Exploration in Excel

by Venessa Brown

 

The goal of the assignment is to exploration and show how excel can be used as a dynamic tools in Mathematics Education.

 

1. Exploring the equations of lines:

With the use of the scroll bar and scatter plot, I explored the equation of a line in the y = mx + b form. As I move my scroll bar for m and b, the scatter plot changes accordingly. The concept of slope is easliy observed, as well as the y-intercept of the line.

 

Equation of a line y = mx+ b
m b
3 2
x y
0 2
1 5
2 8
3 11
4 14
5 17
6 20
7 23
8 26
9 29
10 32
11 35
12 38
13 41
14 44

Excel Spreed Sheet

 

2. Pascal's Triangle

We can use excel to recreat Pascal's Triangle.

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
5 10 10 5 1
15 20 15 6 1
35 35 21 7 1
70 56 28 8 1
126 84 36 9 1
210 120 45 10 1
330 165 55 11 1
495 220 66 12 1
715 286 78 13 1
1001 364 91 14 1
After putting formula to add cell above and the cell above and to the right. The numbers of pascal would be on the left side (reverse of what we are used to seeing). This happened because as we add cells to the right we pass the original cell thus these cell contain a zero. The other fall to the left.

Excel Speadsheet

 

3. Adjusting Pascal's Triangle:

Excel Speadsheet

 

4. Excel is a very useful tool in statistic. Let's take the commonly use "roll a die problem"

and use excel to do to some experimental statistic.

*=int(rand()*6+1*
Rolls Outcome
1 4
2 1
3 1
4 2
5 3 *=countif(array, criteria)*
6 4 1's 4
7 3 2's 5
8 6 3's 3
9 1 4's 2
10 5 5's 4
11 2 6's 2
12 2
13 3
14 2
15 6
16 2
17 5
18 5
19 5
20 1

Excel Spreadsheet

 

5. Fibinacci and Golden Ratio

Fn = Fn-1+Fn-2 ratio (Fn / Fn-1) Fn = Fn-1+Fn-2 ratio (Fn / Fn-1) Fn = Fn-1+Fn-2 ratio (Fn / Fn-1) Fn = 2Fn-1+Fn-2 ratio (Fn / Fn-1)
1 - 2 - 0 - 1 -
1 1 2 1 3   1 1
2 2 4 2 3 1 3 3
3 1.5 6 1.5 6 2 7 2.333333333
5 1.666666667 10 1.666666667 9 1.5 17 2.428571429
8 1.6 16 1.6 15 1.666666667 41 2.411764706
13 1.625 26 1.625 24 1.6 99 2.414634146
21 1.615384615 42 1.615384615 39 1.625 239 2.414141414
34 1.619047619 68 1.619047619 63 1.615384615 577 2.414225941
55 1.617647059 110 1.617647059 102 1.619047619 1393 2.414211438
89 1.618181818 178 1.618181818 165 1.617647059 3363 2.414213927
144 1.617977528 288 1.617977528 267 1.618181818 8119 2.4142135
233 1.618055556 466 1.618055556 432 1.617977528 19601 2.414213573
377 1.618025751 754 1.618025751 699 1.618055556 47321 2.414213561
610 1.618037135 1220 1.618037135 1131 1.618025751 114243 2.414213563
987 1.618032787 1974 1.618032787 1830 1.618037135 275807 2.414213562
1597 1.618034448 3194 1.618034448 2961 1.618032787 665857 2.414213562
2584 1.618033813 5168 1.618033813 4791 1.618034448 1607521 2.414213562
4181 1.618034056 8362 1.618034056 7752 1.618033813 3880899 2.414213562
6765 1.618033963 13530 1.618033963 12543 1.618034056 9369319 2.414213562
10946 1.618033999 21892 1.618033999 20295 1.618033963 22619537 2.414213562
17711 1.618033985 35422 1.618033985 32838 1.618033999 54608393 2.414213562
28657 1.61803399 57314 1.61803399 53133 1.618033985 131836323 2.414213562
46368 1.618033988 92736 1.618033988 85971 1.61803399 318281039 2.414213562
75025 1.618033989 150050 1.618033989 139104 1.618033988 768398401 2.414213562

Excel Spreadsheet

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