Technician

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Technician

• How to make Pascals Triangle

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How to construct IT

• First start with the number 1

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• Then on the next row put a 1, then
  another 1, like this

1
1
0
0
1
2
1

• Assume anything outside the triangle is a 0.

1
3
3
1

• Add the two numbers above the next row.

1
4
6
4
1
See how it works?
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This is how it should look when youve completed
many rows
Note Row 0 is at the top and can have infinite
rows
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Naming Rows and Elements
0th element
1st element
0th element
2nd element
0th element
13th element
Then they are numbered successively from 1st,
2nd, 3rd element and so on.
All numbers on the left side are the zeroth
element.
Rows start at 0 and are numbered successively.
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The Pascal Petal
The shaded regions represent a Pascal Petal.
Notice every other hexagon around the gray
hexagon is shaded a different color.
What is the product of the orange?
6 x 10 x 35
2100
What about the yellow?
5 x 20 x 21
2100
6 x 10 x 35
5 x 20 x 21
Why are these the same?
2
3
2
7
5
5
5
2
2
5
7
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Lets write the prime factorization of the two
equations.
What do you notice about the prime
factorizations?
Thats right. They are the same. This is true
for all Pascal petals.
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How to Fill in Missing Parts
First we will fill in A
As you know, in order to get the numbers for the
next row, you add the two numbers above it. Thus
353570.
B
15
20
For B we will use this equation, B1535
35
35
C
21
When solved, B20
A
56
70
For C, the equation is C3556
C21
Lets do another one!
A1 because its the end of the triangle.
A
1
For B, 141B
13
D
B15
91
14
1
For C, 9114C
B
C
15
115
C115
For D, 1D14
D13
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Completing the Triangle Using Probability
Combinations
Lets say you want to find the 3rd element of the
10th row without having to fill in the rest of
the triangle.
You can do this by using this simple formula.
R!
(R!-E!) E!
Where Rthe row number, and Ethe element
number, thus
720
10!
10987!
120



6
7!3!
(10!-3!) 3!
120
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Bibliography

• http//mathforum.org/dr.math/faq/faq.pascal.triang
  le.html

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And that is that