Mathematical Ideas that Shaped the World. Graphs and Networks. Plan for this class . What was the famous K önigsberg bridge problem? What is a graph? Why was the 4-colour theorem controversial? How are soap bubbles and slime mould good at town planning?
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Graphs and Networks
“now I have fewer distractions”
Look at your handout to learn about these characters.
Can you make them all happy?
Is the bridge problem possible now?
Can any map be coloured with 4 colours so that no two adjacent regions have the same colour?
“A good mathematical proof is like a poem. This is a telephone directory!”
Tokyo train network
Caveat: using today’s fastest supercomputer, solving the 33-city problem using this method would take about 100 trillion years!
The record set with this kind of exact method is 85,900 cities, which took over 126 CPU yearsto computein 2006.
Caveat: these solutions may not always be the best possible.