Proyecto Mate

OPPOSITE CORNERS

A square box is placed on a number grid ranging from 1 to 100 , covering the size of the square chosen. In this math’s project I have to investigate the formula or patternsconnecting any size of square chosen and the difference. the formula will work out the difference between the products of the opposite corners of any square box that can be draw on a number grid rangingfrom 1 to 100.

it is called a 10 grid because it has got 10 columns. I will draw 2 by 2 squares and 3 by 3 in the grid, then i will multiply the opposite corners to find the difference in theproducts.


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I investigated what I can use to predict larger sized squares, for that I try squares with the same length placed on the grid, squares of 4 x 4 and 5 x 5 to see therelationship they have.
4x4 5 x 5
61 x 94 =5734 56 x 100 = 5600
91 x 64 = 582496 x 60 = 5760
5834 - 5734 = 90 5760 - 5600 = 160

1 x 24 = 34 1 x 25 = 45
31x 4 = 12441 x 5 = 205
124- 34 = 90 205 - 45 = 160

As you can see the there is no matter where the square is placed because the difference in the products ofthe opposite corner will be the same. Each time the difference of the square increases by 10, the length subtracted by one squared. This can be use to draw any square on the 1 to 100 grid. If we usethis formula :

10 ( n -1)2 = Dn

10 - is the number of columns that are on the grid, and number of numbers in each line of the grid.
n - is the size of the side of the square.
()2 - the area ofthe square is side of the square x side of the square.


Examples:

10 ( 4 - 1)2 = 90 10 x 9 = 90
10 ( 5 - 1)2 = 160 10 x 16 = 160
10 ( 3 - 1)2 = 40 10 x 4...