Borders Coursework

Wednesday 8th June 2005                Borders Coursework

Borders Coursework

Introduction:

The 2D diagrams below show dark cross- shapes that have been surrounded by white squares to make bigger cross- shapes:

The next cross- shape is always made by surrounding the previous cross- shape with small squares.

Part 1

Investigate to see how many squares would be needed to make any 2D cross- shape built up in this way.

Part 2

Extend your investigation to 3 dimensions.

I will be continuing the above 2D sequence until the 9th term, and then forming equations to find out how to calculate the total squares and extra squares used to make any cross shape.  When these 2 formulas for the 2D shapes are found, I will investigate further onto 3D cross- shapes, and find the formula for the total cubes used to form that shape. The 3D drawings will be similar to the 2D drawings but all six faces of the cube will be surrounded rather than just 4 sides as in a square.

When finding my equations, I will be referring to the terms in the sequence as ‘n’, for example n could be equal to 1 or 2, and so on. These values will then be substituted in the equation with ‘n’ to check that the formulas are working. These are the ‘values of n’. All formulas that I will be calculating will be tested to make sure that they are correct.

Part 1: 2D Shapes:

1st term:                                         2nd term:

3rd term:                                         4th term:

5th term:                                         6th term:

7th term:                                         8th term:

9th term:

Part 1: 2D Shapes:

Table to show the amount of squares in total and the amount of extra squares used for the 2D drawing:

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