Hidden faces investigation.

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Stuart Pelling                                                                GCSE Mathematics coursework

Hidden Faces Investigation

Introduction

I am going to investigate the number of hidden faces when cubes are joined together. The aim of this task is to find a formula, which is common with every cube and hidden face.

I will be using multi-link for this investigation. First I will see how many hidden faces are on 1 cube and carry on until I reach up to 6 cubes.

One cube has one hidden face and it is the one that is on the table. When there is more than one cube there will also be 2 or more hidden faces where they join together.                      

                                                             

                                                        Hidden Face is here underneath         the cube, the face that is on the table.

Prediction

I predict that with 1 cube there will be 1 hidden face and this face is faced down to the table, but because I have to add cubes to the row each time the number of hidden faces will increase, so will the showing faces and the faces altogether. I think that every time a cube is added to the row the amount of hidden faces will rise by 3 every time.

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Results

The nth term of the sequence is 3n – 2 = Hidden face. I have done 7 cubes, now with this formula I can find out how many hidden faces there are on 8 cubes.

                                                  3n – 2 = Hidden faces

                             

                                ...

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