WOLFRAM|DEMONSTRATIONS PROJECT

Draw Your Smiley Face

​
forehead control ( 1-
p
x
)
power p
6
face length control (
2
y
2
f
+
2
x
1)
face length (f )
1.6
eyebrows control
trimming
left eyebrow
100
right eyebrow
79
raising
2
(x-0.35)
2
0.71
+
2
(y+0.18)
2
e
1
left eyebrow (
e
L
)
0.6
right eyebrow (
e
R
)
0.6
iris control
2
(y-0.07)
+
2
(x-i)

2
0.15
left iris (
i
L
)
-0.5
right iris (
i
R
)
0.5
nose control
starting nose (
n
1
)
0.1
nose length (
n
2
)
0.6
mouth control (parabola a
2
x
+b x+c)
smile (a)
1.33
twist mouth (b)
0
mouth position (c)
-0.98
This Demonstration aims to teach the equations of some conic sections: the ellipse, parabola, or circle. Students can see the effect of the exponent in
1-
p
x
on the forehead when changing the value of
p
. Changing the face length changes the length of the major axis in the ellipse
2
x
+
2
y
2
f
=1
. Changing the values of the sliders for the eyebrows changes the lengths of the eyebrows and their heights. Also, you can change the positions of the irises by moving them to the right or left. Furthermore, students can see the effect of changes in
a
,
b
, and
c
on the equation of the mouth (the parabola
a
2
x
+bx+c
) on the smile (
a
affects the smile,
b
the twist of the mouth, and
c
the height of the mouth). Students can have some fun while learning.