By Tyler H,
The best ways to describe me are through my passion for math and my never ending lack of sleep due to sleepwalking. The function z=x^2-y^2, a hyperbolic paraboloid, mirrors my life. Hyperbolic paraboloids dissociate themselves from other functions by the use of a saddle point. I am also different – I break out into the z plane, in the same way that I break out a Pringle when I am hungry. The hyperbolic paraboloid is in the shape of a Pringle. I eat these salty, scrumptious treats when I am tired. The lack of sleep is pervasive. It seeps into all aspect of life, destroying focus and attention span. It’s been said that we see farther by standing on the shoulders of giants, but I argue that each of us as an individual Pringle stand upon the sleep we achieve. The hyperbolic paraboloid along the x axis reveals my progression of mastering my inability to sleep, showcasing through the y axis how my life leads to an ever-deepening parabolic influence.
The first part of the equation,〖 x〗^2, approximates the direction of my life in relation to sleep. With each passing second, x^2grows to represent the amount of the sleep disorder I “grow out” off, lifting the maximum of-y^2.
In a hyperbolic paraboloid, the arc length of z=x^2-y^2 while holding x constant represents the amount of people who I have influenced in my community at various points of x. The partial derivatives of the function z=x^2-y^2 with respect to x and setting y as the constant measures how close I am to my purpose. My life is a tangential climb, becoming steeper and steeper as my life continues. The more vertical the line, the closer I am to achieving my true purpose.
At the point where I was born (0,0,0), there was no sleep, no arc length (no influence), and both partial derivatives were 0 (nothing pointing upwards). I stood upon no Pringles.
In April of 1998, I began to walk. Like any baby, I hardly slept. The number of people I directly impacted can be found by taking the y arc length (holding x=.83 constant). This number is ∫_(-.83)^.83▒〖√(1+4y^2 ) dy〗 ≈ 2 signifying that my sphere of influence was 2 people: my parents. Then, after setting y=2 as constant, x^’=5/3. Once I started walking, I was only pointing upwards at a 5/3 slope. I had a long way to go, standing on these two Pringles.
Jumping to when I was eight, I served as counselor at a camp. The lack of sleep still haunted me, and it showed in the amount of people I talked to. Holding x constant at 8, the y arc length ∫_(-8)^8▒〖√(1+4y) dy〗 ≈ 130, representing the number of people at the camp: 90 kids and 20 counselors. I was in charge of 10 six year olds, tasked with keeping them focused. Setting y = 130 constant, x^’=16. I stand upon ten Pringles.
When I was 14, my mom asked me to help run a major silent auction. My ability to sleep was increasing, also increasing the amount of work I could accomplish. The number of people attending, found by the arc length, holding x constant at 14, was ∫_(-14)^14▒〖√(1+4y^2 ) dy〗 ≈ 394. I pointed upwards at a rate of 16 (x^’=16 when y is constantat 394). I stand upon 394 Pringles.
Today represents the current x point of this function and my life. I have mastered tricks at falling asleep, and the inability to fall asleep that plagued me as a child is gone. My influence as Senior Class President, as a member of the Young Life Leadership Team, and as a participant at my church’s student ministry is approximated at ∫_(-18.83)^18.83▒〖√(1+4y^2 ) dy〗 ≈ 711 people by the arc length of y. Also, F'(18.83,1000)=37.66, the closest to vertical to date, reveals that I am closer than ever to achieving my purpose. Now, I stand upon over a thousand Pringles.
A Pringle chip’s ingenious design as a hyperbolic paraboloid allows the chips to stack perfectly. Sleep has direct consequences on everyday life, and the ability to work through sleepwalking has encouraged me throughout other parts of my life. Sleep propels me upward on the x axis of life, make my derivative vertical, and greatly increase my sphere of influence in this world.