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

A Square Investigation

Extracts from this document...

Introduction

A SQUARE INVESTIGATION Aim: The aim of this investigation is to find any rules, patterns of square numbers. Patterns/ rules will be discussed step by step below. Firstly a square number is a number multiplied by it. The name becomes apparent if one looks at a diagram of a square. e.g. 2^2 = 2*2= 4sq units; we say 4 is the square of 2. Hence a square number gives the area of a square. Method: the first step was to draw the table below. (Explain what each column means, draw a graph). X NUMBER X^2 SQUARE NO. OF TENS DIFFERENCE NO. OF UNITS 0 0 0 0 1 1 0 0 1 2 4 0 0 4 3 9 0 0 9 4 16 1 1 6 5 25 2 1 5 6 36 3 1 6 7 49 4 1 9 8 64 6 2 4 9 81 8 2 1 10 100 10 2 0 11 121 12 2 1 12 144 14 2 4 13 69 ...read more.

Middle

The sequence is : 0,1,4,9,6,5,6,9,4&1 The unit for 40^2 (1600) is 0, so the unit for 41^2 should be 1, because the rule states that after 0 comes1. The third column is based on the number of tens the squared numbers have. So for example, digits 0-9 have no tens inside them. But digits 10-19, all of these numbers have one ten inside them. e.g. T U 1 9 I realised a pattern within the column of tens. The first and second set of numbers have the same number of difference, (the "column of difference" will be explained later. The first set includes squared numbers from 0-9, and this has the same number of difference as set 2, which includes squared numbers from 16-49). The third and the fourth set of numbers also have the same number of difference (the third set includes squared numbers from 64-124 and the fourth set includes squared numbers from 169-289). ...read more.

Conclusion

As the squared numbers are moving up, the peak they reach is always unit number 9. Another pattern I realised was that on the top line (the points form) has four points. The second line (the points form) also has four points, and the third line (formed by the points) has two points. And the lines with the same number of points repeat again, i.e. 4,4,2-4,4,2 The last pattern I discovered was that as the squared umbers were going down, the lowest they fell to was as follows: 2,10,22 & 40. 1 0 2 2 2 3 10 8 6 4 22 12 4 5 40 18 6 So I worked out a formula to work out the lowest reached squared numbers: -2x + 2x^2-2 = 2x^2 - 2x -2 So for example, if I wanted to find out the lowest reached square number for the third number, which works out to be 10 as you can see on the top , then I would do as follows: 2*3^2-2*3-2 2*9-6-2 18 - 6 - 2 = 10 CONCLUSION: ?? ?? ?? ?? MOUDUD HUSSAIN 10 A 4/26/07 ...read more.

The above preview is unformatted text

This student written piece of work is one of many that can be found in our GCSE Consecutive Numbers 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 Consecutive Numbers essays

  1. GCSE Maths Coursework - Maxi Product

    I have found that 5, 5, and 5 are the three numbers which added together make 15 and when multiplied together make 125 which is the highest possible answer which can be retrieved when three numbers added together equal 15 are multiplied.

  2. Maths Investigation - Pile 'em High

    These are odds numbers +5 +7 +9 missing numbers 1 and 3 Constant +2 +2 The reason why row four is tw0 is because the difference between odd numbers is always two. As we have to come down to a third line we are now in a cubic situation.

  1. In this investigation I will explore the relationship between a series of straight, non-parallel, ...

    and the maximum number of open and closed regions all the lines in the diagram must cross over every other line in the diagram. In other words, no two lines in the diagram can ever be parallel. I will apply this rule in the rest of the investigation.

  2. Nth Term Investigation

    x2 and for the third lot (n -1) x3. Also I noticed with the first rectangles the nth term for was n x 2, for the second lot of rectangles it was (n +1) x2 and for the third lot (n +2)

  1. I am to conduct an investigation involving a number grid.

    x2 + 44 [image008.gif] 46 x 10 = 460 (x + 4) (x + 40) x2 + 40x + x + 40 =(x2 + 44x + 40) - (x2 + 44x) = 160 460 - 300 = 160 The difference between the two numbers is 160 Box 2 22 23

  2. Borders - a 2 Dimensional Investigation.

    A 3x3x3 3D cross shape is made up like this: The 3x3x3 shape is made up of one 3x3 cross (13 cubes), two 2x2 crosses (2x5 cubes), and two 1x1 crosses (2x1 cubes). There are 25 cubes in all. A 4x4x4 shape would be made up of one 4x4 cross

  1. Study the topic of trios and work on from that, to discover patterns and ...

    For example, factorial 4 is the number 4 multiplied by every integer down to one inclusive. I.e. Factorial 4 is: 1 x 2 x 3 x 4 = 24 and factorial 5 is: 1 x 2 x 3 x 4 x 5 = 120.

  2. The Towers of Hanoi is an ancient mathematical game. The aim of this coursework ...

    Given a certain number of discs I need to be able to say how many times a desired disc moves. Firstly, I need to analyze my results from the coding. Disc: Disc A Disc B Disc C Disc D Disc E Disc F Total Number of times each disc moves:

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