Wednesday, 22 May 2013

Mazes (Part 3)

See Part 2 for basic maze instructions. When we did this as a class we spent a lot of time exploring the possibilities which result from the fact that, when you join two points together, as long as your line doesn't cross another line or touch it, your maze is topologically the same.  When you join those first two points you can take your line on as many diversions as you like as long as it doesn't cross or touch.  Like this:







When you enter the maze you can reach every part of it.  As long as your line doesn't touch the edge of the page you can reach every part of the page.



Mazes (Part 2)

Here's how to draw a maze.  Sorry it's taken so long!  When you have drawn the first two pictures in the sequence with the cross and the dots and the four right-angled pieces, pick two adjacent ends or dots and join them together with a bridge.  Then take the next pair of points to the right and left and join them with a bridge.  Continue as shown, but don't cross any lines, or let them touch.







Done!

Thursday, 10 January 2013

Mazes (Part 1)

As I remember it, a child came into school with one of those colouring books that have dot-to-dots and the occasional maze that you're meant to find the way through with your pencil.  We started talking about how hard it would be to design your own maze.  It ought to be easy, we thought.  Definitely easier than making a birds nest.  Though these were older children, and not the same ones.

The children quickly figured out that you needed one pathway through the maze to the objective, and lots of dead ends to fool the victim.  But it was hard to make the path through the maze un-obvious, and the dead ends were boring.  Plus, if you went wrong when you were drawing it was hard to put it right without making a mess.  So then we went out into the courtyard with every plastic and wooden brick we could borrow from other classes and made mazes using those.  They were more like winding pathways than mazes, but it was definitely fun to do and we spent a couple of afternoons outside in the sunshine doing it.

We were all thinking that a maze was something to get lost in, a place where it was hard to find your way out.  Then I came across a simple set of instructions for drawing the classical maze in the picture above.  The maze has a single pathway that goes all the way to the centre and the pathway occupies the whole of the space.  There are no dead ends and you can't get lost, but it's definitely a maze. 

So, I wondered how easy it would be to teach the children to draw one of these.  They were 6, 7 and 8 years old, so I figured the older ones could help the younger ones.  It took a couple of days, but eventually we could all do it.  It felt just like being able to do magic.  It's very like when I used to make rings and discovered that most people were completely baffled by the mystery of joining two pieces of gold together invisibly.  People would look at the mazes the children had drawn and not have a clue how they'd done it.

That was just the beginning.

(Instructions for drawing the maze coming up next time!).