# 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

## Cite This Page

### MLA Style

*Science Buddies*. Science Buddies, 20 June 2014. Web. 25 July 2014 <http://www.sciencebuddies.org/science-fair-projects/project_ideas/Math_p010.shtml>

### APA Style

*Throwing You Some Curves: Is Red or Blue Longer?.*Retrieved July 25, 2014 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: 2014-06-20

## 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:

## Variations

For a more advanced project, see:

## Share your story with Science Buddies!

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

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