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 
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.
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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
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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:
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