Over the course of the past week, I created my own math version of Kermit the Frog on Desmos. I chose to do Kermit because I wanted to an image that had defined lines but also with a level of challenge. The image of Kermit I choose had a lot of curved lines but also was two dimensional meaning that I could still complete it within the given time frame and my level of expertise. The biggest challenge I ran into was finding a way to use functions to do curves that were a little irregular. At the beginning, I wanted to do a parabola that was rotated 90 degrees and no matter how many numbers I changed the equation y=x^2 wouldn’t work. However, two days later, I accidentally punched in x=y^2 and found that the parabola rotated. This might not be the most mathematically ‘aha’ moment, but as soon as I punched it in, I realized how simple the solution is. I used this equation a lot in the future.

Another challenge I came across was not knowing where to start. I wanted to start somewhere easy but I realized making art out of math isn’t exactly the easiest thing. As I continued with this project, I found out it’s only gets easier as I start to work on it more. I learned through experience and found different ways to create curved lines and how to create restrictions that helped me build the image. I tried to do inequalities over the weekend, but no matter how I moved it, as soon as I zoomed out the inequality would disappear so I took them out. This is definitely something I want to figure out how to fix in the future. As well as, when I first started, I couldn’t seem to get the lines to match up at all. After asking around, I found out that if I put my curser on the line, it tells me the exact points to the third decimal and that helped a lot. This seems really small but it made the rest of my project smoother.

And so to the actual functions I used:

I primarily used this function because this allowed me to make curves big and small as well as create a loop at the bottom that I used on features like the side of Kermit’s face and the curved edges on his hand. I mainly stretched the parabola to make it larger. I also used horizontal and vertical translations and reflections to move it to the spot that I wanted it to be.

Square Root Function: y=squareroot x OR x=squareroot y

I used this function when I needed a slight subtle curve; for example on his forearms. I used translations left and right to get it to the spot I desired as well as stretching and compressing to get it to be the size that I wanted it to be.

Reciprocal function: y=1/x

I used this function for more prominent large curves such as his mouth.

Linear Equation: y=mx+b

I used this equation to connect all the curves together. The image I chose wasn’t facing forward; the entire image was a little tilted so I used a straight line to connect multiple curves that wouldn’t quite fit together. I changed the slopes and the intercepts to get it where I want.

Circle: x^2+y^2=r^2

Although this is a relation and not a function, I used this equation a lot. I used it for the eyes and to make curves that I couldn’t quite make with the other equations. I used restrictions (both x and y restrictions) to cut it to the curve that I wanted.

Through this project, I learned a lot about graphing and functions but I think I do need to study them a bit more even though I made nearly a hundred of them. For the majority of this project, I would input the equation I wanted and then fiddle with the numbers until it fit. This project helped me wrap my mind around the concept but I need to apply this new knowledge on smaller, relevant numbers.