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Maths Coursework Firstly I drew out a series of patterns so I could study the many different aspects of them. Here is what I found: Black Squares White Squares Diameter Total Squares 1 4 3 5 5 8 5 13 13 12 7 25 25 16 9 41 41 20 11 61 61 24 13 85 85 28 15 113 113 32 17 145 * The number of Black Squares increases each time by the number of white squares. * The number of White squares increases in multiples of four every time * The total squares equals the sum of Black Squares and White Squares * The diameter increases by two every time Because this sequence of patterns follows a sequence and increases by some set amount each time I can assign a Pattern Number or 'N' as an integer to increase by one every pattern. Here is another table but showing N: N Black Squares White Squares Diameter Total Squares 1 1 4 3 5 2 5 8 5 13 3 13 12 7 25 4 25 16 9 41 5 41 20 11 61 6 61 24 13 85 7 85 28 15 113 8 113 32 17 145 Now I can use n as a basis for building equations used to define the different aspects such as the ones in the table above. Here is the equation for the number of white squares: 4 x N...

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