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# Projects #2 #3 and #4

Since my first project (the coin flipping) I have completed three more projects and am in the process of working on another one.

Project #2 and 3 ~ Pascal's Triangle

*Here are the steps I did for this project:*

**1.** I looked up pictures of Pascal's Triangle and searched around until I found a few that I could print and use.

**2.** I printed one that was just a triangle made up of blank circles. And I printed one that was made up of hexagons with the numbers already written in. The third one is just a triangle of only numbers.

**3.** Next I took the triangle with the blank circles and worked on writing all the numbers in. That way I could see all of the different patterns as I wrote them. This took me about an hour just to write the numbers in. The largest number I have is 1,622,275. I was not able to write in a few of the even larger numbers because I did not have enough space.

**4.** After I had filled all of the numbers in, I started searching for information about Pascal's Triangle. I found this website: https://www.mathsisfun.com/pascals-triangle.html which looks like its for kids but actually has a lot of good and complicated information about the Triangle on it. I spent some time searching around on it to find things I wanted to learn more about. I decided to color in the rows going down the side of the Triangle and make a kind of diagram/code for what each row of numbers represented.

**5.** After coloring in the first 8 rows I decided to color the rest of the triangle all one color. For the 8 rows that I colored in I researched what each one represented and wrote the name of the row and what color it is. I talked to John about what some of the numbers mean because by the 6th row I had very little understanding of what "Simplicial Polytopic Numbers (5-simplex)" means... and he said he only knows up to row 4.

**6.** After I color coded the rows I decided to learn more about the Horizontal Sums. I looked at pictures of them written in on other triangles and spent some time figuring out how they work. For every row going down Pascal's triangle the sum of all the numbers gets added up. For the row below it the sum of the one above it doubles and that is the sum of that row. You could also figure this out by going down the rows using 2 to the power of 1, 2 to the power of 2, 2 to the power of 3, and so on.

**7.** The last thing I did for this project was on another piece of paper I wrote out how the Triangular Numbers work and how the Tetrahedral Numbers work. Just to get a better idea of how we can get those numbers.

*I spent at least 3 hours on this project and am counting it as 1 art project and 1 other project. *

Project #4 ~ The Sierpinski Triangle

*Here are the steps I did for this project: *

1. I used the triangle I printed that is made of hexagons and had the numbers already written in.

2. To start I decided what color I would make the even numbers and what color I would have the odd numbers be. Next I started coloring them all in and it took me a a half hour or so to do this.

3. Next I went and looked at the same website I used for my other project: https://www.mathsisfun.com/sierpinski-triangle.html and I read about what the Sierpinski Triangle is. I learned that it is "An ever repeating pattern of triangles" or any other shape. The way it works is after you make one triangle you make one half that size and put it inside of the bigger one upside down. Next you take the half size triangle and make three more triangles half the size of that and put them in the three corners around the middle one. It's kind of hard to explain and I'm not sure how to get a picture onto the blog. If I do a presentation I can show you all a picture.

That's all I did for this project and I am counting it as** 1 art project**. I spent an hour on this project.

This is a lot of writing but hopefully it all makes sense.

#### 16 comments

I give it a 9/10 for all the projects, nice work! Just to let you know none of the links showed up as links, they just showed up as regular words.

Ok thank for letting me know. I’m not sure why they didn’t work… I can show the class the website if I present though.

Nice projects! I am interested to see how the triangles look

For #2/3: 10/10

For #4: 9/10

Wow, these are really, really cool Cedella. 10/10 for the first, 9/10 for the second.

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