Investigation in to How many tiles and borders is needed for each pattern

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GCSE Maths Coursework                                                                Tanbir Hussain 10R

Borders

Introduction: In this I am going to find out how many tiles and borders is needed for each pattern. I am also going to make predictions. I am gong to work out a formula for the tiles and borders needed for the nth pattern. I will also work out a formula for the total tiles for each pattern.  

Diagrams:

1.

4 Borders                                               5.

5 Tiles                                                    

9 Altogether                                                                                                                                                        

                                                                                               

 2.

12 Borders

13 Tiles

25 Altogether

24 Borders

61 Tiles

85 Altogether

3.

                                          6.

                               

16 Borders

25 Tiles

41 Altogether

4.

20 Borders

41 Tiles

61 Altogether

                                                        

                                        28 Borders

                                        85 Tiles

                                        113 Altogether

Join now!

32 Borders

113 Tiles

145 Altogether

Table Of Results:

Here are the table of results in my diagrams.

Prediction:

I predict that the next pattern will have 145 tiles and 36 borders.

Test Prediction:

I have tested the prediction by showing anther diagram of the 8th pattern. This pattern has 145 tiles, 36 borders and a total of 191 tiles together.

36 Borders

145 Ties

191 Altogether

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