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7 Bridges of Konigsberg |
Enrichment PowerPoint Presentation
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This classic problem on the 7 bridges of Konigsberg is a first class presentation that everyone will enjoy and it is given the full treatment. It starts by asking students to draw a selection of (network) doodles and find out which ones can and cannot be drawn without removing pencil from paper. There follows a few slides of interest on Lewis Carroll (Professor Charles Dodgson: a mathematician) and his favourite doodle. Some illustrations from his books are included together with “The Jabberwocky” (Placed at the end of the show for the more eccentric characters that you might teach). A class competition to see who can memorise it usually goes down well.
The class are told that there is strong link between their doodles and the problem of the 7 Bridges. Euler is introduced and his approach and abstraction of the problem is explained. One animated slide shows someone trying to cross all the bridges. The students, then see of they can find a path using a worksheet provided. The idea of a network is clearly explained as is the importance of odd and even vertices. Each student/group is then given a worksheet with a wide selection of networks on. They have to note the number of odd and even vertices for each network and decide whether it is traceable. Hopefully someone will discover the rule (as Euler did) that a network is only traceable when it has exactly 2 odd vertices or all even vertices. Your students should then understand why a traceable path is not possible in Konigsberg. An 8th bridge is discussed and is shown to be traceable (animated). All should by now, be able to tell whether any given network is traceable, no matter how complex. A complicated one is automatically drawn as you click your mouse. Slide 19 provides the WHY without having to look at a formal proof. Again this is fully animated. A slide follows on how it led to a new branch of mathematics (topology) together with some modern day applications. Enjoyable mathematics. Within the reach of all ages.
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£5.00
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