Patterns In Pascals Triangles

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Recommended: Pascal triangle and combinations

Candidate name: Sakariye Abdirizak

Subject: Mathematics SL

Candidate number: 000511-0073

School: Hvitfeldtska Gymnasiet

Patterns in Pascal’s Triangles

I decided to do my math exploration internal assessment on the different patterns in the Pascal triangle. My aim is to discover and elaborate on the many different patterns exhibited in the Pascal’s triangle. One of the main reasons this choice of topic spoke to me is because it relates to a lot of things we do in math class such as Pascal’s triangle, probability, sequences and series, binomial theory, and negative coefficients. Another reason I choose this topic because I am very interested in patterns and I find myself intrigued by patterns and puzzles. It will be interesting to see what I discover.

Blaise Pascal was a French philosopher and mathematician who lived in the 1600s. He is known for inventing the calculator and it is he whom the Pascal’s triangle was named after.

What is the Pascal’s triangle?

The top of the triangle is the number 1 and each new row below contains a number more than the line above. The additional numbers determined by the sum of the numbers to the left and right of the row above. If there is a not figure both to the left and right in the line above then the number the same as the one 's to the left or right in the line above. This means that each line starts and ends with the number 1. As shown in figure 1 .

Figure1

So this is how a Pascal’s triangle looks like. It is mainly used for algebra but what is unique about the Pascal’s triangle is its diversity. As you can see it begins with a 1 at the top and then after shows the coefficients for (a+b)n for all n ≥ 1. You could also say that the ...

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... row. Although the mathematics of it could be easily grasped I think it’s strange the occurrence of this and the pattern that is present. Lastly the Pascal’s triangle could be used as a helpful indicator to how many segments, triangles and such there are in a circle with nth points. This is useful as you can just use the triangle to reach the conclusions, in which otherwise you would have to draw the circle and find out the longer way. To conclude, I feel like this exploration developed my mathematical curiosity, and I appreciate the usefulness and beauty of mathematics. I realized the multi-dimensions of the Pascal’s triangle and its historical perspectives. Lastly, it taught me to explore and analyze patterns and problems and I think that will be useful in both school and real life-situations, because math is a big part of the world we live in.

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