Graphing Calculator Design

Designing with TI-84+ series

Graphing Calculators 2014

Theme: FIFA World Cup

I designed this as an entry to the competition:

Summary:

In soccer, teams kick the ball into different goals; however, in FIFA, all must work together to kick the ball into one goal. Unity. Through the drawing, I aim to encourage athletes to form friendships with people from various “kicks of life”. As FIFA is the most viewed sporting event, their actions can influence powerfully.

I explored not only the GC, but also new math concepts. I felt excited upon discovering parametric and polar equations. I also learned patience. Though I enjoyed figuring out equations I needed, it was tedious to adjust graphs so that curves fit nicely.

These are how I created some of the items.

I. Soccer Ball (polar equations)

(xmin = -17, xmax = 17, ymin = -15, ymax=17, θMin = 0, θmax = 2π)

r1= ((sin2θ)+8) x .5 for the slanted ball effect

r2 = {.2,.3,.4,.5,.6,.7} x (-cos{2.5θ} x.4|+2) for the shaded pentagon

r3 = -|cos1.25θ|x 10 +10 for the 5 lines in the ball

r4 = r3/(r3/r4) to limit the lines

II. Net (parametric equations)

(Tmax=10, Tmin = 0, xmin=-2, xmax=8,ymin=-8.5,ymax=1.5)

Xt = sin(4T)

Yt=1.25sin(9T)

III. Background:

(xmax = -10, xmin = 10, ymin = -10, ymax = 10)

y1= 1.5sin|sin(1.5x+3)|+8/(x>-4) line through the top of the head and arms of audience

y2= 1.2sin(1.5x)+7/(x>-3) line through bottom of the head and arms of audience

y3=2.5sin(1.5X)+9 sine wave for mouths of audience

y4=y3/(y3<7.2)/(x>-3) to limit the sine wave to smiley mouths

y5 = -5.7sin(1.5X)+3 sine wave for eyes of the audience

y6=y5/(y5>7.7)/(y5<8.5)/(x>-3)  to limit the sine waves to dots

y7=-.02x^2 +5.6/(x<-6.5 or x>8) for the hill

IV. Each three soccer player is made of one set of curves (sine, cosine, log, exponential, quadratic and cubic equations) Because there are too many, I’ll just mention the graphs for the drawing of one of the players. The other two also have their own sets.

Bottom-right kicker:

(xmin = -10, xmax = 30, ymin = -15, ymax = 25)

y1 = -|cos(.7x+3.5)|/5x+21 / (x<-2.8)/(x<9)

y2 = .7sin(.6x)-2/(x>-1)/(x>10)

y3=(-.12(x-1)^3 -.15(x-1)^2+.6(x-1)+.5/((x>3.2 and (x<3.8))or((x>4.45)and (x<5.5)))

y4 = 11/(x-1.2)-11/(x>2.7)/(x<5.2)

y5=(-1/(x+3)_.6x+6)/(x>-2.2)/(x<18)

y6= 1.5sin(x-3.5)-1(x>-8)/(x-2)

y7=(-1/(x+4)+.6x+8)/(x>-3)/(x<19)

y8=-6log(x+7)-3>(x<10)

y9=(x+3)^2 -3/3/(x>-4)/(x<-1.2)

y0=-6log(x+8)-5/(x<11)

V. Stars

The equations for the six stars are variations of r=-|sin2.5θ|+1 in different window settings.

There are more equations, e.g. for the wavy hair, the spiky hair, the other two athletes, and other minor things.

Tiffany Chong GC competition entry