# Throwing You Some Curves: Is Red or Blue Longer? *

 Difficulty Time Required Very Short (≤ 1 day) Prerequisites Must understand the concept of a mathematical proof Material Availability Readily available Cost Very Low (under \$20) Safety No issues
*Note: This is an abbreviated Project Idea, without notes to start your background research, a specific list of materials, or a procedure for how to do the experiment. You can identify abbreviated Project Ideas by the asterisk at the end of the title. If you want a Project Idea with full instructions, please pick one without an asterisk.

## Abstract

This a straightforward, but interesting, project in geometry. It is a good first proof to try on your own. You should be able to figure it out by yourself, and you'll gain insight into a basic property of circles.

Figure 1 below shows a semicircle (AE, in red) with a series of smaller semicircles (AB, BC, CD, DE, in blue) constructed inside it. As you can see, the sum of the diameters of the four smaller semicircles is equal to the diameter of the large semicircle. The area of the larger semicircle is clearly greater than the sum of the four smaller semicircles. What about the perimeter?

Your goal is to prove that the sum of the perimeters of the inscribed semicircles is equal to the perimeter of the outside semicircle.

Figure 1. A large semicircle (AE) with smaller semicircles (AB, BC, CD, DE) inscribed in it.

## Objective

The objective of this project is to prove that the sum of the perimeters of the inscribed semicircles is equal to the perimeter of the outside semicircle.

## Credits

Andrew Olson, Science Buddies
Alexander Bogomolny, for the idea

### MLA Style

Science Buddies Staff. "Throwing You Some Curves: Is Red or Blue Longer?" Science Buddies. Science Buddies, 5 Dec. 2015. Web. 29 June 2017 <https://www.sciencebuddies.org/science-fair-projects/project_ideas/Math_p010.shtml>

### APA Style

Science Buddies Staff. (2015, December 5). Throwing You Some Curves: Is Red or Blue Longer?. Retrieved June 29, 2017 from https://www.sciencebuddies.org/science-fair-projects/project_ideas/Math_p010.shtml

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Last edit date: 2015-12-05

## Bibliography

The Math Forum at Drexel University has some good advice on how to build a mathematical proof:

There are many more examples in their FAQ section:

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## News Feed on This Topic

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Note: A computerized matching algorithm suggests the above articles. It's not as smart as you are, and it may occasionally give humorous, ridiculous, or even annoying results! Learn more about the News Feed

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