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.
I will the do the same for a 4x4x4 cube, 5x5x5 cube and finally a
BUT if we want the same perimeter (which we do) we have to take away a
I predict that in a two by two square the difference will always be 10
This shows that there is a difference of 2cm between A and B, and B
letters in it. I will also try and find a formula to find the total
two lines of different lengths, while the lines are the same size. This illustrates the fact
had ever come across, being "a / a / b / b / c / c / d / d / e / e / f
every number. Then move your ruler down to the bottom. No, put it across the bottom. Now
A cube a total of 6 sides, when it is places on a surface only 5 of
If I am to use a square of side length 10cm, then I can calculate the
sides on a cube and this gave rise to idea for a project. The final result
- Suface Area: if you are to change the surface area it is going to
Shapes are two- dimensional surfaces such as circles or squares, and forms are three-dimensional shapes like spheres or cubes. A concave form has a pushed-in surface like the inside of a bowl and a convex form has a raised surface like the outside of a bowl. When you are looking at shapes and forms, the shape that you see first is called a figure or positive shape and the area around it is called the ground or the negative shape. The natural curves in different objects, such as trees or clouds are called organic shapes. Geometric shapes and forms are precise and regular such as cubes, pyramids, and circles. A free-form is an irregular invented shape or form that has qualities of a geometric form or an organic form.
The ratio for length to width of rectangles is 1.61803398874989484820. The numeric value is called “phi”.
We cannot have a negative width, so the negative answer is not considered. Therefore, the