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Transcript of Pascal's Triangle
Relationships If you color in the odd number in Pascal’s triangle you will get something close to the Sierpinski Trianlge which is a triangle where you put a white triangle in each black one until you get the big triangle.
Here Is the Sierpinski Triangle Patterns All the numbers on the sides are always 1’s. All number beside 1’s are natural numbers if you go in a diagonal pattern. Natural number are basically numbers that go up by 1’s (1,2,3,4,5…) After the natural number( moving inwards) you get triangular numbers which are numbers you can arrange into a triangle if each digit was a dot. Here are some of the Trianglular Numbers More Patterns In Pascal’s triangles there is a relationship between the dots and the lines. As you can see in the picture below in each node (knots), (going upward) shows how many paths there are to the first “1”. For example: From “4” to the first “1” there are 4 pathways. These are all the bands of the Pascal’s triangle. All the diagonal colored bands add up to successful Fibonacci numbers. Fibonacci is when the number before adds up to the next number and so on. Basically the sum of the last two numbers like in the numbers below. Class Activities Fill In this Pascals Triangle Was Pascal The first one to discover this triangle? The Numbers after the Diagonal "Ones" are
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