To squaring a rectangle means to construct a square with an area equal to the area of a given rectangle. You may square a rectangle using only a compass and a straight edge in the following activity. (The proof may be found in [1, p.51].)

- Start with rectangle
**ABCD**. - Extend side
**AB**. - Draw an arc centered at
**B**with radius**BC**. Let**E**be the intersection of the arc and ray**AB**. - Construct the midpoint
**M**of segment**AE**. - Construct a circle centered at
**M**with radius**OA**. - Extend side
**CB**. - Let
**F**be the point where the circle and ray**CB**intersect. - Then
**BF**is the side of the desired square. Complete by constructing a square with side**BF**.

This has been done on Geometer's Sketchpad. To see this relationship between a square and a rectangle click on squaring a rectangle sketch.

If you have your own rectangle that you wish to square, you may use the squaring a rectangle script.

Return to Hippias' Quadratrix Page

Go to Historical Overview of Pi

http://www.geom.umn.edu/~huberty/math5337/groupe/squarerect.html

Created: March 1996 ---- Last Modified: July 6, 1997

Copyright © 1996-1997 Michael D. Huberty, Ko Hayashi & Chia Vang