David Little
Mathematics Department
Penn State University
Eberly College of Science
University Park, PA 16802
Office: 403 McAllister
Phone: (814) 865-3329
Fax: (814) 865-3735
e-mail:dlittle@psu.edu

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Constructing A Square
To draw a square that has the red and blue points as adjacent corners, first draw a circle centered at the blue point and passing through the red point. Next, draw circle centered at the red point and passing through the blue point.

Now draw a line perpendicular to the line segment passing through the blue point and another line perpendicular to the line segment passing through the red point.

To draw a square that has the red and blue points as opposite corners, first draw a line segment connecting the two points. Next, find the midpoint of the two points.

Next, draw circle centered and the midpoint going through the blue (or red) point.

Next draw a line perpendicular to the line segment through the midpoint.

Intersect line and circle. The two points of intersection of the line and circle and the original red and blue points form the corners of a square. Can you explain why?