Number Stairs: Totals and Positions
When I have worked out the formulas for 5 different size stairs on 3
different grid sizes, I will go on to investigate the relationship
between all of the formulas. From this I will be able to discover the
ultimate formula that will allow me to work out any stair size on any
size grid and in any position.
As any other formula I will need to predict and prove it, to check
that it is correct. But I also need to investigate if there is
anywhere on the grid that my formula will not work.
Lastly I will write a conclusion to cover in brief, what I have
discovered from this piece of coursework.
3 Step Stair on a 10 by 10 Grid
Firstly I will investigate if there is a relationship between a stair
total and its position on a 10 by 10 grid.
[IMAGE]This is a 3 step stair on a 10 by 10 grid. Its total is 50, I
worked this out by adding up all the numbers inside it.
1+2+3+11+12+21=50
This stair is in position 1. I got this number from the stair’s
bottom-left corner. Using this number it will be easier to understand
what stair I am talking about. In algebra terms n = 1. (n meaning
position number.)
The below stairs are all 3 step stairs on a 10 by 10 grid, but they
are in different positions. I have also added up their stair total.
[IMAGE]
The below grid shows the position number and its total, from this I
will be able to work out an nth term.
[IMAGE]The difference between each total is 6, so this means that the
nth term starts with 6n.
I did 6n and took the answer from the stair total (t). This left me
with 44. 44 goes on the end of the nth term, making the formula 6n+44.
[IMAGE]There is also another way to work out this formula without
working out the nth term. The diagram to the left shows a 3 step
The poem “My Little Residential School Suitcase” reflects the pain and hardships that Petiquay had experienced at residential schools. The residential schools wanted indigenous children to forget about their culture and learn about European culture. He talks about how he, and fellow indigenous children were physically, emotionally, and sexually abused and were taught to forget about their culture and language. An example of this statement would be, “my mother carefully prepared my little suitcase / She took care to put in it everything I would need / My clothes, some toys I would never see again / I was six years old on this first trip / In my little suitcase, my mother had also put / all the love she had, without forgetting the love from my father” (2-8). Here, Petiquay is talking about what had happened before he
In order to begin to solve this word problem equation, we are provided with the given information,
Given Equation we have to find out the summation of natural numbers starting from ‘a’ to ‘n’.
every step by another 1 cm2. At the same time I will be counting the
The Step Pyramid was designed by Imhotep, the Chancellor of King Zoser, and was originally planned as a stone mastaba 7.0 meters high based on a square ground-plan (Aldred 45-46). However, this design underwent six alterations, and in its final form the Step Pyramid rose in six unequal steps to a height of 62.
We can see that if we apply this formula to a 9x9 grid we can find the
to draw together a formula which I could then use to find out how many
the slope of the line passing through 5 and 10. The average of these 5
Text Box: In the square grids I shall call the sides N. I have colour coded which numbers should be multiplied by which. To work out the answer the calculation is: (2 x 3) – (1 x 4) = Answer Then if I simplify this: 6 - 4 = 2 Therefore: Answer = 2
- there are 347 steps to the first level, 674 to the second level and,1,710 steps to the top.(a small platform around the edge.)
be the height of the ramp which in turn would affect the angle of the
However, a heavy material does not physically have to be light, rather visually appear light . For example, tin is relatively heavy, but when produced into a can it is visually and physically light. A similar approach can be taken with concrete through compression . Incorporating thin concrete panels with a white paint finish then presents the staircase as a light structure. The staircase within the atrium is constructed of a steel folded plate staircase structure, with concrete finishes and steel balusters connected to a transparent glass railing. The floor slab is also a polished gray concrete finishing. The primary intent behind the staircase was to achieve a floating structure symbolizing the circulation, from which they can visualize the old and new. Another approach to conveying the staircase as a floating structure would be to remove the concrete, sustaining the steel folded plate structure, representing a development of the new and improved technology against the traditional style. It can then evoke an expression of a floating and light-weight element contributing to the design of the atrium, similar to the Xintai Warehouse
between no. total and stair no. on a 10x10 number grid. I will also be
-------------- 5) 476 45 --------- 26 25 --------
When you climb a stair case you are going up the hypotenuse of a right triangle designed to give you a specific rise for a particular horizontal space available. When we look at a clock the angle of the hands tell you the time.