Pascals Dominick C

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Pscals Triangle Is Cool!

Transcript of Pascals Dominick C

  • 1. Pascals triangle was originally developed by the Chinese Blaise Pascal was the first to actually realize the importance of it and it was named after him Pascal's triangle is a math triangle that can be used for many things. Pascal's Triangle is used in algebra and probability Pascal's triangle is the way to use an amount out of numbers in a divisible way To solve Pascal's ways you have too add the two numbers that are next to each other shown in the diagram on next slide.
  • 2. Hockey Stick Pattern- The hockey stick pattern is when you can start at any number 1 that borders Pascals triangle and make a diagonal of any size to the right or left. Then go one additional hexagon to the opposite of your diagonal. The sum of the diagonal should equal the ending hexagon. Prime Numbers-When the first number of the hockey stick is 1 then the second number will be divisible of the rest of the hockey stick. The 1 is a Prime number but, this makes the rest of the numbers divisible by each other.
  • 3. Born June 19, 1623 and died on August 19, 1662 at the age of 39. He was a French mathematician, Physicist, and religious philosopher. Discovered the importance of the Pascals triangle. It happened in 1653 Invented one of the first mechanical calculators. He was educated by his father. In 1659 he came down with an illness that cost his life. We use the pascals triangle in math such as Geometry.
  • 4. The Catalan numbers express the number of ways that a polygon with N sides can be divided into triangles. Diagonals that are drawn are not allowed to intersect. The rule for Catalan Numbers is-------- Some Catalan Numbers include 1, 2, 5, 14, 42, 132 Catalan Numbers can be found in Pascals triangle. Pascals Triangle and Catalan Numbers are related to each other.
  • 5. Pascals Triangle-The way to use an amount out of numbers in a divisible way. Catalan Numbers-How polygons can be divided into a number of triangles. Geometry-The study of shapes and angles. Probability-The number used too describe the chance of an event occurring.
  • 6. Complete this Pascals triangle and find all of the Catalan numbers. Remember, Pascals triangle starts off with a one. Try to find out some hockey stick pattern.
  • 7. Ptri1.tripod.com www.mathmuseum.org/mathresearc.html Mathsisfun.com/pascalstriangle.html www.gap- system.org/~history/miscellanious/catalann umbers/catalan.html Oregonstate.edu/instruct/ph1302/philosop hers/pascal.html www.thocp.net/biographies/pascal- blaise.html