| David Little | ||||||
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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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Hyperbola
A hyperbola can be constructed using the following paper folding method. First, draw a circle on a piece of paper. Next, draw a point outside 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 outside the circle. Repeat this over and over again, each time selecting a different point on the circle. The creases in the paper will form a hyperbola. 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 outside 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 hyperbola by finding the intersection of the blue line with a line drawn through the red point and the center of the circle. Put another way, a hyperbola consists of the points whose distance from the center of the circle minus the distance to the point outside the circle is equal to plus or minus the radius of the given circle. As you drag the red point around the circle, the blue point traces out a hyperbola. 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.
© 2005 David P. Little |
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