maths grid coursework

Maths coursework

i am going to investigate a pattern by taking a squares and rectangles and multiplying the top corners.

For squares 2x2, 3x3, 4x4, 5x5

for rectangles 2x3,24,2x5,3x2,3x4,3x5,4x2,4x3,4x5

i will be doing this in a nine squared grid and a ten squared grid

after my results if there is a pattern i will make a formula to describe the pattern

2x2 squares on 10 squared grid.

16x25=400 400-390=10

15x26=390

59x50=2950 2950-2940=10

49x60=2940

3x3

22x44=968 1008-268=40

24x42=1008

27x49=1323 1363-1323=40

47x29=1363

Algerbraic

equation.

Key

G= grid size

N= number

w= number of squares.

2x2 sqaure on a 10 size grid

3x3 sqaure on a 10 size grid

I can simpifly this into a forumula G(n-1)²

and i realise i have 2 varibles that can be changed

the number of sqaures

grid size

RESULTS

From these results i can conclude that the formula for this pattern

(when n is the number in and G equals grid size)

G(n-1)²

i will now prove this by finding the square of 9 by 9 on a 12 sqaure grid

example 9=n 12=G

algerbraic equation

Rectangles 10 squared grid

...