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## NRICH-TALK@JISCMAIL.AC.UK

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Mon, 2 Oct 2006 10:02:32 +0100

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 ```Dear all, The October NRICH website is now live at http://nrich.maths.org . The fresh problems and articles this month are all on the theme of Geometry and Algebra, and you will find activities to challenge and excite you, no matter how long you've been studying mathematics. To start off, you could investigate Tubular Path . Can you direct the blue point through the tube by moving the yellow one? It looks easier than perhaps it is! Once you've cracked that, have a look at A Maze of Directions . Again, you need to work out how the trace of the yellow spot is related to that of the blue spot. Can you use what you find out to move the yellow spot from one star to the other? There are also two problems centring on tessellation this month which are well worth tackling: Tessellating Capitals and Escher Tessellations . At a slightly higher level, three inter-related problems will pose some challenges which relate to transformations. Decoding Transformations invites you to describe transformations represented by different letters and then asks you to simplify a series of transformations. This idea of simplification is taken up in the follow-up problems Combining Transformations and Simplifying Transformations . Another series of three problems features at Stage 4 this month, beginning with Points in Pairs . Can you use the relationship between the two points and the radius of the circle to calculate the distance shown? Both The Line and Its Strange Pair and Mapping the Wandering Circle delve more deeply into this same relationship, taking the ideas from static to dynamic. Geometry and algebra are intertwined in all three problems at the highest level. Pick's Theorem is the theme for both Pick's Quadratics and Proof of Pick's Theorem . The former asks you to verify the generalised form of the Theorem for a particular rectangle and the latter leads up to a proof that Pick's Theorem holds for any planar polygon. If this isn't enough, there are also two articles to whet your appetite. Grouping Transformations links to the Stage 3 problems and takes the mathematics in them a little further. Alternatively, something completely different: Have you ever wondered how many ways there are to shuffle a pack of cards? Why not take a sensible guess? Now read Card Shuffle and you might well be surprised. Finally, don't forget that we would still welcome your contributions towards our10th anniversary website in January. If you have a favourite NRICH problem or game then please let us know what it is and your reasons for choosing it. We hope to feature a selection of these in the January site. In addition, we would welcome your suggestions for new problems which we could add to the month for others to try. With best wishes from The NRICH Team. -- Liz Pumfrey NRICH Primary Coordinator University of Cambridge Centre for Mathematical Sciences Wilberforce Road Cambridge CB3 0WA 01223 764246 www.nrich.maths.org _______________________________________________ To post to the list send an email to [log in to unmask] To unsubscribe send an email to [log in to unmask] with the message body UNSUBSCRIBE NRICH-TALK or unsubscribe via the web at http://www.jiscmail.ac.uk/cgi-bin/wa.exe?REPORT&Z=3```