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NRICH-TALK  October 2006

NRICH-TALK October 2006

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Subject:

NRICH October Newsletter

From:

Liz Pumfrey <[log in to unmask]>

Reply-To:

Liz Pumfrey <[log in to unmask]>

Date:

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

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text/plain

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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 
<http://nrich.maths.org/public/viewer.php?obj_id=5040&part=index> . 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 
<http://nrich.maths.org/public/viewer.php?obj_id=5039&part=index> . 
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 
<http://nrich.maths.org/public/viewer.php?obj_id=4976&part=index> and 
Escher Tessellations 
<http://nrich.maths.org/public/viewer.php?obj_id=4975&part=index> .

At a slightly higher level, three inter-related problems will pose some 
challenges which relate to transformations. Decoding Transformations 
<http://nrich.maths.org/public/viewer.php?obj_id=5331&part=index> 
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 
<http://nrich.maths.org/public/viewer.php?obj_id=5332&part=index> and 
Simplifying Transformations 
<http://nrich.maths.org/public/viewer.php?obj_id=5333&part=index> .

Another series of three problems features at Stage 4 this month, 
beginning with Points in Pairs 
<http://nrich.maths.org/public/viewer.php?obj_id=5472&part=index> . 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 <http://nrich.maths.org/public/viewer.php?obj_id=5473&part=index> 
<http://nrich.maths.org/public/viewer.php?obj_id=5473&part=index> and 
Mapping the Wandering Circle 
<http://nrich.maths.org/public/viewer.php?obj_id=5474&part=index> 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 
<http://nrich.maths.org/public/viewer.php?obj_id=5440&part=index> and 
Proof of Pick's Theorem 
<http://nrich.maths.org/public/viewer.php?obj_id=5441&part=index> . 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 
<http://nrich.maths.org/public/viewer.php?obj_id=5336&part=index> 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 
<http://nrich.maths.org/public/viewer.php?obj_id=5402&part=index> 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

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