don steward
mathematics teaching 10 ~ 16

Thursday, 5 April 2012


this exploration of the maximum number of sides a closed polygon can have on a square dotty grid has a straightforward context
generalisations can emerge
and created patterns can be justified


  • it is simple to experiment, and record (dotty paper is better than squared)
  • you can appreciate why longer diagonal lines don't seem to help
  • it is helpful to have a regular pattern, sometimes symmetrical, as the length increases
  • people can have different routine patterns and these can be compared
  • number patterns are created from a diagram so any justifications can relate to the pictures
  • odd and even 'n' numbers need to be considered - as is often the case 
  • you can question how confident people are that their pattern will continue to give the 'maxagon'
  • there are obvious depth (proof) and breadth (e.g. angle sums as well as other widths) extensions 

the 36 sided maxagon for a 6 by 6 grid

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