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Borders - Investigation into how many squares in total, grey and white inclusive, would be needed to make any cross-shape of this kind  

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Borders This investigation involves diamonds of grey squares, surrounded by a number of white ones, for example: And the initial investigation is into how many squares in total, grey and white inclusive, would be needed to make any cross-shape of this kind. To start with for this investigation, I drew out the first four possible build up of these cross-shapes and recorded the results in a table: Width: 1 Grey Square Width: 5 Grey Squares Width: 3 Grey Squares Width: 7 Grey Squares Width / Grey Total / Shaded Total / White Total / All 1 1 4 5 3 5 8 13 5 13 12 25 7 25 16 41 This table shows there is a relationship between each of the set of numbers produced. As the width increases by two each time, letting the width = n means that: N1 = 1, N2 = 3, N3 = 5 and N4 = 7 This relation between which term applies to a width can be shown as: Nno. = Width + 0.5 2 From hereon, each suffix will...

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