Conics Project

During this project, I demonstrated creative thinking in many different ways. I started by using formulas that we had learned throughout the course, such as quadratic, cubic, exponential, and radical functions. However, I quickly realized that these four equations would not be enough to achieve the facial structures at the level I aimed for. I wanted to make my portrait more complex so that I could exceed expectations. I then conducted some research, along with trial and error, until I discovered a general equation that could be used repeatedly. This equation would help me achieve any line or curve needed, its formula being √a(x-h)^n-y. This formula allowed me to sketch almost any structure simply by adjusting the “n” exponent value and the “a” value. After experimenting with this formula, I regained the confidence to start my second attempt at the portrait. Unfortunately, my second attempt was short-lived as I quickly ran into another problem—the difficulty in sketching out a perfect face using equations. After contemplating how to create a perfectly symmetrical face, I learned that Desmos has a feature allowing users to import a photo into the graph. I realized I could import a photo and use the face structures as guidelines for basic features such as the mouth, ears, and face shape. Then, I could personalize more unique features such as hair, eyes, and nose. After all this preparation, I was finally ready to begin sketching out the guidelines. This process taking way longer than expected, but after countless hours and 165 different equations, I managed to finish my portrait. Here are the highlights and the parts I struggled with the most: Eyes contained 2 ellipses and 2 circles; the ellipse formula I used was (x-h)^2/b + (y-w)^2/z = r^2. Some troubles I ran into included overlapping corners to make them appear round. I tried my very best to smooth sharp corners; however, you can still see imperfections at the top of the lips and ears. Overall, this project required much patience to get the numbers right for the equations and restrictions. However, once I could anticipate how each variable would change in the graph, it became easier in the end due to the repetition of similar equations.

Desmos Link: https://www.desmos.com/calculator/tyytg6lxh4

Core Competency Self-Assessment

Thinking CC

I demonstrated creative thinking in many different ways throughout this lab. I had to come up with a clear hypothesis using my previous knowledge about diffusion and membranes. I also had to think on my feet and problem solve any issues that we ran into. As my partner and I were prepping and putting the dialysis tubing in the distilled water, we realized that the water already had glucose concentration in it, meaning that it was leaking. We had to think about all the possibilities of where glucose might have come from, which could’ve been excess glucose around the tubing and the string, or the tubing might have been pierced.

Communication CC

During the lab, I demonstrated very high communication skills. To start, I not only talked and worked out problems with my own group, but I also collaborated with other groups when my group was stuck. I was able to work on my teamwork and use my critical thinking abilities as we had to problem-solve and come to conclusions as a group. I actively engaged in discussions with my partner. We thoroughly evaluated our mistakes, reflecting on what worked well and what areas we could have improved on.