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Pascal’s Triangle
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By. Ms. Barnes
What is Pascal’s Triangle?
•
Pascal’s Triangle is a geometric arrangement of binomial coefficients
•
In other words, it is an array of entries formed by adding the two entries above which
continues infinitely
•
This triangle represents many patterns, combinations, and sequences which have
been used throughout mathematics for thousands of years
Who Created Pascal’s Triangle?
Pascal’s Triangle was used thousands of years ago by the Chinese and Greeks;
however Blaise Pascal, a french mathematician, was the first person to recognize the
importance of what this infamous triangle contained, thus it was named after him.
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How do you create Pascal’s
Triangle?
•
It’s quite simple actually, start with a 1 for the first two rows of the triangle (the top then
the following row). Next, you must form the next entries by adding the two above entries
and you continue this down the triangle.
As it turns out, the sum of the numbers in the rows is equal to the 2 to the nth
power, when n is the number of the row. For example,
2º = 1
2¹ = 1+1 = 2
2² = 1+2+1 = 4
2³ = 1+3+3+1 = 8
Class Activity
How many times can we spell the word MATH using different paths on this triangle?
M
M A M
M A T A M
M A T H T A M
Answer:
MATH = 4 Letters
2^4 = 16
But we accounted for the middle Math twice so we must subtract 1
16 – 1 = 15
OR
We know math is 4 letters long, so let’s look at the forth row in the triangle and find the
sum of the numbers in that row:
1+3+3+1=8
Answer = 2Triangle – 1
2(8) – 1 = 15
Now it’s your turn…
How many times can you spell the word
MATHEMATICS using every different path
on the triangle?
References
All You Ever Wanted to Know About Pascal's Triangle and More. Web.
14 Nov. 2010. <http://ptri1.tripod.com/>.
"Pascal's Triangle." Mathwords. Web. 14 Nov. 2010.
<http://www.mathwords.com/p/pascal's_triangle.htm>.