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Pascals Triangle is really cool!

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- 1. Pascal’s 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 Pascal’s 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 Pascal’s 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 pascal’s 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 Pascal’s triangle. Pascal’s Triangle and Catalan Numbers are related to each other.
- 5. Pascal’s 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 Pascal’s triangle and find all of the Catalan numbers. Remember, Pascal’s 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

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