• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

shapes investigation coursework

Extracts from this document...

Introduction

GCSE Maths Coursework - Shapes Investigation

Summary

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).

...read more.

Middle


14        4        10
16        3        10
18        2        10
20        1        10
22        0        10

13 Squares (Q=10):

P=        D=        T=
16        6        13
18        5        13
20        4        13
22        3        13
24        2        13
26        1        13
28        0        13

16 Squares (Q=16):

P=        D=        T=
16        9        16
18        8        16
20        7        16
22        6        16
24        5        16
26        4        16
28        3        16
30        2        16
32        1        16
34        0        16

Firstly I will test my previous formulas, P=T+2-2D, D=(T+2-P)/2 and T= P+2D-2, to see if they hold true – of course, substituting T with Q. If the formulas still hold true, I will be able to save lots of time trying to find a formula linking P, D and Q. Even if they don’t, all will not be lost – all the answers may be incorrect by, say, 4. Therefore I could make slight modifications (i.e. +4) to the existing formulas to get a new, working formula for squares.

So where P=14, D=4 and Q=10…

P=10+2-8 Ð P=4 DP is out by –10, or -Q

D=(10+2-14)/2Ð D=-1 DD is out by –5

Q=14+8-2 Ð Q=20 DQ is out by +10, or +Q

And where P=16, D=6 and Q=13…

P=13+2-12 Ð P=3 DP is out by –13, or -Q

D=(13+2-16)/2Ð D=-0.5 DD is out –6.5

Q=16+12-2 Ð Q=26 D Q is out by +13, or +Q

And where P=16, D=9 and Q=16…

P=16+2-18 Ð P=0 D P is out by –16, or -Q

D=(16+2-16)/2Ð D=1 D D is out by –8

Q=16+18-2 Ð Q=32 DQ is out by +16, or +Q

From these trials it is clear that the formulas for triangles doesn’t work properly, but there is some correlation which could help me to find a formula for squares. For example, the formulas always give a value of Q to be twice its real value, and the value of P is always less than its real value by whatever Q is.

So, in theory, all I need to do to get a working formula for Q= is to change the formula from Q=P+2D-2 to Q=(P+2D-2)/2, or more simply Q=P/2+D-1.

...read more.

Conclusion

I also successfully found a formula that will give you the maximum perimeter of a shape, so long as you know what shape it is and how many there are.

Evaluation

I would say that this investigation has been a success. I managed to find a link between P, D and T, which progressed into a link between P, D and Q or H, then on to my universal formulas. After that I went a stage further and developed a formula that would tell you the maximum possible perimeter of a shape.

Unfortunately, my investigation was hindered by 2 things – foremost was my lack of time to carry out the investigation as far as possible (i.e. researching 3D shapes, and irregular tessellating shapes, such as ‘L’ and ‘T’ shapes), and second I did not have any dotted paper capable of drawing regular pentagons or heptagons, as I could have looked at these along with my triangles, squares and hexagons.

If I were to redo this investigation, I would make sure that I set aside enough time to do a proper job of it, and looking at my own made-up shapes to see if my formulas still applied. I also would have very much liked to have been able to move on to looking at 3D shapes, but doing this means wither physically making paper or card squares / pyramids etc, which is vastly time-consuming, or using multi-cubes, of which I have none.

...read more.

This student written piece of work is one of many that can be found in our GCSE Hidden Faces and Cubes section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Hidden Faces and Cubes essays

  1. An investigation to look at shapes made up of other shapes (starting with triangles, ...

    say this is sufficient evidence to prove that my three formulas work for triangles. It also shows that I have rearranged my first formula correctly - so if one formula works for a certain number of triangles, they all will.

  2. Borders Investigation Maths Coursework

    To find the quadratic sequence I will use the equation below tn = an� + b n + c Where it says tn, this equals the total number of squares. In the formula above first I will work out a n�, c and then b n To find a I

  1. Cubes and Cuboids Investigation.

    Exceptions 'font-size:14.0pt; '>There are though times when my formulae will not work. These can be divided into two categories, cuboids with one dimension of one and the other is for cuboids with two dimensions of one. Again as a cube is a special cuboid you can also add a third category of a cube with dimensions of 1.

  2. Skeleton Tower Investigation

    Two 'arms' are needed to form a rectangle. For Example, a tower with three wings will form 1.5 (3/2) rectangles and the centre stack will be added. This formula can be simplified: 1.5 (n (n - 1) + n 1.5 (n� - n)

  1. Border coursework

    I that I have this information, I can construct a table to find a formula for the numbers. Just before that I will construct a table of the differences found in between the sequence results. n 1 2 3 4 5 6 Seq no.

  2. The aim of my investigation is based on the number of hidden faces and ...

    hidden faces each set, the second, which was by seven hidden faces or the third set, which was by eight hidden faces. This set seems to increase ten faces more then the third set of hidden faces. A huge enlargement in hidden faces could be due to the number of

  1. "Great Expectations" by Charles Dickens Chart Pip's growth in the novel from childhood ...

    Estella, begin to turn him against his friend and guardian Joe Gargery, the blacksmith, whom he now considers beneath him. His ambitions and their effects are echoed by the aspirations and ambitions of numerous other characters. Up till now Pip has been miss-educated and because of his poor background, and

  2. How far is it true to say that the work of solicitors and barristers ...

    It also may lower the standards of advocacy because of the general lawyer s lack of courtroom experience, though as mentioned before, handling a case all the way through might ensure better results. Fusing the profession will make it difficult for lawyers to specialise in narrow areas of work in

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work