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GCSE Coursework Borders Here are the first four examples of the shapes in this sequence: The sequence begins with a single white square, which is then surrounded by black squares to form the second shape. Each new cross is then formed by completely surrounding the previous cross with a border of black squares. In each new cross, the previous cross can be seen as the area of white squares in the centre. In this investigation I will try to get algebraic formulas from the sequence, each expressing one property in terms of another (e.g. defining the area as the diameter squared). These formulas can then be checked and, proven, using a variety of maths skills. Defining N The variable that I will be using to refer to terms in this investigation will be n. As there could be confusion over this matter I thought that it is important to state that the first term in the...

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