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

I am investigating how many regions can be created when n circles overlap. After I have looked at circles I will look at other shape and try to find if they have a general formula.

Extracts from this document...

Introduction

I am investigating how many regions can be created when n circles overlap. After I have looked at circles I will look at other shape and try to find if they have a general formula. When 2 Circles overlap When 3 Circles overlap When 4 circles overlap A maximum of 3 regions a maximum of 7 regions a maximum of 13 regions Can be created. Can be created. Can be created. Term U 1 2 3 4 Sequence 1 3 7 13 1st difference 2 4 6 2nd difference 2 2 2 After looking at my results so far I can see that the 1st difference is changing but the 2nd difference is constant. This tells me my equation is quadratic, and there's a formula which applies to all quadratic equations. It is: Un = an*+ bn+c First of all to find out what a is I must half the 2nd difference so A = 1, So my formula now is: Un = n*+bn+c, to find b I have to make a new sequence. ...read more.

Middle

Of 37 can be made Already I can see that there is a pattern developing that is similar to that of the circles, however the old formula does not work: U2 = 2* - 2 + 1 = 2 so it is not the same as the circles however I can work out what the formula is by using the same methods: Term U 1 2 3 4 Sequence 1 7 19 37 1st Difference 6 12 18 2nd Difference 6 6 Now from looking at this set of results I can see that this formula will be quadratic. Now to find my new formula I must do as I did first time round and half my 2nd difference, which means it is 3 so, my formula so far is now. Un = 3n - bn + c Now using the same method as before I will find out what b is Term 1 2 3 4 Sequence 1 7 19 37 3n* 3 12 27 48 New -2 -5 -8 11 Sequence 1st ...read more.

Conclusion

Un = 4n - 4n + c And I can also see that c will be +1 so my formula is now Un = 4n - 4n + 1 This is my final formula for squares I will now test it for 5 squares U5 = 4 x 5* - 4 x 5 +1 U5 = 100 - 15 + 1 = 81 This is correct as it follows the pattern so that is my final formula for squares. I do not need to draw 5 squares as I know this is right as it worked for the circles Conclusion After looking over and analysing my results I can see that a & b is always the same and is always equal to the amount of sides the shape has for example triangle 3n and square 4n the circles did not show this as circles have no sides I have also found the general formula for finding out how many regions are in any shape is: Un = an*+ bn+c Created by Anthony Godsell ...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 will try now in fractional numbers if I can get a number higher than 16. (4 1/20, 3 19/20) =8 --> 4 1/20+3 19/20 --> 4 1/20x3 19/20 =15.9975 (4 1/50, 3 49/50) =8 --> 4 1/50+3 49/50 --> 4 1/20x3 49/50 =15.996 (4 1/100, 3 99/100)=8 --> 4

  2. Investigate the Maxi Product of numbers

    Testing my Theory The maximum product that can be retrieved by the number 8 is 16. You get this by halving 8, which is 4 and then multiplying by itself, which gives you, 16. I will test this now. (1,7)= 8 à 1+7 à 1x7=7 (2,6)= 8 à 2+6 à

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

    Diagram 3C: (all 3 lines cross each other, regions are depicted with numbers, crossover points are high-lighted with red circles) Diagram 3 C represents the most regions and crossover points possible for three straight lines. Therefore I can deduce that in order to create the maximum number of crossover points

  2. Investigating a Sequence of Numbers.

    c4 + c5 + c6 = 5 + 22 + 114 + 696 + 4920 + 39600 = 45357 Tn 5 27 141 837 5757 45357 Looking at the column of (n + 1)!, (n + 2)! and Tn, when I add (n + 1)!

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

    32 + 16+ 8 + 4 + 2 + 1 To get the next term suing the general geometric sequence rule, it says that we have to multiply 32 by a constant. a --> ar. So: a --> ar is the same as ar divided by a. 16 = 0.5.

  2. Investigation to Find the number of diagonal of any 2 Dimensional or / and ...

    + something Compare these values with the ones in the actual sequence - it should be obvious that the value of the something is +2 So the formula for the nth term is 3n + 2 Now let's do the second example.... n 1 2 3 4 5 . .

  1. Nth Term Investigation

    x 2 8 404 398 99 Cuboids 2 Another set of cuboids. Here is a table showing my results: n x n x n 1 x 3 x 3 8 16 8 0 2 x 3 x 3 8 20 16 4 3 x 3 x 3 8 24 24

  2. Round and Round -nà(+1) à(¸2) à

    number which is now "2". I can now see quite clearly, that if the (a) number in the sequence is for example, "20" the number, when divided by two and after been passed through the sequence, the answer will be "20".

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