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

Ellipse
An ellipse can be constructed using the following paper folding method. First, draw a circle on a piece of paper. Next, draw a point inside the circle. Now, select any point on the circle and fold the paper in half so that the point on the circle is directly on top of the point inside the circle. Repeat this over and over again, each time selecting a different point on the circle. The creases in the paper will form an ellipse.

This construction is simulated in the applet below. The black circle represents the circle drawn on the piece of paper. The black point represents the point inside the circle while the red point represents the point on the circle. The gray line represents the fold made in the paper.

We can specify a particular point on the ellipse by finding the intersection of the gray line with a line drawn from the red point to the center of the circle. Put another way, an ellipse consists of the points whose distance from the center of the circle plus the distance to the point inside the circle is equal to the radius of the given circle.

As you drag the red point around the circle, the blue point traces out an ellipse. Can you explain why this point has the property described above?

Double click on any object to see how it's position changes as you move the red point around. Type "ctrl-c" to clear the screen.