In the short story “The Lottery”, the author Shirley Jackson write of a village where tradition is never questioned. For centuries the townsfolk have been taking part in a “Lottery” every summer. While some find the tradition outdated, many of the higher society families believe in sticking to the behaviors they were taught—contained violence—and the tradition that has led them for centuries. The head of each family draws a slip of paper from an old black box in the town square, and one mans, Mr. Hutchinson, is marked with a black dot. The Hutchinson family is then directed to redraw from a smaller grouping of slips inside the box. When his daughter Tessie draws out the black slip, chaos erupts. The townsfolk pick stones from the street and stone Tessie to death. Humans are creatures of habit that will follow the masses. They avoid change out of a fear of what they do not understand and seek to belong with others, therefore causing them to follow the majority. The theme of this short story is that following traditions and habits without question is dangerous.
My equations: For the basic head shape, nose and eyes I used a circle relation and a quadratic equation to form a more prominent chin. For the hair and mouth I again used two quadratic equations, for the eyebrows I used a trigonometric equation, neck and shoulders used a cubic equation and the shirt uses just a basic linear equation.
My struggles: When doing this assignment I really struggled with the eyebrows. When I initially tried to make them I tried to use a square root function (y=√x), but I couldn’t use that formula to make my right eyebrow properly no matter how hard I tried, so I eventually ended up getting help online by finding someone else’s portrait and based my equation off of that one. I ended up using a trigonometric function instead which required a lot of trial and error but eventually I got the right shape.
Aha Moments: I wouldn’t say I had any aha moments, but something that really moved things along for me was when I discovered how to use domain and range to shorten my graph so that it had a start and end point.
Help: I got some really helpful tips from my online source on how to use the sine ratio on my graph to properly shape even eyebrows as well as how to do the inverse eyebrow on the right side.
Strategies: The main strategy I had was to use negatives and positives in front of different parts of the equation to create a mirror image for the other side of the face. I found this really helpful to not only speed up the process but also make sure that my features were all symmetrical.
What I learned: The biggest takeaway I have from this project is the shapes that various functions and relations will take when graphed. This is something that will be extremely useful to me in the rest of my math experience throughout high school, before graphing on desmos I had no clue the shape most relations or functions would take and now I can look at an equation and have a relatively clear idea of what shape it might take.
In this Lab we were able to measure the Flagpole outside of the school using trigonometric expressions. Using a clinometer we found a rough estimation of the angle from the flagpole to our point on the ground, and used a trundle wheel to calculate our distance from the flagpole. Our final result was 10.4 meters tall, after adding Angelo’s eye height off of the ground.