I wondered what a good and easy way was to construct an ellipse. I fooled around with formulas and decided (slightly frustrated by the lack of progress) to look it up on Wikipedia, the “source of all knowledge” (wink-wink). As often is the case, those subjects are written in a kind of language normal people don’t speak or write, so I decided to make it simpler to understand for anyone.
Step 1. Draw a rectangle and divide it into four equal parts by drawing two lines, each line parallel to one of the pairs of parallel sides of the rectangle, and equal distance away from each side. The lines should intersect at the center of the rectangle.
You want to give your ellipse some dimension, and a bounding box is the most usual way to do that. Be sure the line parallel to the short sides extends well outside the rectangle.
Step 2. Measure the length of half the short and half the long side of the rectangle.
Mark the length of half the short side as point B on your ruler.
Mark the length of half the long side as point A on your ruler.
Step 3. While changing the angle of the ruler, keep point A on the line parallel to the short sides, and point B on the line parallel to the long sides of the rectangle. Mark on the paper where the zero mark Z is on the ruler.
Mark several points to have enough to connect them into an ellipse.
Step 4. Connect the points into an ellipse.
A steady hand helps. I wish I had one of those.
I have made this tutorial in Art Rage, but if you use a real ruler and real paper, I suggest you use masking tape (or similar) to mark points A and B.
Remember, the long distance on the ruler should be on the short axis of the ellipse, and the shorter distance on the ruler should be on the long axis of the ellipse. The short and long axes of the ellipse are the same as the lines parallel to the short and long sides of the rectangle, respectively.
That is all.