Investigating Octagon Loops

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Investigating Octagon Loops

Introduction

I am primarily investigating Octagon Loops. In the investigation I plan to find out the relationship between the number of tiles used in the loop and the total number of free edges. Also, I will find the relationship between the number of tiles and the inside free edges and the number of tiles and the outside free edges.

What I Will Do

I plan to do this by first using octagon shapes and positioning them into loops, I will then put the results into a table so that it’s easier to analyse.

I’ll start by making a loop with the least amount of shapes and then build up the number of shapes to give me a good range of values. Then I will analyse the results and hopefully discover some rules.

What I did

First of all I moved the octagon shapes around to find out the minimum amount it would take to make a loop. After discovering this (4) I made a table like the one in my results section and made more loops to get a more varied range of results which would make it easier for me to make a rule. I then set about trying to find out rules for the relationship between the 4 main aspects of the loops (number of tiles, inside free edges, outside free edges and total free edges).

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The diagrams page shows what shapes I made with the octagons to gather my results.

Results

My results for the octagon loops are shown below: 


Diagrams

1st loop:                        2nd loop:                                        3rd loop:

Conclusion

When I looked at the results I discovered that there ...

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