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

Home > Shapes > Geometry
SQUARECOMPASS (Posted on 2011-01-30) Difficulty: 4 of 5
For the following use a compass and straightedge procedure.

Given a unit square ABCD construct 4 circles centered at each corner and having diagonal radius. Form the smallest of the squares defined by the points where these circles intersect.

Use this process on the new square to create a third square.

1. Find and provide the area [in surd format] of each square so formed.

2. Following this process find a general expression for the area of the nth square.

See The Solution Submitted by brianjn    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re: solution | Comment 2 of 4 |
(In reply to solution by Charlie)

Charlie(?),
  would you please reconcile your general formula for values of 'n'?

I believe that you should be seeing increasing values:
1.354...
1.833...
2.483...
.....
.....

Your values seem to fluctuate. 
I do agree that the area of the second square [(sqrt(7) - 1)^2 / 2] is: 1.354......


  Posted by brianjn on 2011-01-31 05:51:50

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 (11)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information