11/28/11

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.

Parade Balloons

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

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.

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.

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.

Parade Balloons

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

Parade Balloons

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

Parade Balloons

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

Parade Balloons

• Watch this video about the balloons being inflated and note how the balloons start flat. Also, make a note of the seams in each balloon to see the flat shapes that were used to construct the balloon.

http://youtu.be/TGeEZDFdkMg