Constructing an Ellipse

Date: 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/