Pascal's Triangle slideshow

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Wouter and Ajwad's Pascal's Triangle slideshow

Wouter and Ajwad's Pascal's Triangle slideshow

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Transcript

  • 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.