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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