Mechanics Maths Coursework on Cubes

Number Squares

In this coursework I will be investigating any patterns or correlations that occur within a set scenario. I will conduct this experiment using 10x10 number squares.

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

I then will draw a 2x2 grid anywhere on the larger grid. This will result in us selecting four numbers. I will refer to the smallest number in the top left as the starting number. For Example if our starting number was 47, we would have a 2x2 grid which would resemble:

47

48

57 58

As you can see, this will result in us having four numbers. Next we multiply the number in the top left with the number in the bottom right, and do the same with the top right and bottom left numbers.

This procedure leaves us with two results: 47x58=2726

57x48=2736

Finally we subtract the results from each other which give us the difference between them.

2736-2726=10

As we can see this first answer leaves us with 10. I will now conduct this procedure with as many different starting numbers as needed for some kind of