In this issue we look at the geometry of parade balloons. For more math media resources, go to http://www.media4math.com.

1. 11/28/11

2. Parade Balloons
• Parade balloons and hot
air balloons are made of
fabrics stitched
together. You can
always see the seams in
such balloons, where
the sections meet.

3. Parade Balloons
• The sections of the
balloon are made of flat
parts that have
curvature. The
curvature is what gives
the balloon its shape.

4. Parade Balloons
• Suppose you peel an
orange into similar
shapes. If you flatten
these shapes then you
remove the curvature
from that portion of the
orange. Building a
balloon starts with a flat
shape.

5. Parade Balloons
• The curvature of a
sphere is defined as 2
over r-squared, where r
is the radius of the
sphere. This is a rational
function.

6. Parade Balloons
• The graph of this
function reveals that for
a small radius (like that
of an orange), the
sphere has a high
curvature. But as r
increases in value, the
curvature decreases.

7. Parade Balloons
• As r approaches infinity,
then the curvature
approaches zero, which
is the curvature of a flat
plane.

8. Parade Balloons
• So, the advantage that
large inflatable balloons
have is that flat sheets
with minor curvature
can still result in a
spherical shape.

9. Parade Balloons
• The flatness of the
strips and the lightness
of the fabric makes it
easy to transport a
balloon.

10. Parade Balloons
• Watch this video about
the balloons being
inflated and note how
the balloons start flat.
Also, make a note of the http://youtu.be/TGeEZDF
seams in each balloon dkMg
to see the flat shapes
that were used to
construct the balloon.