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Introduction

n Maths Coursework - N Lines Please note that this coursework depends heavily on the graphics available in the attached word document. RULES To find out the regions it is: Lines + lines + closed regions (n+n= closed regions) To find out crossovers it is: Lines ? (lines - 1) 2 n? (n-1) 2 To find out open regions it is: Lines ? 2 (n?2) To find out closed regions it is: Region - open regions 3 lines 1 2 3 4 5 6 7 7 regions 6 open regions 1 closed region 3 crossovers 5 lines 1 2 3 4 5 6 7 8 9 10 11 12 13 16 regions 10 open region 15 6 closed regions ...read more.

Middle

24 26 27 28 My prediction was correct Introduction We have been asked to draw a number of lines which cross over each other. e.g. 1 2 3 9 4 10 11 5 7 6 8 This is an example of 4 lines. Each line has to go over all the other lines. There are 6 cross over points. There are 11 regions, 1-8 are open regions and 9-11 are closed regions. We had to these trying lines of 3-6, and choose the one with the maximum cross over points. We have to put this on a table and come up with a rule to find out how many cross over points, how many regions and how many open and closed regions it has. ...read more.

Conclusion

e.g. 7 >4 11 >5 16 >6 22 >7 29 This also happens to the closed regions. The open regions go up by two every time. If you know the ones before you can work out what the next one will be. When you work out the crossovers, you multiply the number of lines by one less than the number of lines because each line crosses over all the other lines but it doesn't cross over its own line that is why you have to minus one. You have to divide it by 2 because each cross over has two lines going through it and it has been counted twice, if you don't divide it, it will have twice as much as it should have. Harpreet Sekhon 9.1 ...read more.

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