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

Home > Shapes > Geometry
Squaring shapes: (Posted on 2004-09-22) Difficulty: 3 of 5
The ancient Greeks, being masters of geometric manipulation, often tried their hand at "squaring" various shapes. This involved using only the most fundamental rules of geometry to construct a square whose area equals the area of the original shape.

Can you follow in their footsteps and square a simple triangle?

The solution must hold for all types of triangles.

See The Solution Submitted by Benjamin J. Ladd    
Rating: 2.4000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution | Comment 5 of 10 |

Call the triangle ABC.

Construct a perpendicular bisector to BC, marking the midpoint of BC as M.  Then erect a perpendicular from A to the perpendicular bisector, calling the point of intersection D. 

Place the point of the compass on BC at its midpoint and measure off distance equal to MD on line BC (extended if necessary), in the same direction from M as C, marking the new point E. Now segment AE is equal to the height of the triangle plus half the base.  Bisect this segment, and construct a semicircle with center at this midpoint and going through A and E.  Where it intersects MD (extended if necessary) mark point N.  Segment MN has length that is the geometric mean between the height of the original triangle and half the base; its square will have the same area as the original triangle, so just construct perpendiculars at the endpoints of MN and mark off lengths on these equal to that of MN, and all the corners of the square are now marked.


  Posted by Charlie on 2004-09-22 15:01:07
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 (14)
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