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.
What is it? • The Pascal’s Triangle isone of the most interestingnumber patterns inmathematics. This issomething that the Chineseand the Persians used inthe eleventh century andmathematicians today stilluse it.
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 today.
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.
If you make all the even numbers blackand the odd numbers red you can see thereis a pattern of even numbers. All thecorners are the same with one big trianglein the middle. red: odd black: even
Fibonnaci NumbersThe Fibonacci numbers can be found in Pascal’striangle. If you add the numbers in Pascal’striangle in diagonal lines going up as shown inthe picture you get one of the Fibonaccinumbers.
DiagonalsFirst diagonal line is ones, second is countingnumbers, and third is triangular numbers. Trianglenumbers means you ﬁrst add 1 to 0 then add 2then 3 and so on.
Horizontal SumsIf you add all the numbers in a horizontal line youthe answer will double to make the next horizontalsum as shown in the picture.
SymmetryIf you put a line through the middle of thetriangle, the numbers on the left are the same asthe numbers on the right.
Bibliography• Colledge, Tony. Pascals Tirangle. England: Tarquin Publications, 2004. Print.• "Pascals Triangle." Math is Fun. N.p., n.d. Web. 9 May 2010. <http://www.mathsisfun.com/pascals-triangle.html>.• "Pascals Triangle." PayPal. N.p., n.d. Web. 10 May 2010. <http://ptri1.tripod.com/#ﬁb>.• Pascals Triangle." tutor.com. N.p., 2010. Web. 10 May 2010. <http://mathforum.org/dr/math/faq/faq.pascal.triangle.html>.
Conclusion• We hope you enjoyed the presentation and at least learned something new from it.