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Q&A #1532 |
From: Marielouise
To: Teacher2Teacher Public Discussion
Date: 2001021815:29:42
Subject: Re: ovals
Hi, Chris, I will give you an answer. It may not be the "correct answer" or what you want. An ellipse is a conic section. In this way it is a slice of a right cone not perpendicular to the axis of symmetry of the cone. An ellipse can be constructed from two fixed points, called its foci and a fixed distance that is greater than the distance between the two foci. By definition as a conic, the ellipse is the set of all points such that the sum of the distances to the two fixed points is a constant greater than the distance between the two foci. An oval is not a conic section but it is an egg-shaped solid when the oval is rotated around its one axis of symmetry. You can construct an oval in the following manner. 1. Construct a circle. Draw a diameter. Label it AB. Bisect the diameter AB to locate the perpendicular bisector CD. Extend CD through point C. 2. Using A as a center and AB as a radius, draw an arc from B to where the arc intersects CD. Similarly using B as a center and AB as a radius draw an arc from A to where the arc intersects the extended perpendicular CD. 3. Draw a chord from A to C and from B to C. Extend both of these chords until they intersect the two arcs at E and F. 4. Using C as a center and the distance CE or CF as a radiua, draw a quarter circle from E to F. The oval is the semicircle ADB, the two portions of the arcs AE and BF and the quarter circle EF. This clearly is not an ellipse. It is now a great exercise for your students to determine the area of the oval. (Thanks to Harold Jacobs from whom I learned this about 20 years ago.) -Marielouise, for the T2T service
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