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Investigating Borders.

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8 “Borders”

Investigating Borders

The 2 squares, which are shown on the sheet, consist of added squares on each side making a boarder. One the first 2 squares there have been 6 other squares added, which has made the first border. I am going to investigate these borders using simple mathematical methods into researching how the borders work. From this I will hopefully be able to come to a conclusion about how the borders function and if it is possible to achieve connections and patterns between each added boarder.

    I will be adding one boarder at a time to each separate diagram, which will obviously both increase the area and perimeter of each shape. For this I will need the following equipment: A     variety of information, a pen, a pencil, a ruler and paper.

    In this investigation I will hope to find a formula, which could be used to find out the number
of squares needed to build the pattern at any sequential position.

...read more.


Pattern Number

Number Of Squares











1.     2.     3.     4.     5.

6     10    14    18    22

    4      4      4      4

Obviously from this we can learn that the amount between each pattern, which has been compared, adds up to a total of 4. Therefore this is an already clear pattern into investigating borders. The simplest name then given to this kind of pattern is linear so this is defiantly is a linear pattern. The number of squares in each pattern can be more closely analysed if I went into more depth with finding out the Mean, Median and Mode of the totals.

Mean = 46

Median = 41

Mode = N/A

From these we can explore more aspects of the original and find out if there is any connection between them. To go even in more detail in investigating borders it would be optional to explore borders on different shapes. I have done this and have this time used 3 template squares instead of 2 for the borders to occupy round. It proves to be a very different kind of pattern as it created a entirely different shape compared to the first, where only 2 squares were used. For this pattern I have only added 3 borders, which however will still gives us enough information. The results from this new pattern are shown below:

Pattern Number

Number Of Borders

Number Of Squares













...read more.


    However in the other two different patterns and especially the second one there was no connection whatsoever made between each diagram on that sheet. This was mainly because of the shape itself as there were 3 squares used for the template and I have found out that using even numbers not odd numbers for the squares in the template makes the investigation much easier and clearer. That is indeed a connection.

    Therefore I have found out a great deal because of the template. I believe that it can defiantly affect the entire pattern and it is much easier to find a connection between each diagram with the same template if it is of even numbers and not odd.

    The first pattern with the template with two squares was indeed the easiest one to find a connection between. As I shown in the diagram the total between each pattern number went up by 4 each time making it the simplest connection to be found out of the entire 3.

...read more.

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