| 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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Parabola
A parabola can be constructed using the following paper folding method. First, draw a straight line on a piece of paper. Next, draw a point not on the line. Now, select any point on the line and fold the paper in half so that the point on the line is directly on top of the point not on the line. Repeat this over and over again, each time selecting a different point on the line. The creases in the paper will form a parabola. This construction is simulated in the applet below. The black horizontal line represents the line drawn on the piece of paper. The black point represents the point not on the line while the red point represents the point on the line. The gray line represents the fold made in the paper. We can specify a particular point on the parabola by finding the intersection of the blue line with a line drawn through the red point and perpendicular to the black horizontal line. Put another way, a parabola consists of the points that are equidistant from a line and a point not on the line. As you drag the red point back and forth along the horizontal line, the blue point traces out a parabola. 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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