Send in the Clowns
Descriptive Research Project on Conic Sections
When was the last time
you were entertained by a clown? Most of us have seen clowns at a circus,
a party, or in a street show. Many cultures enjoy the art of
clowning. Clowns can depict many emotions depending on their dress
and makeup. As you work through the project, you will use graphs of
quadratic relations to create designs for clown faces. You will try
to capture specific emotions in your designs then you will organize a display
of your designs.
1. Design a clown face using only graphs (or
parts of graphs) of parabolas. When you have a design you like, record
the equations you use, including any restrictions on the domain or
range of each. Give the equations for your clown face to two classmates.
Ask them to sketch the face from the equations. Compare their
sketches with yours. Check your equations to resolve any differences
amoung the graphs.
2. Design several clown faces using graphs (or
parts of grapsh) of conic sections. Each face should convey a different
emotion, such as anger, sadness, joy, or surprise. For each face, record
the equations you use, including any restrictions.
3. Find two classmates. Collect measurements
for the distance h from the top of the head to the chin and the distance
w across the face at the eyes. Analyze th data to design an elliptical
outline for a clown face that will fit the "average" student. Record
the equation you use. How well does your ellipse fit your own face?
do you think an ellipse is a good approximation for the shape of a
human face? Why or why not?
4. Create a display for your designs. Choose any meduim you
like and be creative. Set your display in the glass case in the foyer
by the office.