Shapes Investigation

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Shapes Investigation

I am doing an investigation to look at shapes made up of other shapes

(starting with triangles, then going on squares and hexagons. I will

try to find the relationship between the perimeter (in cm), dots

enclosed and the amount of shapes (i.e. triangles etc.) used to make a

shape.

From this, I will try to find a formula linking P (perimeter), D (dots

enclosed) and T (number of triangles used to make a shape). Later on

in this investigation T will be substituted for Q (squares) and H

(hexagons) used to make a shape. Other letters used in my formulas and

equations are X (T, Q or H), and Y (the number of sides a shape has).

I have decided not to use S for squares, as it is possible it could be

mistaken for 5, when put into a formula. After this, I will try to

find a formula that links the number of shapes, P and D that will work

with any tessellating shape - my 'universal' formula. I anticipate

that for this to work I will have to include that number of sides of

the shapes I use in my formula.

Method

I will first draw out all possible shapes using, for example, 16

triangles, avoiding drawing those shapes with the same properties of

T, P and D, as this is pointless (i.e. those arranged in the same way

but say, on their side. I will attach these drawings to the front of

each section. From this, I will make a list of all possible

combinations of P, D and T (or later Q and H). Then I will continue

making tables of different numbers of that shape, make a graph

containing all the tables and then try to devise a working formula.

As I progress, I will note down any obvious or less obvious things

that I see, and any working formulas found will go on my 'Formulas'

page. To save time, perimeter, dots enclosed, triangles etc. are

written as their formulaic counterparts.

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