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Introduction

Julian Coxell        Lines, Crossovers And Regions        15/11/07

## Aim

During this investigation I intend to find the rules and patterns linking lines crossovers and regions. To do this I will produce a series of tables and graphs and look closely to find visible patterns between different parts of my investigation.

## Prediction

I predict that during my investigation I will find patterns that will lead me to be able to make rules about the relationships between lines, cross overs and regions.

## Plan

During my investigation I will investigate the sets of lines with the most amount of cross overs from 1 to 6 lines. I will investigate the amount of cross overs the number of enclosed regions, the number of open regions, difference between the number of cross overs and the amount of closed regions, difference between the number of

Middle

0

+1

+2

+3

+4

+5

Difference Between X/O

2

3

3

2

0

3

As you can see from this table you can already see patterns emerging on the below table I have labelled the patterns.

 1 Line 2 Lines 3 Lines 4 Lines 5 Lines 6 Lines Crossovers 0 1 3 6 10 15 Closed Regions 0 0 1 3 6 10 Open Regions 2 4 6 8 10 12 Difference Between O/C +2 +4 +5 +5 +4 +2 Difference Between X/C 0 +1 +2 +3 +4 +5

Conclusion

I use my formulae to produce this table bellow.

 7 Crossovers 21 Closed Regions 15 Open Regions 14

Conclusion

During my investigation I have found enough formulas to find data for X amount of lines it was a massive success the process I used to find the formula clearly worked and I found it quite easy. If I did this investigation again I would investigate with lines up to 10 for a more in-depth investigation and I would have produced more graphs and tables other than that I think that my investigation was a success.

During my investigation I learnt that graphs and tables are the ultimate way to find otherwise hidden patterns, which with a bit of work will lead you to formulas.

I have also learnt that you should carry out a limited investigation in depth rather than carry out a complicated investigation baisicly.

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