In my mathematics GCSE coursework I shall be investigating the total and difference in sets of stairs in different grid sizes.
So I then went on to investigate the same step size on another different size of grid, this time a 6 x 6 size grid.
Here is what I found: When I investigated the different sized grid I noticed that each different grid size gave the stair total a different formula because each time a different number was added.
Part 1- Three Step grid I have investigated the three step stair (some of my findings can be viewed on the graph paper in the back).
During my investigation I believe that I have worked out the formula for the total inside the three step stairs on a 10 x 10 grid.
Therefore I have found out that that the formula for steps of this size is; 10x 10g 10.
Next I shall attempt to find out about a one step stair.
After finding the totals for each of the stairs that I will use I shall work out the formula by using the same method as before.
Here is what I found out: X x 1 x 2 x 3 x g x g 1 x g 2 x g g x g g 1 x g g g = 10x 10g 10 Looking at the above information it is visible to know that the four step stair shape follows the same simple pattern as the three step stairs in the way that the letter g is added vertically and the numbers added horizontally.
I have shown this below representing the grid size by using the letter ‘g’.
x x 1 x 2 x g x g 1 x g g = 6x 4g 4 After checking this formula to see if it works for each size of grid it has been proven that it does work.