The TOP5 Inpirations in Mathematics for December 2012 concern the common theme “Mathematics and Strategies”. Strategies to win an election, strategies to select a best option under certain constraints, strategies to group people together for an optimal output , or strategies to look for new drugs ... all these problems seem to be quite different real-world problems. Nevertheless, the thinking behind it is mathematical rather than anything else, and it is worth the effort to look out for common denominators. Here are a few selected suggestions.
The "top five" of March 2011 (communicted by the student's team of the Freie Universität Berlin)
1. http://www.youtube.com/watch?v=1X-gtr4pEBU From Wikipedia, the free encyclopedia: Langton's ant is a two-dimensional Turing machine with a very simple set of rules but complicated emergent behavior. It was invented by Chris Langton in 1986 and runs on a square lattice of black and white cells. The universality of Langton's ant was proven in 2000. The idea has been generalized in several different ways, such as turmites which add more colors and more states.
4. Metamath - http://www.metamath.org From their Webpage: Metamath is a tiny language that can express theorems in abstract mathematics, accompanied by proofs that can be verified by a computer program. This site has a collection of web pages generated from those proofs and lets you see mathematics developed in complete detail from first principles, with absolute rigor. Hopefully it will amuse you, amaze you, and possibly enlighten you in its own special way.
http://greenfootgallery.org/about This site introduces a nice and simple platform for building ‘scenarios’ for games – and for learning. Including learning mathematics? Can you apply this or other similar environments for teaching and for learning? What do you think? Can you set up a game where the goal for the player is to learn how to solve quadratic equations? Or even better: Can you set up a game where the goal for the player is to construct such a game for himself or herself - using only the simplest possible programming tools – such as this green foot? Not to mention the prospect of learning Singular Value Decomposition in this way – or any other one of your favorite theorems. Please let us know if you have any experiences, ideas, or further examples on how to set up game based learning environments for mathematics. (Communicated by Steen Markvorsen, Denmark.)
http://www.youtube.com/watch?v=_A-ZVCjfWf8 A couple of thought provoking quotes from this video, stated by two young students: “I will have 14 jobs before I am 38 years old. Most of those jobs do not exist today” – “Teach me to think, to create, to analyze, to evaluate, to apply.” Mathematics is clearly in demand – we must, we can, engage the students into mathematics and into the future. (Communicated by Klaus Fink, Denmark.)
http://www.imaginary2008.de/ Watch the imaginary lemon x^2 + z^2 = (1-y^3) y^3 on display – together with several other very well prepared mathematical sculptures. (Communicated by Martin Raussen, Denmark.)
http://vimeo.com/9953368 A wonderful video about Fibonacci numbers and the golden ratio. These topics are common in many popularization activities, but here Voronoi tessellations and Delaunay triangulations are also introduced. All the information “behind” the video is given (in English and Spanish) at the following address: http://www.etereaestudios.com/docs_html/nbyn_htm/intro.htm (Communicated by Maria Dedo, Italy.)