From: Marielouise 
To: Teacher2Teacher Public Discussion
Date: 2001021816:29:42
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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