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Investigating three step stairs.

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Introduction

Aim I am set the task of investigating three step stairs (which I will go into some more detail on later on) and how their position on the number grid and the step total corresponds to the step number. Prediction My basic prediction is that... Definitions Step total - the total of all the numbers in the stair added up Stair number - this is the lowest number in the stair and is found in the bottom left hand corner of them Number grid - this is a ten by ten square with the numbers from one to one hundred in it as ten time ten is 100. The ten by ten grid is the grid we will be using in the first part of the investigation but in the second stage of the investigation other smaller and larger number grids will be tested. Step number - this is the number of steps the stair is comprised of. As I have stated the step number I will be using for the main part for this investigation will be a three step stair, with a three step number there will be six numbers within the stair. ...read more.

Middle

Lets say I am given the task of finding out the rest of a three step stair where the n=5. In order to do this I would like at the pattern that all three step stairs follow (see left) all that is required for me to do is to fill in n as 5 and do the appropriate calculations for each box in the three step stair. My finished three step stair with all the calculations done looks like this: By using the pattern grid I have accurately found the missing numbers. However this is not exactly a formula and whilst it may be useful for a question like the one I just answered its uses are limited. A formula to calculate the step total from just the stair number would be ideal and so I began to experiment and using trial and error. To start with I looked at the number of numbers in a three step stair and began to look back on the pattern that was found to be behind all three step stairs. I looked at what was actually done to n and how much overall was added to n in a three step stair. ...read more.

Conclusion

I based my theory that the source of the problem would be easier to spot with lower stair numbers on that with lower numbers those that are unnecessary would be removed and I would be able to look and spot any problem more easily dealing with a stair number of one. Much like if I had to draw a cross on the exact centre of a circle it would be easier for me to do it holding the pencil at a close distance away from the circle rather than doing it with a metre long pencil and holding it by the end and at arms length. Things have a tendency to get exaggerated the further they are from the actual problem and the problem is often hidden better when surrounded by a larger problem than by a small problem. In order to stop a problem it must be stopped at the root or source (where it most vulnerable and exposed). Anyway, I went back and looked at stair number one and looked how far off I was from the stair total; I was six off the stair total. I then moved along to stair number two and saw how far off I was from its stair total; I was ...read more.

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