For this assignment, we were tasked with having to create a self-portrait using desmos. The only requirements were 2 circles, 2 ellipses and at least 1 hyperbola. This project proved to be much more challenging than I thought it’d be and over 13 hours of work were put into it in the end. I credit about half that time to the head shape and perfecting the strands of hair. The chin was a simple parabolic equation but the hairline and ears proved to be a challenge. I ended up using half-ellipses for the ears and a large circle with multiple restrictions to line up the hairline and forehead. I used a parabola for my face because my real face is slightly oblong rather than square or circular. And thankfully my hairline is quite straight so that wasn’t too much of an issue. I spent close to 3 hours only on the ears, simply because I was trying to make them realistic. I didn’t end up finding a way to really do that by the end, but I’m proud of them nonetheless. As for my hair, I knew that I needed to find a way to make it look like it was combed to the left like it normally is, and I did this by doing a bunch of circles and restricting them so that they were almost curved in a way. I also used a few trigonometric equations. I did these when I wanted the segment to curve in multiple directions. The hair is probably the part I’m the most proud of, because in real life it’s what makes me different from being any other generic white person. The eyebrows were next, and they proved to be very frustrating. I had started off trying a square root equation and a circle equation but that never really turned out. I settled on a few circle equations, but it meant that my eyebrows had no real depth to them. The eyes were challenging as well. I used an inequality to shade my eyes blue. For the mouth I had 2 options, smile or no smile. I decided on having a smile because it meant that I could use two parabolic equations, which is what I ended up using. I was contemplating adding teeth, but they’re crooked enough in real life that it scared me off doing it.

On a side note, over the semester break I am going to try and figure out the shading of my self-portrait, so I can implement skin colour and hair colour. I think it would add complexity and depth to this assignment, which it’s definitely lacking.

In conclusion, I’m exceedingly proud of what I was capable of accomplishing for this project, and though my self-portrait is simple, so am I, so it works out.

Collaboration

Collaboration in Pre-Calculus 12 is mostly demonstrated by doing in-class questions on the whiteboards in class. Every lesson the class is given a small set of questions to do and you along with a randomly selected group have to do them. In this particular problem, my group and I had to figure out 3 consecutive integers that equaled a product of 120. By putting our heads together and using the correct methods, we were able to achieve a correct answer. This was the best example of working together I’ve experienced in this class, and I think it was for a few reasons. Collectively we were accepting of all strategies proposed by the group, and tested them all for verification until we found one that made sense to everyone. The groups that I’ve been a part of have been far more successful and efficient when everyone contributes, compared to just one person doing all the work. If there was something that I had to improve on personally, I would try to progress to become more vocal in my groups. Usually I have the right idea, but since I’m not entirely sure it’s correct I stay silent. With any future board work we do I will make it my goal to speak up and become more involved.