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 http://youtu.be/TGeEZDF seams in each balloon dkMg to see the flat shapes that were used to construct the balloon.