Math in the News: 11/28/11
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Transcript of Math in the News: 11/28/11
![Page 1: Math in the News: 11/28/11](https://reader036.fdocuments.in/reader036/viewer/2022062617/54c23e554a7959be598b456b/html5/thumbnails/1.jpg)
11/28/11
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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.
![Page 3: Math in the News: 11/28/11](https://reader036.fdocuments.in/reader036/viewer/2022062617/54c23e554a7959be598b456b/html5/thumbnails/3.jpg)
Parade Balloons
• The sections of the balloon are made of flat parts that have curvature. The curvature is what gives the balloon its shape.
![Page 4: Math in the News: 11/28/11](https://reader036.fdocuments.in/reader036/viewer/2022062617/54c23e554a7959be598b456b/html5/thumbnails/4.jpg)
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.
![Page 5: Math in the News: 11/28/11](https://reader036.fdocuments.in/reader036/viewer/2022062617/54c23e554a7959be598b456b/html5/thumbnails/5.jpg)
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.
![Page 6: Math in the News: 11/28/11](https://reader036.fdocuments.in/reader036/viewer/2022062617/54c23e554a7959be598b456b/html5/thumbnails/6.jpg)
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.
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Parade Balloons
• As r approaches infinity, then the curvature approaches zero, which is the curvature of a flat plane.
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Parade Balloons
• So, the advantage that large inflatable balloons have is that flat sheets with minor curvature can still result in a spherical shape.
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Parade Balloons
• The flatness of the strips and the lightness of the fabric makes it easy to transport a balloon.
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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