Constructing an EllipseDate: 04/15/97 at 16:08:21 From: Tim Brantley Subject: Construction of ellipses My math teacher said there was a way to construct a sphere using only a compass and straight edge. However, he said that he can't remember how to do it. Do you? Tim Brantley Date: 04/16/97 at 12:17:17 From: Doctor Marilyn Subject: Re: Construction of ellipses Hi Tim, Neither an ellipse nor a sphere is actually constructible with a compass and straight edge. The ellipse is impossible because the only curves that you can ever draw with a compass and straight edge are straight lines and arcs of circles (neither of which is part of an ellipse). The sphere is impossible because to draw because it doesn't lie in the plane. However, there IS an easy way to construct an ellipse if you don't use a compass and straight edge, but rather 2 thumbtacks and a piece of string. Tie the ends of the string together in a loop. Put the 2 tacks in a board. Put the string around them, put your pencil in the loose loop of string, pull it taut, and let the pencil trace out an ellipse around the 2 thumbtacks. You see, an ellipse is just the set of points in which the total of the distances from two points is the same. The loose loop of string is fixed at the two points and its length doesn't change. To construct a sphere, you need to do it in 3 dimensions, not in the plane. This means that again, this isn't a compass and straight edge construction because those all take place in a plane. The sphere will be a solid object, and it is all points the same distance from the center. You could just measure from the center with your ruler. Hope that helps. -Doctors Marilyn and Ken, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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