Constructing Axes of an Ellipse with Straightedge and CompassDate: 01/23/2006 at 15:41:53 From: philip Subject: I want to find the centerline of an ellipse If you encounter an ellipse in a CAD drawing or on a blackboard, how can you determine the centerline? Either the short or long axis would be acceptable. I think there must be a way to construct these lines working just from the ellipse itself, using straight edge and compass. I have an idea how this could be done, however, I don't have the math skills to prove my method. My definition of an ellipse is the shape you get from sectioning a cylinder at an angle other than 90º to the cylinder's axis. Date: 01/25/2006 at 13:51:02 From: Doctor Wilkinson Subject: Re: I want to find the centerline of an ellipse Hi, Philip. Thanks for the interesting problem! The first step is to find the center of the ellipse. To do this we use the fact that the line through the midpoints of two parallel chords of the ellipse passes through the center. So take any chord. Take another point on the ellipse and construct a parallel chord. Then bisect the chords and draw a line through the midpoints. Do the same for another chord and you will have the center. Once you have the center, just draw a circle intersecting the ellipse. This gives you four points which will be the vertices of a rectangle and you can now easily construct the axes of the ellipse. For example, join the opposite corners and take the angle bisectors of the angles formed at the center. - Doctor Wilkinson, The Math Forum http://mathforum.org/dr.math/ |
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