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. I will add 4 more borders to the beginning pattern in separate diagrams.

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At first glance I have achieved the following information by adding each border and extending upon it.

It is clear from this first glance that the number of squares increases dramatically. The number of squares on each pattern increases like this.

Pattern 1 – 2 = 10

Pattern 2 - 3 = 14

Pattern 3 - 4 = 18

Pattern 4 - 5 = 22

Pattern 5 - 6 = 26

Obviously from this we can learn that the amount between each pattern, which has been compared, adds up to a total of 4. Therefore ...

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