OPPOSITE CORNERS

... Opposite Corners Introduction: For this piece of Mathematics GCSE coursework I am going to find out the difference between the products of the numbers in the opposite corners of any squares that can be drawn on a 10 x 10 grid composing of 100 squares. I shall try to use tables to present my findings; I will make the predictions and proving my predictions right or wrong with examples. I will be using algebra to prove any of the rules I manage to create by analysing my results. Method: I will find out the difference between products for squares of 2 values in 10 x 10 grid. I will do this to find out the general case for this grid. 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 Example 1: 1 2 11 12 (11 x 2) - (1 x 12) = 22 - 12 = 10 Example 2: 25 26 35 36 (35 x 26) - (25 x 36) = 910 - 900 = 10 Example 3: 63 64 73 74 (73 x 64) - (63 - 74) = 4672 - 4662 =

want to read more? →