Shapes Investigation :: Papers

Shapes Investigation doing an probe to go to at shapes made up of other shapes (starting with triangles, then going on squares and hexagons. I each(prenominal)ow try to cause the relationship between the mete (in cm), dots enclosed and the amount of shapes (i.e. triangles etc.) used to light upon a shape. From this, I pass on 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 pertinacious not to use S for squares, as it is possible it could be irrational 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 wo rk 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 gaunt (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 afterwards Q and H). Then I will continue making tables of different amount of that shape, make a graph containing all the tables and then try to design a working formula. As I progress, I will utterance down any obvious or less obvious things that I see, and any working formulas found will go on my Formulas page. To scavenge time, perimeter, dots enclosed, triangles etc. are written as their formulaic counterparts.