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# Two Projects

Here are summaries of my first two projects that I completed before we made our new and improved standards.

**Penny Flipping:**

For this project, I used five 2013 pennies, five 2014 pennies, five 2015 pennies, and five 2016 pennies (twenty pennies total). I flipped all of these pennies together ten times. I recorded how many head and tail of each year I got from each toss. I graphed heads and tails separately. I made a line graph and a bar graph for both heads and tails with the x-axis set as the toss number and the y-axis set as the amount of heads or tails I got. In the line graphs, only the points matter, not the lines between them, but I found it was easier to see the changes in numbers with the line graph instead of a scatter plot. I will attach a PDF of my graphs in a comment to this post.

**Quarter Circle in a Box (Pi Estimation):**

For this project, I took a small box lid (a 2-inch square) and drew a quarter circle inside of it. The center of the circle was at one corner of the square and the radius was two inches (so the quarter-circumference stretched from one corner to the opposite corner). I sprinkled millet into the box lid. I counted how many pieces of millet landed inside the quarter circle and how many landed outside the quarter circle, discounting any pieces of millet that landed on the quarter circle line. I repeated this process three times. Below are my results.

Trial 1: 421 millet total, 296 millet inside quarter circle, 125 millet outside quarter circle

Trial 2: 64 millet total, 50 millet inside quarter circle, 14 millet outside quarter circle

Trial 3: 59 millet total, 41 millet inside quarter circle, 18 millet outside quarter circle

To estimate pi, I set up a ratio of areas to values and solved for pi. My ratios were: (area of quarter circle)/(area of square) = (millet inside quarter circle)/(total millet). I then plugged in my values and solved for pi. I estimated pi for each trial and then took the average of my estimations. My estimation of pi was not as close as I had hoped (2.81, 3.13, and 2.78, averaging 2.91), but if I did more trials, ideally my average would move closer to the real value of pi. I learned a lot from this project.

PDFs of both projects will be attached in comments right below this post.

#### 17 comments

Cool work Dylan! Looks like you put in a good amount of time into these projects.

I give it a #1-8/10, and for #2-9/10

These are really good!

#1 - 9/10

#2 - 10/10

Counting the millet is really impressive to me it sounds so tedious haha.

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