All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
Two Crescents (Posted on 2004-08-11) Difficulty: 2 of 5
Given a right triangle, draw the three following semicircles:
  1. The semicircle with diameter formed by one of the legs and extending away from the triangle.
  2. The semicircle with diameter formed by the other leg and extending away from the triangle.
  3. The semicircle with diameter formed by the hypotenuse and extending towards the triangle.

Prove that the area of the two crescents (shown in RED and BLUE) formed by the three semicircles equals the area of the triangle.

No Solution Yet Submitted by ThoughtProvoker    
Rating: 3.2000 (10 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Too Familiar | Comment 8 of 15 |
It would be unfair for me to answer this as I am very familiar with a proof. However it isn't my proof. The crescents are known as The lunulae of Hippocrates. A square treated similarly develops four crescents whose sum equals the area of the square. It was because of these lunulae that many mathematicians, including Hippocrates, searched in vain for a method of squaring the circle. -CeeAnne-
  Posted by CeeAnne on 2004-09-28 02:14:05
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information