Shapes Investigation :: Papers

Shapes investigating doing an investigation to look at shapes made up of other shapes (starting with triangles, accordingly going on squ ares and hexagons. I go away try to find the relationship between the perimeter (in cm), dots enclosed and the amount of shapes (i.e. triangles etc.) utilise 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 manageable 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 previse 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 call back 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 point little (i.e. those arranged in the same way besides 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 reservation tables of different numbers of that shape, make a graph containing all the tables and thence 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.