The Patterns, Rules and Formulae Found in a Number Grid
For this coursework I shall investigate and explain thoroughly the patterns, rules and formulae found in a number grid when placing a square at any point in the grid, multiplying the top left and bottom right corners and the top right and bottom left corners and finding the difference. I will look at all the variables and use systematic methods when doing this.
Suggested Variables:
Width of grid
Size of Square
$#$#1$#$# Tables
Width of Grid: Does the width of the grid make a difference to formulae? I shall keep the size of the square at a constant (2 x 2)
Width of Grid size 10)
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22
…show more content…
Now I shall try to answer the question "does this differ with a different size grid?"
I shall try to fill the table shown underneath to get a clear view on all the data and try to see a formula from this data.
Grid Width Difference
4x4 10
3x3 9
2x2 8
Square size 2x2 grid width 10
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
12 x 23 = 276
22 x 13 = 286
286 - 276 = 10
I shall now use letters to prove this correct
X
X+1
X+10
X+11
X(X+11) = X² + 11X
(X+1)(X+10) = X²+11x+10
(X²+11x+10) - (X²+11X) = 10
Square Size 2x2, Grid Width 9
1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 21 26 27
11 x 21 = 231
20 x 12 = 240
240 - 231 = 9
I shall now use letters to prove this correct
X
X+1
X+9
X+10
X(X+10) = X² + 10X
(X+9)(X+1)=X²+10X+9
(X²+10X+9) - (X²+10X) = 9
Square size 2x2, Grid Width 8)
1 2 3 4 5 6 7 8
9 10 11 12 13
teacher I am required to take into account both dimensions. So this became my goal and tool to use.
The perimeter of a square is 8 inches. What is the area of the square if each side is a whole number?
perimeter of big rectangles equals scale factor times perimeter of small rectangle equals scale factor times 58 & it results with 4.5.
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Problem Statement: 1- How many different squares of various sizes are on a standard 8x8 checkerboard. 2- How can you determine the total amount of squares altogether on any size of checkerboard
Step Three: Then calculate the area of the big square in two ways by creating the equation; (a+b)2=4ab/2 +c2. (When simplified you will get the required identity.)
Use the full data set that you uploaded to answer all questions. Be sure to include the graph for ALL questions.
The author of A Mind for Numbers, Dr. Barbara Oakley, grew up with a strong dislike for math and science because she never excelled in those subjects. When she was in seventh grade, her father lost his job after a severe back injury. Due to the lack of his income, she had to transfer schools. At her new school, she had a "crotchety math teacher" who made her sit for hours doing simple addition and multiplication problems. This teacher caused her distaste of math and science to increase dramatically, which eventually led to Dr. Oakley's failure in many future math and science courses. Although she did not enjoy math and science, she loved learning a new language, Russian. Due to her Russian language studies, she received an ROTC scholarship to the University of Washington. Right after she received her bachelor's degree, Dr. Oakley enlisted in the army. Eventually she found herself commissioned in the U.S. Army Signal Corps, where technology was key. Because she was not good in math and science, she was treated as a second-class citizen in her workplace. Dr. Oakley then reflected on her career and decided to go back to college as a result of the funds she had received to continue her education
Unlike many of my peers, my identity comes through not a singular talent or belief I possess, or an experience I’ve been through. The best way to describe me is with my name. Wilfrid. It’s a name whose implications don’t quite fit my background. The name Wilfrid implies aristocracy or British to most people. Despite most people assuming that I’m ashamed of my name, I’ve always taken pride in it because it sets me apart. Wilfrid is a family name passed down from my Dad’s side of the family from first born son to first born son. My great-grandfather owned a cheese factory in the miniscule town of Tescott, Kansas (Population: 312). My grandfather became a very successful patent lawyer. My father didn’t complete college but managed to start his own telecommunications business. I’m the 4th Wilfrid in my family and despite the success of my predecessors in business, they failed in key areas I want to succeed in. None of the previous Wilfrids in my family were particularly known for their compassion, service, or changing the world in an impactful way other than having other sons to continue the family line. I’m motivated every day by my predecessors to be more
Alexis King10/24/171st Hour25 Checkerboard Write-UpIn this problem, the question is how many squares can fit on an 8 by 8 checkerboard? Also, the dimensions are whole numbers no fractions or decimals.I had to keep multiple things in mind when I did this problem. For problem number 1; I got 204 squares total, because someone helped me with this problem they told me that multiple squares can fit within others. If you want to find out how to know the amount of squares that can fit in any size checkerboard, just use the table I have below in the solution. All you have to do go the opposite up and down; so 1 by 1 squares you can fit 8 squares going one way and 8 squares going the other, so 8 * 8 = 64, 1 by 1 squares
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As a fourth shape, the area of a square was found by using basic geometric equations. We could easily assume each side was equal to four inches, since the total of all three sides had to be equal to 12.
I hope I was able to address your query. If you have any further questions, please do not hesitate to write to me.
Surface area is a two-dimensional measurement, and is proportional to the square of its length.
Formulae = == == ===