Investigating the Relationship of the Dots Inside a Shape of Different Sizes

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Investigating the Relationship of the Dots Inside a Shape of Different Sizes

AIM: I have been set a task for my coursework to find out the

relationship of the dots inside a shape of different sizes.

PLAN:I have planned to use a specific quadrilateral shape for my

investigation in which lines will be 45o (diagonal), one dot to the

other; touching each others ends and being closed from all sides. I

will be using the following technique for my investigation. First of

all I will commence with the shape-size being 1 cm2 increasing it

every step by another 1 cm2. At the same time I will be counting the

dots inside that particular shape. I will be using this method until I

find a pattern; thereafter I will generate a suitable formula from

that pattern.

METHOD: I will be using more or less 5 diagrams and possibly the 6th

one for my prediction.

[IMAGE]DIAGRAM 1

AREA

DOTS

PERIMETER

1 cm2

1

4

[IMAGE]

DIAGRAM 2

[IMAGE]

AREA

DOTS

PERIMETER

2 cm2

5

8

DIAGRAM 3

[IMAGE]

AREA

DOTS

PERIMETER

3 cm2

13

12

It seems that a pattern is forming for both. Firstly for the dots and

area you add 4, there after you double the number, secondly for the

perimeter you just add four at each level.

DIAGRAM 4

[IMAGE]

AREA

DOTS

PERIMETER

4 cm2

25

16

DIAGRAM 5

[IMAGE]

AREA

DOTS

PERIMETER

5 cm2

41

20

I have realised that the comment I made before for the dots and area

is incorrect. What I said was that after starting with four the number

will double itself on each stage i.e. 4, 8, 16… etc.

PREDICTION: I think that the shape with the area of 6 cm2 will have 61

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