Home Store Project Ideas Project Guide Ask An Expert Blog Careers Teachers Parents Students

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 (applet or image): Prove that the sum of the perimeters of the inscribed semicircles is equal to the perimeter of the outer 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 Staff. "Throwing You Some Curves: Is Red or Blue Longer?" Science Buddies. Science Buddies, 1 Oct. 2014. Web. 1 Nov. 2014 <http://www.sciencebuddies.org/science-fair-projects/project_ideas/Math_p010.shtml>

APA Style

Science Buddies Staff. (2014, October 1). Throwing You Some Curves: Is Red or Blue Longer?. Retrieved November 1, 2014 from http://www.sciencebuddies.org/science-fair-projects/project_ideas/Math_p010.shtml

Share your story with Science Buddies!

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


Last edit date: 2014-10-01

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 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

If you like this project, you might enjoy exploring these related careers:

Mathematician at work

Mathematician

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 helping student at blackboard

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

Looking for more science fun?

Try one of our science activities for quick, anytime science explorations. The perfect thing to liven up a rainy day, school vacation, or moment of boredom.

Find an Activity