# Maths Patterns Investigation

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Introduction

Malachy Gillespie 12P Maths coursework

Introduction.

In this part of my coursework I will try to work out a formula to a particular shape. The task is to find a formula which when given a number will tell you how many blocks is going to be in this shape. The shape that I am going to use for part 1 is going to be pyramid, I will have to find a formula that will yell me how many blocks is in the pyramid when I put a number in.

- First I am going to make a number of shapes so I can get try to work out a pattern in them. I will make 7 shapes.

This is a single box it doesn’t support any thing and nothing supports it.

Two blocks are supporting this shape and on top of them there is one block.

This shape has three boxes on the bottom row which supports two blocks on top of them there is one block.

This shape has four boxes on the bottom and these support the three boxes on top of them which support the two boxes, which hold up the top block.

The boxes in the shape follow the same pattern than the shape before except there is an extra row.

Middle

## C=

1st B=

2nd A=

2a=1 a+b=1 c=0

a=0.5 b=0.5

## The line is here to separate the differences from the nth term

As we can see here in the quadratic equation the second differences are constant and we have got all the nth terms.

Next I am going to give a certain part of the pyramid a letter so that I can use that letter in the formula.

4)

X= The number of blocks on the bottom of the pyramid

Y= The number of boxes in the pyramid

Now that I have done that I will now move on to making the formula. I will use the nth terms and there letters and I will also use the letters that I have given to the pyramid.

Y=ax2+bx+c

Now that I have what I think is the formula I am going to do a few examples first to make sure that the formula that I have is the right one.

X=1 Y=1

Y=a * 12+b * 1+c = 1

X=2 Y=3

Y=a * 22+b * 2+c = 3

X=3 Y=6

Y=a * 32+b * 3+c = 6

X=4 Y=10

Y=a * 42+b * 4+c = 10

What I have done here is added X and Y too the formula so that the formula is complete. When the numbers from X and Y

Conclusion

R= The number of blocks on the bottom row.

N= The number of boxes in the cube.

Now that I have this done I am able to make a formula. Here I am going to make the formula, which will tell me how many blocks are in a square when I put in a number.

N2=ar+br+c

Now that I have a formula for my problem all I have to do now is to try it out to make sure it works. So I am going to give my formula a set of numbers and see if it gives me the right answer.

R=1 N=1

N2=a * 1+b * 1+c=1

R=2 N=4

N2=a * 2+b * 2+c=4

R=3 N=9

N2=a * 3+b * 3+c=9

R=4 N=16

N2=a * 4+b * 4+c=16

From the above I can see that my formula works and that it gives me the right number of blocks out when I put a certain number in. When the numbers from X and Y where added I worked the formula so that in the end I would get the number of boxes in the square. When I thought I had the answer I checked the pictures on pages 11,12 to make sure that they where correct.

This is the formula that when you put in a number it will give you the number of blocks in the square.

N2=ar+br+c

01/05/2007

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

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