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

## Cite This Page

### MLA Style

*Science Buddies*. Science Buddies, 5 Dec. 2015. Web. 26 May 2016 <http://www.sciencebuddies.org/science-fair-projects/project_ideas/Math_p010.shtml>

### APA Style

*Throwing You Some Curves: Is Red or Blue Longer?.*Retrieved May 26, 2016 from http://www.sciencebuddies.org/science-fair-projects/project_ideas/Math_p010.shtml

## Share your story with Science Buddies!

I Did This Project! Please log in and let us know how things went.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:

## News Feed on This Topic

*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

## Share your story with Science Buddies!

I Did This Project! Please log in and let us know how things went.## Ask an Expert

The Ask an Expert Forum is intended to be a place where students can go to find answers to science questions that they have been unable to find using other resources. If you have specific questions about your science fair project or science fair, our team of volunteer scientists can help. Our Experts won't do the work for you, but they will make suggestions, offer guidance, and help you troubleshoot.Ask an Expert

## Related Links

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Mathematicians are part of an ancient tradition of searching for patterns, conjecturing, and figuring out truths based on rigorous deduction. Some mathematicians focus on purely theoretical problems, with no obvious or immediate applications, except to advance our understanding of mathematics, while others focus on applied mathematics, where they try to solve problems in economics, business, science, physics, or engineering. Read more### Math Teacher

Math teachers love mathematics and understand it well, but much more than that, they enjoy sharing their enthusiasm for the language of numbers with students. They use a variety of tools and techniques to help students grasp abstract concepts and show them that math describes the world around them. By helping students conquer fears and anxieties about math, teachers can open up many science and technology career possibilities for students. Teachers make a difference that lasts a lifetime! Read more## News Feed on This Topic

*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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