Coursework.Info - Inspiration in an Instant

On the left is an image preview of every page of this document, and below are the first 150 words with formatting removed:

"BORDERS" INVESTIGATION Introduction The starting point for this investigation is the following sequence of cross shapes: 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. The aim of this investigation is to derive algebraic formulae from the sequence, each expressing one property in terms of another (e.g. defining the area as the diameter squared). These formulae can then be examined and, hopefully, proven, using a wide variety of mathematical tools. The next stage will then be to apply this same process to the three-dimensional counterpart of this sequence of shapes. This sequence would begin with a single white cube, which would then be surrounded on all...

To see the full version of this document, and 145,348 others