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

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 Areas of Science Pure Mathematics 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: For this science project you will need to develop your own experimental procedure. Use the information in the summary tab as a starting place. If you would like to discuss your ideas or need help troubleshooting, use the Ask An Expert forum. Our Experts won't do the work for you, but they will make suggestions and offer guidance if you come to them with specific questions.

If you want a Project Idea with full instructions, please pick one without an asterisk (*) at the end of the title.

## 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.

## Bibliography

The Math Forum at Drexel University has some good advice on How to Build a Proof.

There are many more examples in their FAQ section.

## Credits

Andrew Olson, Science Buddies
Alexander Bogomolny, for the idea

General citation information is provided here. Be sure to check the formatting, including capitalization, for the method you are using and update your citation, as needed.

### MLA Style

Science Buddies Staff. "Throwing You Some Curves: Is Red or Blue Longer?" Science Buddies, 3 July 2020, https://www.sciencebuddies.org/science-fair-projects/project-ideas/Math_p010/pure-mathematics/red-blue-curves-longer?class=AQUbaRUrLFw1TImfSUp0HmvjvLQtADwoUFx0YYkqnjTRtJqd3WNXah0r3NoRdnodqs1faLnzY7BAA00hy9hCl7naCgnibshnscKMZSMEjzAjPA. Accessed 13 Aug. 2020.

### APA Style

Science Buddies Staff. (2020, July 3). Throwing You Some Curves: Is Red or Blue Longer? Retrieved from https://www.sciencebuddies.org/science-fair-projects/project-ideas/Math_p010/pure-mathematics/red-blue-curves-longer?class=AQUbaRUrLFw1TImfSUp0HmvjvLQtADwoUFx0YYkqnjTRtJqd3WNXah0r3NoRdnodqs1faLnzY7BAA00hy9hCl7naCgnibshnscKMZSMEjzAjPA

Last edit date: 2020-07-03

## Experimental Procedure

For this science project you will need to develop your own experimental procedure. Use the information in the summary tab as a starting place. If you would like to discuss your ideas or need help troubleshooting, use the Ask An Expert forum. Our Experts won't do the work for you, but they will make suggestions and offer guidance if you come to them with specific questions.

If you want a Project Idea with full instructions, please pick one without an asterisk (*) at the end of the title.

## Share your story with Science Buddies!

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.

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