The document discusses Pascal's Triangle, including its history, patterns, and applications. The triangle was used in the 11th century by Chinese and Persian mathematicians, though the French mathematician Blaise Pascal studied its properties more extensively in the 1600s. The triangle exhibits several patterns, such as the Fibonacci sequence appearing in its diagonals and horizontal lines doubling in sum. It is used in algebra, probability, and combinatorics.

1. The Pascal’s Triangle
By Ajwad and Wouter

2. Introduction
• Essential Question: What is the Pascal’s
Triangle and how does it apply?
• We will be showing you how the Pascal’s Triangle
works and where it came from. We will also be
showing you how to use it.

3. What is it?
• The Pascal’s Triangle is
one of the most interesting
number patterns in
mathematics. This is
something that the Chinese
and the Persians used in
the eleventh century and
mathematicians today still
use it.

4. History of the Triangle
• French mathematician;
Blaise Pascal is the founder of
the Pascal’s Triangle, but the
Persians and Chinese also used
it before the birth of
Pascal-1623. It is said that
mathematicians used this
method even in the eleventh
century by the Persians and
Chinese. But in 1654, Blaise
Pascal completed the Traité du
triangle arithmétique, which
had properties and applications
of the triangle. Pascal had made
lots of other contributions to
mathematics but the writings of
his triangle are very famous

5. Patterns in the Pascal Triangle
• We use Pascal’s
Triangle for many
things. For example we
use it a lot in algebra.
We also us it to find
probabilities and
combinatorics. We will
be telling you about
some patterns in the
Pascal’s Triangle.

6. If you make all the even numbers black
and the odd numbers red you can see there
is a pattern of even numbers. All the
corners are the same with one big triangle
in the middle.
red: odd
black: even

7. Fibonnaci Numbers
The Fibonacci numbers can be found in Pascal’s
triangle. If you add the numbers in Pascal’s
triangle in diagonal lines going up as shown in
the picture you get one of the Fibonacci
numbers.

8. Diagonals
First diagonal line is ones, second is
counting numbers, and third is
triangular numbers. Triangle numbers
means you first add 1 to 0 then add 2
then 3 and so on.

9. Horizontal Sums
If you add all the numbers in a horizontal line you
the answer will double to make the next horizontal
sum as shown in the picture.

10. Symmetry
If you put a line through the middle of the
triangle, the numbers on the left are the same as
the numbers on the right.

11. Bibliography
• Colledge, Tony. Pascal's Tirangle. England: Tarquin Publications, 2004. Print.
• "Pascal's Triangle." Math is Fun. N.p., n.d. Web. 9 May 2010.
<http://www.mathsisfun.com/pascals-triangle.html>.
• "Pascal's Triangle." PayPal. N.p., n.d. Web. 10 May 2010.
<http://ptri1.tripod.com/#fib>.
• Pascal's Triangle." tutor.com. N.p., 2010. Web. 10 May 2010.
<http://mathforum.org/dr/math/faq/faq.pascal.triangle.html>.

12. Conclusion
• We hope you enjoyed the presentation
and at least learned something new from
it.