of George Polya (Mathematics is not a spectator sport) and Jean Piaget (Learning is provoked adaptation) Age range: 4-adult. Book prices: US$8.95-$9.95. Visit http://www.mathplace.net/

i) STATISTICAL DICTIONARIES in Afrikaans-English or English-Afrikaans can be downloaded as free PDF's fromhttp://www.sastat.org.za/diction.htm

j) A lovely TILING SLIDE SHOW with many examples is available at http://www.spsu.edu/math/tiling/index.html

k) Have a look at and download for free YACAS (Yet Another Computer Algebra System) - runs on many platforms. Go to the homepage at http://yacas.sourceforge.net/homepage.html and look at the Tutorial and My Yacas tabs for examples of its algebraic computational power.

l) Read the Notices of the American Mathematical Society for free online at http://www.ams.org/notices/201009/ Contains many mathematical articles of general interest, as well as some mathematics education articles.

m) Some nice lesson plans and teaching ideas from Grades 3-8 on Patterns, Tiling, Graphs, Bridges, etc. are available at the NCTM website at:

n) Some interactive animations and interesting facts of TETRAHEDRA at http://www.ac-noumea.nc/maths/polyhedr/tetra_.htm

o) For learners 5-19 visit Cambridge University's NRICH for a wide variety of problems, activities and investigations.http://nrich.maths.org/public/

p) Dancing with Geometry: A professional dancer and an orthopedic surgeon demonstrate the fundamental role geometry and technology play in keeping dancers performing at the highest level. Watch the movie:http://www.thefutureschannel.com/dockets/realworld/dancing/

q) The Simon Stevin Institute for Geometry www.geometryinstitute.org has some interesting information on the history of geometry and current research.

r) Read and discuss the article "Life After WolframAlpha: What You (and Your Students) Need to Know" about how this new computing technology can influence what we do in our math classrooms. Go to: http://mathdl.maa.org/mathDL/23/?pa=content&sa=viewDocument&nodeId=3365

6.

**CONFERENCES**a) Mathematical Art Exhibition will be held during the Joint Mathematics Meetings, New Orleans, January 6-9, 2011. More info:http://www.ams.org/meetings/national/jmm/2125_intro.html

b) SAARMSTE 2011 Conference. 18 – 21 January 2011. Mathematics, Science and Technology Education, North-West University, Mafikeng Campus. More info athttp://www.nwu.ac.za/export/sites/default/nwu/mc/documents/SAARMSTE_CONFERENCE_HOME_PAGE.pdf

c) The 7th Congress of CERME, the European Society for Research in Mathematics Education will be held in Rzesz¬óow, Poland, from 9-13 February 2011. Papers and poster proposals should use the CERME7 WORD template, and conform to the guidelines atwww.cerme7.univ.rzeszow.pl/?id=cerme-guidelines-for-authors

d) The Annual Conference of the Mathematical Association, 14-16 April 2011, Univ. of Loughborough at http://www.m-a.org.uk/jsp/index.jsp?lnk=100

e) ATM Conference 2011, 'Celebrating Gattegno', 18 - 21 Apr 2011, Univ. of Wolverhampton, Telford Campus athttp://www.atm.org.uk/events/conferences/

f) NCTM 2011 Annual Meeting & Exposition, Indianapolis, IN, April 13-16, 2011 - Geometry: Constructing and Transforming Perspectives – more info at http://www.nctm.org/conferences/content.aspx?id=25947

g) 17

^{th}National Congress of AMESA, Theme: "Mathematics in a globalised world", 27 June – 1 July 2011, Johannesburg, www.amesa.org.zah) BRIDGES 2011 Conference: Connections between Mathematics, Music, Art, Architecture, Culture, Univ of Coimbra, Portugal, July 27-31, 2011. URL: http://bridgesmathart.org/bridges-2011/

h) The 15th ICTMA Conference (International Conference on the Teaching of Mathematical Modeling and Applications) will be hosted by the Australian Catholic University, Melbourne, 14-19 J u l y 2 0 1 1. Visit: http://dlibrary.acu.edu.au/staffhome/jibrown/ictma.html

i) 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. For ALL further conference

j) 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.

7.

**QUOTES &****POINTS TO PONDER**"

*Formulation of a problem is often more essential than its solution which may be merely a matter of mathematical or experimental skill*." - Albert Einstein"

*The greatest scientific and philosophical breakthroughs by humanity's finest minds, from Darwin to Einstein, Socrates to Descartes, can usually be summed up in a few words. Only the mediocre dress up their 'genius' in long-winded lectures or heavy volumes. Extraneous complexity often conceals a lack of true substance*." - Author, Hector Macdonald"

*Anyone who conducts an argument by appealing to authority is not using his intelligence; he is just using his memory*." - Leonardo da Vinci8.

**HUMOUR IN MATH ; SCIENCE**Proof by insignificance: "Who really cares, anyway?"

Proof by mumbo-jumbo: " (B √Ø¬øΩ P ) , $ (C √Ø¬øΩ W )

Proof by profanity: (example omitted)

Proof by definition: "We define it to be true."

Proof by tautology: 'It's true because it's true."

9.

**PROBLEM PUZZLER**Challenge your FET learners with the two concurrency problems at: http://math.kennesaw.edu/~mdevilli/bmo-concurrency.html

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

Geometrically yours

Michael

---

On being asked what ideal qualities the trustees should seek in a director of The Institute for Advanced Mathematical Studies at Princeton, Albert Einstein replied: "

*You should look for a very quiet man who will not disturb people who are trying to think*."----

Prof Michael de Villiers

(Dynamic Math Learning)

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

Dynamic Mathematics Learning Online Store: http://www.FreeWebStore.org/DynamicMathematicsLearning

---

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

---

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

## No comments:

## Post a Comment