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Introduction A particular number tiles are laid down vertically. Border tiles are laid around these main tiles. Each layer of border tiles creates one border. This is a typical diagram showing how border tiles, original tiles and borders are arranged. In this diagram the red tile indicate the tiles first laid down (original tiles: OT). The blue tiles show the border tiles (BT). Each shade of blue represents each border (B) - Border 1 is in dark blue while border 2 is filled in with a lighter shade of blue. In this coursework, I would investigate to find out the number of border tiles required to complete a particular border. In order to find this I would have to carry out investigations, which would lead me into finding an appropriate formulae, which could be used to calculate the number of border tiles in a specific border and finally the number of border tiles laid when in a particular border number. Investigation 1 First, I will look at the relationship between the number of border tiles and the border number when it is increased. The number of original tiles laid down on this occasion is five. 5 12 16 20 24 5 10 15 20 25 30 This diagram clearly shows a pattern between the increase of border tiles per number of border. After the first border, which increases by seven compared to the original four tiles, the number of border tiles per each border after this increases by four: +1 +1 +1 +1 Therefore: 1BT = 12 2BT = 1BT + 4 = 16 3BT = 2BT + 4 = 20 4BT = 3BT + 4 = 24 5BT = 4BT + 4 = 28 6BT = 5BT + 4 = 32 7BT = 6BT + 4 = 36 8BT = 7BT + 4 = 40 So on
When looking at this pattern, a formulae that could identify the number of border tiles for each border when there is five original tiles could be identified: BT = OT( B 1 ) + 12 B = BT -12 + 1 OT Using this formula, the number of border tiles in the hundredth border (when there were 4 original tiles) could be calculated : BT = 4( B - 1 ) + 12 BT = 4( 100 1 ) + 12 BT = 396 + 12 BT = 408 Investigation 2 Now that I have calculated the number of border tiles in the hundredth border when there are four original tiles, I would now investigate and find out what would happen to the number of border tiles when the number of original tiles is changed.
Approximate Word count = 1480
Approximate Pages = 5.9
(250 words per page double spaced)
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