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### Constructing an Ellipse

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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/
```
Associated Topics:
High School Conic Sections/Circles
High School Constructions
High School Geometry
Middle School Conic Sections/Circles
Middle School Geometry

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