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Pascal’s Triangle
By Jessica Yaemmongkol
HistoryPascal was not the first to study the patterns on the
triangle. The reason the triangle was named after him was because he was able to discover the
importance of the entire pattern, with the help of a French mathematician , Pierre de Fermat.
Al-Karaji of
Persia
Yanh Hui of
Ancient
China
Yanh Hui’s Triangle
Building the Triangle
To create the triangle start with the number 1.
To get the bottom number, add the top two numbers.
Sequences and Patterns
Diagonals
Sequences and Patterns
Odd and Even
If you color all the odd
numbers in the triangle you
will get a pattern that
similar to Sierpinski
Sequences and Patterns
As you go down the triangle the sum of
the horizontal numbers doubles
Power of 2
Sequences and Patterns
Start at a 1 on the left side, go up and to the right.
Add up the numbers and you get the Fibonacci sequence
Purpose of Pascal’s TriangleTo determine the probability of a
coin landing on heads or tails.◦For example, if you toss a coin twice
you can have four different combinations
Probabilit
y HH
HT THTT
Or 1,2,2,1on Pascal’s triangle
Formula for combination
Purpose of Pascal’s Triangle
(x+4)4 = 1x4 + 4x3 + 6x2 + 4x + 1
Binomial Expansion
Credits
Pictures credited by
“Pascal’s Triangle.” Math is Fun. 2011 Mathisfun.com. 13 March 2011. <http://www.mathsisfun.com/pascals-triangle.html>.