Opposite Corners.

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                                Opposite Corners  

Investigation:

Given a 100 Square, I am to investigate the difference between the products of the numbers in the opposite corners of any rectangle that can be drawn on the 100 square.

2x3

A rectangle has been highlighted in the 100 square 1 and 13/11 and 3 are the numbers in the opposite corners product of the number in these opposite corners are

1x13=13

11x3=33

 

The difference between these products is 33-13= 20 

A rectangle has been highlighted in the 100 square 4 and 16/14 and 6 are the numbers in the opposite corners product of the number in these opposite corners are

4x16=64

14x6=84

The difference between these products is 84-64= 20

A rectangle has been highlighted in the 100 square 7 and 19/17 and 9 are the numbers in the opposite corners product of the number in these opposite corners are

7x19=133

17x9=153

The difference between these products is 153-133=20

Conclusion:

                 I have Concluded that my prediction was correct and that a   2 by 3 rectangles have a difference of 20.

2x2

A rectangle has been highlighted in the 100 square 1 and 12/11 and 2 are the numbers in the opposite corners product of the number in these opposite corners are

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1x12=12

11x2=22

The difference between these products is 22-12= 10

A rectangle has been highlighted in the 100 square 3 and 14/13 and 4 are the numbers in the opposite corners product of the number in these opposite corners are

3x14=42

13x4=52

The difference between these products is 52-42=10

A rectangle has been highlighted in the 100 square 7 and 18/17 and 8 are the numbers in the opposite corners product of the number in these opposite corners are

7x18=126

17x8=136

The difference between these products is 136-126= 10

Conclusion:

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This is a brief investigation grounded only in the experimental examples. In order to improve this investigation it needs to move from the literal into the formulaic. Algebraic expressions need to be formed and simplified to verify any patterns found.