Link to the Desmos page

I found this assignment to be one of the most interesting assignments we have done yet. What we had to do is use math equations and put them in Desmos and try to create a self-portrait with them. I spent a lot of time on my portrait and I am very happy with the results. Although there are a few things I would change I was overall content with my portrait.

My first step to doing this project was I pictured in my head what I wanted my portrait to look like and then I proceeded to do a rough draft on a piece of paper. My drawing on paper looked absolutely horrible except for the shoulders and neck so I decided to do that first on Desmos and I tried to duplicate my drawing. I spent around an hour doing just doing the shoulders and neck and trying to perfect that. It took me a long time to get the curve I wanted in the shoulders and the size of them as well. After I had done the shoulders and neck I decided that I wanted to start with my face. I had tried to just do a circle and add a coefficient so it made it like an oval but I didn’t like the look of it and didn’t think it looked like my face at all and it looked horrible if you added ears so I knew I had to try something else. So, I decided that for the jawline that I would use a parabola and then connect it with the rest of the head with my ears. I lined up the parabola perfectly and my only regret is that I made the jaw a little too wide which caused my entire face to be wider. Then my next step after this was adding ears, to do this I used circles that I had added coefficients and played around with the domain and range to make them look like how real ears would look without them looking crazy and unrealistic. After all of this, I decided to work on the hairline for my head to do this I used many series of circles and found a good combination. The sideburns that are on both sides of my head are both part of the same circle that I cut the range to make them look like sideburns. I then used another cirlce and made it a very flat circle to use as the top of my hairline. Then it was time to add hair, to do this I used many cirlces and placed them around my hair and then I used the domain and range to make them look like my hair is flicking to the side like it normally does. Then to add a little bit I added a few trigonometry equations just to say I used them and it looked really good. I was very happy with how the hair turned out but it was a little bit taller then my hair normally looks like now. After I had done all of the outlines of my chest, head, and hair, it was time to start doing the facial features. For the facial features, I used a lot more different kinds of equations. For the eyebrows, I used a square root equation and a circle equation. For the eyes, I used circle equations, parabola equations, and an inequality. For the nose, I used cubic equations and linear equations. Then finally for the mouth, I used 2 parabolas.

I think I did a very good job on this project and I do think it does look like me but I do think the face is a little too wide and I should’ve made it a bit skinnier but I would have to change everything if I wanted to change that now. I am also very happy with the shoulders and that took me a very long time and I got them to be exactly how I wanted them.

The biggest challenges that I faced while doing this project were doing the shoulders and the hair. The shoulders were difficult because I had no idea how I would do it and when it finally worked I was really happy and felt accomplished. With the hair it took me a long time because I had to make a bunch of circles and then make the domain and range different on every single one and the circles had to be placed in different spots so there was no equation that I copied more than once for the hair.

This assignment has helped me understand the graphs and relations a lot because I got to learn and mess around with them to learn what their properties are and how they work. For example, I learned that if you raise the coefficient for x for the equation of a circle, the circle will get thinner. By doing this assignment I am much more comfortable working with graphs and relations and I really enjoyed doing this project.