This coursework will be to investigate to see how many squares would be needed to make any cross-shape build up in this way.

... Introduction The figure below shows a dark cross-shape that has been surrounded by white squares to create a bigger cross- shape: The bigger cross- shape consists of 25 small squares in total. The next cross- shape is always made by surrounding the previous cross-shape with small squares. This coursework will be to investigate to see how many squares would be needed to make any cross-shape build up in this way. Method First of all I'm going to work out a sequence which consists of a formula. Then I will draw a maximum of six cross-shapes adding on to each sequence, at the end I will produce one extra to testify the formula. After creating two tables to work out the first and second differences between the number of squares, I'll use those to find the values of a , b and c. Table 1 Shape Number 1 2 3 4 5 6 Number of Squares 1 5 13 25 41 61 1st Difference 4 8 12 16 20 24 2nd Difference 4 4 4 4 4 4 No of squares: 1 5 13 25

want to read more? →