Number stairs

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Asad Rajabali                Number Stairs

Number stairs

Introduction:

I have drawn a number grid above with the stair below (ie the 25 one inserted)

The above is a stair shape. This is the numbers I am going to use to analyze for future workings.

The following stair shape is a 3 step stair. The total of the numbers in the stair shape can also be expressed by a formula.  

        

        The stair number 25 can be expressed as X=25

                              St(25) = 25+26+27+35+36+45

        St(25) =  194

St(25) is the stair total for this particular stair shape. For other stair shapes for you to get the stair total then you would look for the number in the bottom left hand corner of the stair shape.

The following terms that I will use throughout my project are:

Grid: This is the grid that you are going to use to find out the numbers i.e. the original     grid is with 10 by 10 numbers.

   

Stair Shape: This is the shape found in the grid.

   

Stair Number: This is the number in the bottom left hand corner of the stair shape.

 

Stair Total: This is total of the numbers in the stair shape.

   

Blocks: This is how many blocks there are in the stair shape.

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Steps:  This is how many steps there are in the stair shape.

Finding a formula the Stair Total

A formula can be used to work out the numbers in a stair total. I am now going to find out how to get the formula.

The above stair shape can be expressed further in terms of the stair number X.  

For example see below:

 

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