Number grid Essay Example | Topics and Well Written Essays - 1500 words

Number grid - Essay ExampleUpper Left No.UL*LRUR*LL divagation1236340261248126840331815185540483360340040554235427540625208524840787800784040 TABLE 2As the table indicates, no matter where we place the red-blooded in the grid the difference in the ware of the corners for a 3 x 3 square is always 40. postpone 3 below are the results of a square that is 4 x 4 placed haphazard on the grid.Upper Left No.UL*LRUR*LLDifference134124901785094090241368145890362484257490413034312490534558464890676700679090 TABLE 3As the table indicates, no matter where we place the square in the grid the difference in the product of the corners for a 4 x 4 square is always 90.Table 4 below are the results of a square that is 5 x 5 placed randomly on the grid.Upper Left No.UL*LRUR*LLDifference1452051601696011201602315411701160352765292516042361237721605656005760160 TABLE 4As the table indicates, no matter where we place the square in the grid the difference in the product of the corners for a 5 x 5 square is always 160.Table 5 below are the results of a square that is 6 x 6 placed randomly on the grid.Upper Left No.UL*LRUR*LLDifference1563062501510501300250231794204425023179420442502115961846250322784303425045450047502504139364186250 TABLE 5As the table indicates, no matter where we place the square in the grid the difference in the product of the corners for a 6 x 6 square is always 250.Table 6 below are the results of a square that is 7 x 7 placed randomly on the grid.Upper...This is true for a 2 x 2 square and all other sizes. However, the difference in the product of the corners is open upon the size of the square. As the size of the square gets larger, the difference in the product of the corners also increases.But is there an algebraic relationship between the size of the square and the difference of the product of the corners Can we calculate the difference by knowing the size of the square Table 10 lists the results from the previous investigations.As we have seen, no matter w hat size square is used, we can use algebra to calculate the number of possible squares and the difference in the product of their corners. This applies to all possible combinations placed on the grid.