### Overview of process

Below are pictures showing how to create a large ellipse (half of one but can also be used to draw a full ellipse). I used this technique to make arc sections in a set of bookcases. No complicated jig to build; just a board, clamp and stick with slot for pencil and nail to set minor axis length.

### The Mathematics

The Y Axis represents a guide board perpendicular to board upon which you want to draw the ellipse.

• Segment E1E3 is the stick used in the operation
• Point E2 is where the nail is placed
• Point E3 is the notch for the pencil.
• See diagram below for an illustration.

$x = \overline{E1 E3}*sin(\alpha)$
and
$y = \overline{E2 E3}*cos(\beta)$
and from geometry
$\alpha = \beta$

Using these as parametric equations and eliminate the angle $\alpha$ and $\beta$ we get equation of an ellipse:

${\LARGE \frac{x^2}{\overline{E1 E3}^2} + \frac{y^2}{\overline{E2 E3}^2} = 1}$

Illustration on coordinate system

Page where you can simulate the drawing of the ellipse with different parameters.