Investigation into Numerical 4 by 4 Squares - page 1
Keywords: Investigation into Numerical 4 by 4 Squares maths Formula, maths sqaure formula
By Mose. on 01/09/2008
Level: GCSE Key Stage 4 (Years 10-11)
Page Number: 1 of 5 pages: 1 2 3 4 5
Introduction
I am going to investigate and observe what happens when I find the product of the top left and bottom right hand side of a square, and vice versa find t he product of the top right and the bottom left hand side of a square. I will then calculate the difference between the two squares and try to see if there is a genuine or pattern with the numbers.
I am first going to use a two by two square and see what happens.
12 13
22 23
12 X 23 = 276 Here we can see that the difference is equal to ten.
22 X 13 = 286
54 55
64 65
55 X 64 = 3520 The difference equals ten.
54 X 65 = 3510
68 69
78 79
68 X 79 = 5372 The difference equals ten.
69 X 78 = 5382
I have observed that the difference is always ten between the two totals. To prove that my results were accurate I did another example.
81 82
91 92
81 X 92 = 7452 I was correct as my concluding example also had a difference of
91 X 82 = 7462 ten.
To further my investigation I am now going to observe what happens with a three by three square.
1 2 3
11 12 13
21 22 23
1 X 23 = 23 Here we can see that the difference is forty.
3 X 21 = 63
35 36 37
45 46 47
55 56 57
35 X 57 = 1995 The difference is forty
37 X 55 = 2035
71 72 73
81 82 83
91 92 93
71 X 93 = 6603 The difference is forty.
73 X 91 = 6643
This time the difference is always forty. To prove my results were correct I did another example.
78 79 80
88 89 90
98 99 100
78 X 100 = 7800 My results were correct.
98 X 80 = 7840
I then decided to do the same thing with a four by four square.
1 2 3 4
11 12 13 14
21 22 23 24
31 32 33 34
1 x 34 = 34 In this example the difference is ninety.
4 X 31 = 124
7 8 9 10
17 18 19 20
27 28 29 30
37 38 39 40
10 X 37 = 370 The difference is ninety.
40 X 7 = 280
56 57 58 59
66 67 68 69
76 77 78 79
86 87 88 89
59 X 86 = 5074 The difference is ninety
56 X 89 = 4984
I proved my results with a fourth and final example.
61 62 63 64
71 72 73 74
81 82 83 84
91 92 93 94
64 X 91 = 5824 My findings were correct, the difference was again ninety.
94 X 61 = 5734
I am now going to observe what occurs in a five by five square.
1 2 3 4 5
11 12 13 14 15
21 22 23 24 25
31 32 33 34 35
41 42 43 44 45
1 X 45 = 45 The difference is one hundred and sixty.
41 X 5 = 205
6 7 8 9 10
16 17 18 19 20
26 27 28 29 30
36 37 38 39 40
46 47 48 49 50
6 X 50 = 300 The difference is one hundred and sixty.
46 X 10 = 460
51 52 53 54 55
61 62 63 64 65
71 72 73 74 75
81 82 83 84 85
91 92 93 94 95
51 X 95 = 4845 The difference is one hundred and sixty.
91 X 55 = 5005
I did an
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