Hidden faces

Authors Avatar
Introduction

My investigation is to find out the number of hidden faces when x amount of cubes are placed on a table.

E.g.

1 cube

6 faces

5 faces visible

1 face hidden

Number

Visible faces

Hidden faces

5

2

8

4

3

1

7

4

4

0

5

7

3

6

20

6

7

23

29

8

26

22

9

25

29

0

28

32

It is clear from the table that there is a common pattern apparent in both the progression of visible faces and the progression of hidden faces. In fact both share the same pattern in that they both progress by 3 with each addition of a block.
Join now!


Finding the Nth term

From this pattern and from the table I make the formula for the progression of visible faces:

3n + 2

e.g. Number of cubes = 2

Number of visible faces = 2

2 x 3 = 6 + 2 = 8 =

3n + 2

I have proved that this formula works by calculating the 9th and 10th terms by using it.

From the pattern and from the table I make the formula for the progression of hidden faces:

3n - 2

e.g. Number ...

This is a preview of the whole essay