p.o.w. 4: cUTTING THE pIES
Table #1
Self AssesmentI feel like I used the Habit of a Mathematician “Be Confident, Patient, and Persistent” the most. It took me a while to find the largest number of pieces for each amount of cuts. It took me a while to finally find a pattern. It took me a while to find the pattern. At first, I tried to create a graph to find a formula. However, this was futile since my numbers were wrong. When I went back, I realized that I had made a mistake with one of my cuts in the 6th circle. So, I persisted working on to make sure that it worked. I worked hard on this problem and devoted quite a bit of time towards, so I feel I deserve a good grade.
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In this problem we had to find a pattern with the largest possible amount of new shapes that could be created by drawing a specific amount lines within a circle, and use the pattern to find the largest amount of shapes 10 cuts could create. I first started by creating a circle with one line it, which obviously created 2 new shapes. I then created a circle with 2 lines within it, which created 4 new shapes. I continued drawing lines which created 7, 11, 16, and 22 steps for 3, 4, 5, and 6 cuts respectively. I then drew a circle with no cuts in it to test my equation which had 1 shape within it. After reviewing my table I discovered that if the In = x, the Out = y, and the Out in the previous row = n, then y=x+n. For example, 2+2=4, 1+1=2, and 5+11=16. If this pattern continued then the In-and-Out table would look like this So, using the table based off of my formula, I was able to discover that 10 cuts can create a maximum of 55 shapes. This definitely would’ve of been tedious to find without my formula. tABLE #2
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