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February 2019 MATH e-NEWSLETTER

This more or less twice a year 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 (without spaces) 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).

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Dear Colleagues & Friends

Wishing everyone a belated Happy New Math year, filled with interesting and challenging new mathematical results. Please note I am sending this Math e-Newsletter from my g-mail account(s), which I don't check regularly.


My Downloadable Articles Homepage has been updated with the following new items:
1) A surprising 3D result involving a hexagon Mathematical Gazette, July 2018.
2) A cyclic Kepler quadrilateral and the Golden Ratio At Right Angles, March 2018.
3) mathematics/science cartoon and mathematics quote (at bottom of page)

My Dynamic Mathematics Sketches site has been updated with the following new sketch (as well as some updates to older sketches):
1) A cyclic Kepler Quadrilateral and the Golden Ratio

My Student Explorations site has been updated with the following new sketches (as well as some updates to older sketches):
1) Toshio Seimiya Hexagon Theorem

WebSketchpad: My latest Dynamic Geometry Sketches all use WebSketchpad, which are more easily accessible across a range of platforms from cellphones to tablets as well as laptops and PC's without the need to constantly update Java, or to change your security settings.


All parents, teachers and students please note that the closing date for the South African Mathematics Olympiad (SAMO) entries is 1 Feb 2019. Download the entry form here. Currently about 100 000 high school learners participate, but we'd like to see even more learners involved and stimulated.


1) Long time colleague and friend, Helena Wessels from Stellenbosch University, South Africa, passed away in February last year in a tragic accident. She specialized in the use of the TinkerPlots software in early statistics education as well as the teaching and learning of modeling. Read a short tribute to her at: "Tribute to an outstanding lecturer in mathematics".
2) Another long time colleague and friend, David Henderson from Cornell University, USA passed away tragically in an accident in December last year. He was a great geometer and an extremely gifted geometry educator as well, and I was privileged to attend many of his lectures and workshops, and have a signed copy of one of his books on spherical geometry. More information regarding David is given at "Sad loss to Cornell Math Dept".
3) Sir Michael Atiyah's passing on January 11, 2019. Atiyah was one of the most important mathematicians of the twentieth century - he has been described as a visionary, a genius, and even as the best mathematician since Isaac Newton. Read more at "Farewell to a Legend".


a) Exciting Web Sketchpad news is that the developers of Sketchpad have announced two new beta-test websites - a Tool Library site and a WebSketch Viewer site. The TOOL LIBRARY allows you to create websketches online without desktop Sketchpad and includes over 50 tools to include with your websketch. These websketches can then be downloaded and shared with your students. The WEBSKETCH VIEWER site allows students to open your websketches and conduct their mathematical explorations. With this approach, there is no need to host websketches on your own website. When students have completed their work, they simply download their websketch and share it with you. And finally, using the same WebSketch Viewer, you can upload the work of multiple students to review their websketches simultaneously on one webpage.
b) Interesting and valuable life lesson from Ramanujan, the famous Indian mathematician: "An Elbow Lesson".
c) A list of famous mathematicians and a short summary of some of their work at: Famous mathematicians.
d) Read this paper by George Maarkowsky at: Misconceptions about the Golden Ratio.
e) Read the informative "Mathematics News Snapshots" which aims to bridge the gap between developments in contemporary mathematics and high school mathematics.
f) This free 2001 book at: Future of Teaching and Learning of Algebra Proceedings is a very valuable resource.
g) The Springer book "The Legacy of Felix Klein" edited by Weigand, H.-G., McCallum, W., Menghini, M., Neubrand, M., Schubring, G., which came out of the thematic afternoon at ICME-13, is available as a free download.
h) View/play an excellent video clip on randomness in probability that would be of great value to use with students in the class at: Randomness is random.
i) Can you spot the error in these at: BOGUS PROOFS?


a) 10th International Mathematics Education and Society Conference (MES10), Jan 28 - Feb 2, 2019, Hyderabad, India. URL:

b) Eleventh Congress of the European Society for Research in Mathematics Education (CERME11), Utrecht, Netherlands, 6-10 February, 2019. URL:

c) The Fourth Interdisciplinary Scientific Conference Mathematical Transgressions (ISCMT), 13-16 March 2019, Cracow, Poland. Organized by Institute of Mathematics of the Pedagogical University of Cracow. URL:

d) PME & Yandex Russian Conference Technology and Psychology for Mathematics Education, March 18-21, 2019, Moscow. URL:

e) NCTM Annual Meeting and Exposition, April 3-6, 2019, "Empowering the mathematics community", San Diego, CA. URL:

f) Joint Annual Conference Mathematical Association (MA)/Association of Teachers of Mathematics (ATM), 15 - 18 April 2018, Chesford Grange, Warwick. URL:

g) Conference 'Mathematical Ability' with title “Digital Turn in Epistemology”, 15 - 17 April 2019, Utrecht University, the Netherlands. Website:

h) The Mathematics and its Connections with the Arts and Sciences (MACAS) symposium, McGill University, Montreal, June 18-21, 2019. Website:

i) The 2019 Annual Congress of AMESA will be held at the University of KwaZulu-Natal, Edgewood, South Africa, 25-29 June 2018 with the theme "Developing deep mathematical thinking through mathematics teaching". Website: 

j) The 43st PME Annual Conference will be in Pretoria, South Africa, from July 7-12, 2019. URL: 

k) Bridges Linz 2019 Conference on Mathematics, 16–20 July 2019, Art, Music, Architecture, Education, Culture. Johannes Kepler University & Arts Electronica Center, Linz, Austria. URL: 

l) The Conference on Applications of Computer Algebra ACA2019 (Montréal, Canada, July 16-20, 2019) URL: 

m) The 15th International Conference of the Mathematics Education for the Future Project, "Theory and Practice: An Interface or A Great Divide?", 4-9 August 2019, Maynooth University, Kildare, Ireland. Email: URL:

n) The 15th Bi-annual Conference on Elementary Mathematics Teaching, SEMT '19, August 18-22, 2019, Prague, Theme: 'Opportunities in Learning and Teaching Elementary Mathematics'. Website address:

o) The 11th International Conference on Mathematical Creativity and Giftedness, August 22-24, 2019 in Hamburg, Universitat Hamburg. URL:

p) The Summer School Mathematics Education at Utrecht University., August 19-30, 2019. URL:

q) Sixth International Conference on the History of Mathematics Education (ICHME-6) CIRM, Marseille (France), September 16-20, 2019. Website:

r) Third International Conference on Mathematics Textbook Research and Development (ICMT3), 16-19 September 2019, Paderborn, Germany. URL:

s) The 14th International Congress on Mathematical Education (ICME-14), Shanghai, China, July 12-19, 2020. URL:


The Cheshire Cat in Lewis Carroll's "Alice in Wonderland": "Imagination is the only weapon in the war against reality".

"The myth of totally rigorous, totally formalized mathematics is indeed a myth. Mathematics in real life is a form of social interaction where 'proof' is a complex of the formal and the informal, of calculations and casual comments, of convincing argument and appeals to the imagination. The competent professional knows what are the crucial points of his argument - the points where his audience should focus their skepticism. Those are the points where he will take care to supply sufficient detail. The rest of the proof will be abbreviated. This is not a matter of the author's laziness. On the contrary, to make a proof too detailed would be more damaging to its readability than to make it brief. Complete mathematical proof does not mean reduction to a computer program. Complete proof simply means proof in sufficient detail to convince the intended audience - a group of professionals with training and mode of thought comparable to that of the author." - Davis & Hersh (1986:73) in The Mathematical Experience.


Law of Gravity - Any tool, nut, bolt, screw, when dropped, will roll to the least accessible corner.

An engineer thinks that his equations are an approximation to reality. A physicist thinks reality is an approximation to his equations. A mathematician doesn't care.

Teacher: Now suppose the number of sheep is x...
Student: Yes sir, but what happens if the number of sheep is not x?

"This is a one line proof...if we start sufficiently far to the left."

"The problems for the exam will be similar to the discussed in the class. Of course, the numbers will be different. But not all of them. Pi will still be 3.14159... "


Mathematically yours


Prof Dr Michael de Villiers
(Dynamic Mathematics Learning)
South Africa
Dynamic Geometry Sketches:
Dynamic Mathematics Learning Store:


Visit the SA Mathematics Olympiad at