Drawing An Ellipse
Date: 11/24/97 at 03:53:03 From: Andy Liu Subject: Draw an ellipse with only a straight edge and compass Hello Dr. Math, I am stuck on a homework problem. I would like to know how to draw an ellipse with only a straightedge and a compass. Thank you, Andy
Date: 11/24/97 at 11:51:54 From: Doctor Rob Subject: Re: Draw an ellipse with only a straight edge and compass You cannot draw an ellipse with a straightedge and compass alone. The curved line which constitutes the ellipse is not the arc of any circle, and no part of it is a straight line. You can plot lots of points on the ellipse with these tools, but to draw the curve you will have to either use an additional tool or do it freehand. To plot points proceed as follows. Pick two points A and B in the plane which will be the foci of the ellipse. Separately draw a line segment CD whose length is greater than the distance AB. Pick any point P between C and D on CD. Set your compass to length CP. Draw a circle with center A and radius CP. Now set your compass to length DP. Draw another circle with center B and radius DP. The points where the two circles intersect will be points on the ellipse. Repeat this for several new choices of P. For each you will get 2, 1, or 0 points on the ellipse. When you think you have enough points, draw the ellipse freehand. -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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