Take a look at the little lady.

For my art piece, I chose a portrait of a little lady. In the beginning, I was only looking for an aesthetic picture, so there wasn’t much thought concerning the difficulty and sophistication of the image. I only realized that I had chosen a picture that had a lot of small details after I began. So, without a plan, I just charged into this project headfirst.

The first part I decided to do was the Collar Texture (you’ll see it labelled so), because it was relatively simple. It consisted of straight lines, so all I used were linear equations and functions. This was simple, although time-consuming, and allowed me to get into the groove of adjusting different values, such as slope.

The next part I decided to work on was the Collar Lace. I used circles for the majority of the lace because all of the lines were curved. Circles were also very simple to manipulate, but I had to make a lot of them! Over time, I realized that it was easier to copy and paste similar looking lines and adjust them accordingly, which made my work more efficient. In order to match the lace with the circles I had created, I used a lot of circles for just one line, which made the Collar Lace take a long time.

Afterwards, I worked on the rest of the Clothing. I used exponential, quadratic, square root, and linear functions, as well as circles. The lines for the Clothing weren’t as curved, so I had to make the decision of whether I wanted to use circles or not. After experimenting with different graphs, I decided on the functions depending on how similar they looked to the line in comparison. Sometimes, if the result was dissatisfactory, I simply tried a different graph.

The Face and Neck were the next areas I focused on. The Face and Neck were a lot simpler than the earlier parts, as there were fewer lines. I used a combination of reciprocal, quadratic, and linear functions, as well as circles. The only trouble I ran into concerned linear equations. It was a struggle to make sure I had the correct slope because I would often have to adjust the slope number by number.

Next came the Hair. The Hair was similar to the Collar Lace. I used reciprocal, quadratic and linear functions, as well as circles, to create the Hair. Similar to the Collar Lace, there were lots of curved lines. Luckily, the Hair had very similar lines within itself, so once I had finished layering a line, I would copy and paste the functions and adjust accordingly, which saved me a lot of time.

Finally, I had to do the Eyebrow and the Eye. The Eyebrow and the Eye were simple. There were few lines, and after working on the rest of the drawing, I had a good idea of what I was doing. I used linear and quadratic functions, as well as circles. However, when I began to use inequalities in order to shade the Eye and the Eyebrow, it began to become confusing. It was simple to shade the initial region, but the real challenge came with setting limits. After experimenting, I realized that a lot of what I had done resulted in the ‘!’ mark, motioning that my inputs were not applicable. After struggling for a while, I wondered, why not put the entire function as a limit within brackets? I was just trying something out, without much hope that it would be successful. Luckily, it worked, and I was able to apply it to the rest of the regions I had to shade. (Refer to Eye and Eyebrow- Inequalities)

Throughout this project, I didn’t feel the need to ask for help, although I was asked by my tablemates to help out sometimes! I got through the majority of my problems by experimenting and testing out things I thought would work or were interesting. After a lot of experimenting, I came to understand that even though different types of functions have diverse results, manipulating functions is predictable and consistent. For example, adjusting ‘y’ within a bracket makes the entire function move vertically because, with the addition of the new value, the value of ‘y’ must adjust itself to maintain, essentially, the value of zero within the bracket. Same with manipulating ‘x’ within a bracket. Something intriguing I learned was that switching the positions of ‘x’ and ‘y’ causes the function to be reflected diagonally, I’m going to assume, along the line created by ‘y=x’ in a square root equation (refer to Clothing- the second equation). In addition, I learned that with inequalities, if I want the region shaded to be limited by another function, I can input that equation into another set of brackets as a limit itself, after changing it into an inequality by changing the ‘=’ sign to an inequality, such as ‘<‘ or ‘>’.

Overall, this project brought lots of joy and was surprisingly relaxing. I might go as far as to say that it was therapeutic! I understand the nature of functions a lot better and how different coefficients and values affect the way a function moves. Even though a lot of concepts were covered in Math 11 already, I was able to deepen my understanding. This project was an opportunity to apply the knowledge I had gained and perhaps, I will begin to draw on Desmos as a stress-relief technique! :))))