The Patterns, Rules and Formulae Found in a Number Grid

In this coursework My spouse and i shall research and describe thoroughly the patterns, guidelines and formulae found in many grid when ever placing a sq . at any point in the grid, multiplying the top remaining and bottom right sides and the top rated right and bottom still left corners and finding the big difference. I will take a look at all the variables and use systematic strategies when doing this kind of.

Advised Variables:

Width of grid

Size of Sq

Copie Tables

Width of Grid: Will the width of the grid make a difference to formulae? I shall keep the size of the sq at a constant (2 times 2)

Width of Grid size 10)

12345678910

11121314151617181920

21222324252627282930

12 x 3 = 276

22 x 13 = 286

286 - 276=10

I actually shall now use letters to prove this kind of correct

X

X+1

X+10

X+11

X(X+11) sama dengan XВІ + 11X

(X+1)(X+10) sama dengan XВІ+11X+10

(XВІ+11X+10) - (XВІ+11X) = 10

Width of Grid Size 9)

123456789

101112131415161718

192021222324252627

11 back button 21 sama dengan 231

20 x 12 = 240

240 - 231 sama dengan 9

I shall now use letters to show this accurate

Times

X+1

X+9

X+10

X(X+10) = XВІ + 10X

(X+9)(X+1)=XВІ+10X+9

(XВІ+10X+9) - (XВІ+10X) = being unfaithful

Thickness of Main grid Size 8)

12345678

910111213141516

1718192021222324

15 x nineteen = one hundred ninety

18 x 10 = 198

198 - 190 = eight

I shall now use letters to prove this correct

X

X+1

X+8

X+9

X(X+9) = XВІ + 9X

(X+8)(X+1) = XВІ+9X+8

(XВІ+9X+8) - (XВІ+9X) sama dengan 8

Width of GridDifference

10 twelve

being unfaithful 9

8 almost eight

Following doing these several widths I could see a certain pattern emerging, using a 2x2 square the difference is always corresponding to the main grid width.

W=D

To prove this We shall use another main grid width of 5. In the event my equation is correct the should be a few.

12345

678910

1112131415

six x 13 = 91

doze x almost 8 = ninety six

96 - 91 = your five

We shall utilize letters to prove this correct

X

X+1

X+5

X+6

X(X+6) = XВІ+6X

(X+5)(X+1) = XВІ+6X+5

(XВІ+6X+5) -(XВІ+6X) = five

This kind of proves my equation accurate as the outcome is as We predicted.

I shall now work with changing the square size. To begin with We shall maintain the width from the grid by a constant size (10) nevertheless I shall experiment with the two to try and look for a formula that works with both elements.

Size of Square:

Does the size of the rectangular affect the method. I shall keep the grid width precisely the same size in the first place but I will change it after i find a 1st formula.

Size of rectangular 2x2)

12345678910

11121314151617181920

21222324252627282930

12 by 23 sama dengan 276

22 times 13 = 286

286 -- 276=10

I shall now use letters to prove this appropriate

By

X+1

X+10

X+11

X(X+11) = XВІ + 11X

(X+1)(X+10) = XВІ+11x+10

(XВІ+11x+10) - (XВІ+11X) = twelve

Scale Square 3x3)

12345678910

11121314151617181920

21222324252627282930

31323334353637383940

12 times 34 = 408

32 times 14 = 448

448 - 408 sama dengan 40

I shall now use words to demonstrate this accurate

X

X+2

X+20

X+22

X(X+22)=XВІ+22X

(X+20)(X+2)=XВІ+22X+40

(XВІ+22X+40) - (XВІ+22X) = 40

Size of Square 4x4)

12345678910

11121314151617181920

21222324252627282930

31323334353637383940

41424344454647484950

12 x forty-five = 540

40 x 15 = 630

630 - 540 = 80

I shall now use letters to prove this kind of correct

X

X+3

X+30

X+33

X(X+33)=XВІ+33X

(X+30)(X+3)=XВІ+33x+90

(XВІ+33X+90) -- (XВІ+33X) = 90

Size of SquareDifference

2x2 10

3x3 forty

4x4 90

After looking at this I can see that through 1 through the height or width with the square and square that number then increase it by 10 you will definately get the difference.

(S-1)ВІx10=D

To confirm this equation...