Pascals Triangle

Over the course of Prove It or Lose It for the term we have went over a lot of things. Went went over topics like combinations, permutations, Pascal's Triangle and how to determine how many routes to get from one place to another. This lead to making an online poster and some even graphed theirs. In prove it or Lose it we have also learned about some history of math, and we also watched an informational video. To me what was really fun was that I got to work with my classmates and problem solve through some activities. We would debate and brainstorm about one problem for the whole class period until someone could prove how they got there answer. This was unique and interesting.

Combinations

A combination is a sequence in numbers which order doesn't matter. They could be posted as a selection or a lottery.

Example word problem: Nakiyah has 7 songs to pick from and will play 3. How many different ways can he perform each song 7C3=

J.L  Combination Example. (2018)
  

What is a Pascals Triangle

In mathematics, Pascal's triangle is a form of the binomial coefficients. It is named after the French mathematician Blase Pascal, although other mathematicians studied it centuries before him in India, Persia, China, Germany, and Italy.

A unique mathematical pattern within Pascal’s triangle

The diagonals going along the left and right edges contain only 1's.

Another observation that I made was that in the two triangles above the second one adds up to get the one below it. (example) 4 and 3 in the top and that would mean 7 in the one below it

J.L  Example of Unique Pattern. (2018)

Create an artistic representation of Pascal’s Triangle.

Example of Pascals Triangle. (2018)

Pascals Triangle (Wills Copy)

J.L Drawing of Pascals Triangle. (2018)

My Pascal's Triangle (J.L)

For my Pascal's Triangle representation I choose to create a triangle depicting a smiley face on it.
On the sides I noticed that there are all ones, and this was interesting for me. In this image I am conveying that my combination problem relates to my triangle. If you go down 7 and over 3 you'll find the answer 140 .My triangle although does not have equal proportions in each side but thats why I did it. I wanted it to be different by adding extra triangles and bigger triangles. Pascal's Triangles portions are the same, and so is the numbers on each side. But I also noticed that in both are triangles we had smaller triangles also.

Here's what I mean

(J.L)

From this project I have learned about combinations and Pascal's Triangle. The process for me trying to understand what we were trying to do was kinda challenging. The thing that was rewarding was that I learned something new and had fun doing it. But if I was to take Prove it or lose it aging I would like a better explaining of the project, and be able to get more help.