# Opposite Corners Maths Coursework

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S = Stair size, eg a 3 x 3 stair s = 3 G = Grid size, eg a 10 x 10 grid = 10 A = Amount of ‘n’ N = bottom left hand corner of shape in 2 steps: 1) (Sx (S 1) /2) = A 2) AN (G 1) x ( (sxsxs-s) /6) = THE ANSWER SOME EXAMPLE WORDINGS TO USE IN YOUR WRITE-UP… At the time I was not really experienced with liquor, but willing to ... 1 Number Grid From the formula (10 wy-0 w 10 x 10), when x is substituted with 5 and y is substituted with 1 (5 and 1 being the coordinates of the keystone of the step stair positioned lower on the grid above), an answer of 140 is calculated. aka the “Gregory Newton Formula.” I’ve searched on the internet for this formula and help on it… it’s like too complicated with all those wacky symbols.

[ (wy-w x) 3] [ (wy-w x) w] [ (wy-w x) w 1] [ (wy-w x) w 2] [ (wy-w x) 2 w] [ (wy-w x) 2 w 1] [ (wy-w x) 3 w] This can be simplified to: 10 wy-0 w 10 x 10 From these formulae, when x is substituted with 2 and y is substituted with 2 (2 and 2 being the coordinates of the keystone of the step stair positioned lower on the grid above), an answer of 230 is calculated. hotel I got out of the car crawling to the steps, and fell asleep there. So we were having our fun there and by this time I was tired of drinking beer, needed a little change ... 5 6 7 8 13 14 15 21 22 29 = 140 From the formula (10 wy-0 w 10 x 10), when x is substituted with 2 and y is substituted with 6 (2 and 6 being the coordinates of the keystone of the step stair positioned higher on the grid above), … The one my teacher taught is: (If the value of n = 0) s x (1 st Difference) [s (s 1) ]/2 x (2 nd Difference) [s (s-1) (s-2) ]/6 x (3 rd Difference) Ok I have almost no clue how to do this…

There is one main rule: the product of the top left number and the bottom right number must be subtracted from the product of the top right and bottom left numbers. I plan to achieve my aim by attempting a series of different methods and comparing the answers to see if they are the same.

The first method I will do is to draw diagrams, using excel.

These will give me a clearer picture of what is involved in this investigation.

I will write all the calculations of how I worked out the answer beside each diagram.There are many different types of number grid, but I will start with square grids.I will also assume that the starting number is one and that the numbers in the grid are consecutive.I hope to learn some aspects of mathematics that I previously did not know.The product is when two numbers are multiplied together.Your formula gives 10*5(5 - 2) 10 = 10*15 10 = 160. You can simplify the formula even more: 10n(n - 2) 10 = 10[n(n - 2) 1] = 10[n^2 - 2n 1] = -- The method that you used for squares can be extended to rectangles.Suppose we have an n x m rectangle (n units wide, m units tall).A booklet that attempts to guide students through the 'Opposite Corners' investigation.Designed to help students see how to approach a problem solving task.Thanks guys, I hope you guys can help, 'cause I am bummed right now. I've got "For any square on the 10 x 10 grid, we would have to make a formula for an ‘n x n’ square.The thing is I expanded the brackets of the formulas for (top left corner x bottom right corner) and (top right corner x bottom left corner) and found the difference, but I expanded wrong, yet I still got a formula that worked like a beast, like, everytime, but now I've redone it, it doesn't work! If ‘n’ is the number of squares across the square, the formula should be the difference between (x n-1)(x 10n-10) and x(x 10n-10 n-1) These two equations with expanded brackets look like this: x² 11nx-11x 10n²-20n 10 And x² 11nx-11x Making the clear difference between them, 10n²-20n 10, which can be simplified to 10n(n-2) 10" But this formula, when used on 34x48 and 44x38 gets: 90, when it should clearly be 40!

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