Logged out
Access All our Essays in an Instant
Swap your work for FREE access, or pay £4.99 for instant access
e.(mc)2
Member rating: No Rating | Words: | Submitted: Tue Sep 02 2003
Page Preview
On the left is an image preview of every page of this document, and below are the first 150 words with formatting removed:
GCSE Advanced Mathematics Coursework Number Grids 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 Ahmed Nafi Squares Hypothesis The difference of products of the diagonally opposite numbers will be constant throughout the grid and the difference of 2 by 2 square boxes in any grid will be equal to the grid length. Example 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 35 36 45 46 * Analysis 10 by 10 Grids 13 14 23 24 66 67 76 77 18 19 28 29 x y Difference D1 D2 1 1 0 10 2 2 10 20 30 3 3 40 20 50 4 4 90 20 70 5 5 160 20 8 by 8 Grids 57 58 65 66 11 by 11 Grids 101 102 112 113 12 by 12 Grids 42 43 54 55 13 by 13 Grids 140 141 153 154 14 by 14 Grids 91 92 105 106 Conclusion From the analysis, we can observe that the difference of products of the diagonally opposite numbers is always constant, which proved the first part of the hypothesis as true. The difference of 2 by 2 squares for any grid is always equal to the grid-length and thus proves the second part of the hypothesis as true. From the series of these results, a formula can be developed, as shown below. ....... (i) The above formula is of quadratic format,. It may be pointed out here that if the difference between D & D1 (Figure 1 &...
Get instant access
- Instant, unlimited access to our documents in full
- Swap your work for free access, or pay £4.99
- To see the full version of this document and 147,228 others
Receive email updates for this category
- Simply tell us your email address and receive a weekly Study Help Email for FREE
- Receive 3 FREE essay views with each email
- Get all the latest essays from Coursework.Info & discussion from TheStudentRoom.co.uk
