Number Grid Coursework
My task is to investigate a 2x2 box on a 100 square
I will take a 2x2 square on a 100 square grid and multiply the two
corners together. I will then look at the relationship between the two
results, by finding the difference.
Test 1
======
54 55 54 x 65= 3510
64 65 55 x 64= 3520
3520-3510= 10
DIFFERENCE = 10
Test 2
======
5 6 5 x 16= 80
15 16 6 x 15= 90
90-80= 10
DIFFERENCE = 10
Test 3
======
18 19 18 x 29= 522
28 29 19 x 28= 532
532-522= 10
DIFFERENCE = 10
Prediction
==========
I predict that in a two by two square the difference will always be 10
Proof
=====
83 84 83 x 94= 7802
93 94 84 x 93= 7812
7812-7802= 10
DIFFERENCE = 10
Algebraic Explanation
=====================
[IMAGE]I will assign a letter to the first number in the 2 x 2 square,
n.
The next number to the right will therefore be n+1
The number directly below it will then be n+10
The number diagonally across from it will be n+11
I will then times the corners together, like In did on the above
examples.
Top Left hand corner x bottom right hand corner = n(n+11) = n² + 11n
Top right hand corner x bottom left hand corner = n² +1n+10n+10
n² +11n+10
(n² +11n+10) - (n² + 11n) = 10
Therefore the difference between the corners multiplied together will
always be 10.
Expanding the Task
==================
I now feel it will be interesting to look at a 3x3 number square on a
100 grid. I will take a 3x3 square on a 100 square grid and multiply
the two corners together. I will then look at the relationship between
Given Equation we have to find out the summation of natural numbers starting from ‘a’ to ‘n’.
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