Drawing the Perfect Ellipse

If you've ever tried to draw an ellipse using the standard "stick pin, pencil and string" method you already know that drawing the ellipse is the easy part...getting the ellipse drawn to the right size and shape is the tough part!

Well, here's a simple method of creating an ellipse to your exact specifications. You will still need the pencil and string, as well as three stick pins, and a tape measure that is as long as the long dimension of your ellipse.

Start by laying out the length and width of your ellipse on your work surface. Using the straight edge, measure and draw a line along the long (x-axis) dimension of your ellipse. Through the midpoint of this line, measure and draw a line along the short (y-axis) dimension of your ellipse so that the two lines are perpendicular and cross at their midpoints. Put a stick pin at one end of the shorter line.

Next, measure the distance along the x-axis from the midpoint to one end of the longer dimension. Let's call that measurement length L.

Now, move your tape measure along the y-axis, putting the end of your tape measure at the stick pin. Measure the distance L and adjust your tape measure until that distance L crosses the x-axis. Put a stick pin on the x-axis at this point.

Repeat this measurement in the other direction of the x-axis and put a stick pin on the x-axis at this point.

Finally, tie your string around the three stick pins. Remove the stick pin from the outer edge of your shorter line and put your pencil inside the loop of the string. Keeping tension on the string, draw your ellipse on to your work surface.

That's all there is to it!

DOING THE MATH

Consider your two dimensions - the length and width of your ellipse. As you got the very end of the longer dimension, the loop of the string essentially becomes 2 equal lengths of string. Each length is equal to the distance from the midpoint to the outer edge of the longer dimension (L) plus the distance from the midpoint to the stickpin (F) farthest from that outer edge. So the total length of the string (T) can be expressed as:

T =2L + 2F or T = 2(L + F)

When you stretch this same piece of string out to the very end of the shorter dimension, the string now forms a triangle, where one side is formed by distance between the 2 stickpins in the center, or 2F, and two other equal length sides which we will call H. Why H? If you consider that the y-axis splits the string triangle into two right triangles, then these two equal length sides are actually the hypotenuses of two right triangles. So the length of string (T) in this position can be expressed as:

T = 2F + 2H or T = 2(F + H)

Since the length of string remained constant, whether it was stretched to the longer or the shorter dimension, these expressions are equal.

2(L+F) = 2(F+H)

Divide both sides by 2, and subtract F from both sides and you get:

L = H

In other words, the length from the outer edge at the widest point on the ellipse to the stick pin, or focus, furthest away is equal to the distance from the outer edge at the shortest point to either of the foci of the ellipse.

QUESTIONS
If you have questions, or need further assistance, feel free to contact us at: propdaddy@propdaddycreations.com