Throwing You Some Curves: Is Red or Blue Longer? *
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 
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.
Share your story with Science Buddies!
Yes, I Did This Project! Please log in (or create a free account) to let us know how things went.Credits
Andrew Olson, Science Buddies
Alexander Bogomolny, for the idea
Cite This Page
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
APA Style
Last edit date: 20181203
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
Share your story with Science Buddies!
Yes, I Did This Project! Please log in (or create a free account) to 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
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 moreMath 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 moreNews Feed on This Topic
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 ActivityExplore Our Science Videos
DIY Toy Sailboat

Make A Tissue Paper Parachute  STEM Activity

Stretchy Balloons! Fun STEM Activity
