Associated Topics || Dr. Math Home || Search Dr. Math

### Accurate Drawing of an Ellipse

```
Date: 02/14/99 at 13:43:32
From: Patrick
Subject: Accurate Drawing of an Ellipse

I am an architectural student and am designing a building with an
ellipse shape. My problem is that I have forgotten how to draw it on my
drafting table. I know an ellipse can be drawn using 2 fixed pins tied
with a thread, but this method is not accurate enough. So my question
is, having my 2 foci fixed, how can I draw an ellipse accurately using
simple tools?

Thanks.
```

```
Date: 02/16/99 at 08:53:11
From: Doctor Peterson
Subject: Re: Accurate Drawing of an Ellipse

I think what you're looking for is a way to plot an ellipse using
standard drafting tools without the error introduced by the thickness
of the string or by varying tension in it. There are several ways to
plot points of an ellipse, which you can then fill in to make the
curve. Probably the easiest is the method using two circles. For this
you need to know the minor and major axes; I'm not sure what you're
given to start with, but even if it is the foci and the string length,
you can figure out the axes from that. (The major axis is the string
length, and the minor axis can be found using the Pythagorean theorem
from that and the distance between foci.)

Here's an attempt to draw the method. Draw two concentric circles whose
diameters are the major and minor axes of the desired ellipse. To plot
a point of the ellipse, draw a radius of the larger circle, and draw a
line vertically from the large one and a line horizontally from the
small one. Where these intersect is a point on the ellipse. Draw enough
of those and you can make an accurate curve.

***********     |/
******           *****+
***                     /|***
***                       / |   ***
*                         /  |      *
*                         /   |       *
**          .....*********./... |        **
*      ......  ***        -+**---+-...      *
*    ...      **           /   ** |    ...    *
* ...        *            /      *        ... *
*..          *            /        *          ..*
*           *            /          *           *
*           *           +           *           *
*           *                       *           *
*..          *                     *          ..*
* ...        *                   *        ... *
*    ...      **               **      ...    *
*      ......  ***         ***  ......      *
**          .....*********.....          **
*                                     *
**                                 **
**                             **
***                       ***
*******         *******
*********

Let me know if that doesn't meet your needs for some reason.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Conic Sections/Circles
High School Geometry
High School Practical Geometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search