Tautology much?

In AS Use of Maths recently we have been studying graphs and networks.

We started by looking at why they were useful by examining the tube network and comparing the real scale:

with the nicely arranged map

We did some practise about graphs, networks, eulerian, non-eulerian etc. etc.

Then we did something more interesting.

We grabbed the computer lab (and later some laptops back in my room), and the power of The Internet and I set them this task:

The results were pretty cool. We had some chaotic networks:

Some really nicely laid out ones:

[The highlighter on some networks is using Prim to find a minimum spanning tree for the network.]

And some HUGE matrices.

We got some interesting questions; like the problem of which Ashford I meant (Ashford (Surrey) compared to Ashford International) when finding the time between stations on National Rail (opposite sides of London – solved by looking at a map!); or the fact that actually, London isn’t one big station! It has lots of ways out. We went with whatever the ‘best’ route out was as one student noted:

The whole process took a little over two lessons (so about 2 and a half hours) including an extension piece using a simplified motorway network done by a few students:

I found the process worthwhile because the students could see where the complex networks shown here here come from. However, I think if I was to do it again, I would use less class time on the building of the network and more on what we can do with it – perhaps having the network algorithms ready and using this as a ‘complete the network before class, use it in class’.

I am also tempted to see what they can do with some maps and some highlighters. What roads would they choose as important on their network, what would they ignore? Can they cope with that much information? I may build that into a revision task later in the term.

Hopefully we can come back to this when we’ve done Travelling Salesperson and Djikstra’s to get some time around the network/between locations.

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