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Topology & Graph Theory

 

Postcard Trick

How to climb through a postcard
Version 1   Version 2

Mobius Strip     

Y8 Möbius Strip – Powerpoint presentation giving an overview of the history and some tasks
YouTube Clip: Making and Cutting a Mobius Strip - Online
YouTube Clip: Motorbike on Mobius Highway - Online

References:  General - Click here

Tasks: Various strip making and cutting tasks – see the slides in the resources

Graph Theory

Introductory Activity

Sprouts Game (Conway) Online Version

Chinese Postman Problem and Other Network Tasks

Chinese Postman Problem - 21 Page Workbook - Sample Material from Pearson Publication (Decision 1 Ch 3 on right) - Link
Chinese Postman Problem and Other Network related Problems - Click here
Königsberg Bridge Problem (interactive tool) http://nrich.maths.org/2327
Traversable Problem 1     Problem 2     Problem 3     Problem 4
Traversability Workbook

Chinese Postman Problem - Standards Unit Task

Hamilton Circuits

Graph Theory – PowerPoint presentation giving an overview of the history
Dodecahedron net’ – for printing or displaying for Hamilton’s Game
Building an origami dodecahedron  Click here
Nets of a range of Solids in pdf form Click here

Extension Tasks

A Wide range of activities and problems relating to networks - Click here
Tree Graphs Proof Task:  http://nrich.maths.org/453
An article on Circuits in Graph or Network Theory  http://nrich.maths.org/2414

Tasks

  • Good starter – Conway’s Sprouts Game (see reference above)
  • Several Nrich tasks in References above
  • Königsberg Bridge problem and variations (see Powerpoint slides)
  • Solving Hamilton’s Game.  Either by building dodecahedra or using the 2D version.  Putting other solids in 2D form and seeing if you could make Hamiltonian Circuits.  How many different Hamiltonian Circuits can you find for the vertices of a cube?

Knights Tour

One of the earliest problem involving chess pieces is due to Guarini di Forli who in 1512 asked how two white and two black knights could be interchanged if they are placed at the corners of a 3 × 3 board (using normal knight's moves).

Knights Defeated  http://nrich.maths.org/473