## Another way to create an elliptical 1/2 (or 1/4) plan

A true ellipse is, in my opinion, is one of the most beautiful shapes in the universe.  Unlike an oval that is drawn with two mirrored radii (or three in the case of a true “egg” shape), the radii of the ellipse continually change.  It’s incredibly strong shape in structural terms and it’s one of the best shapes for table tops.  There are many ways to draw an ellipse.  But here’s an old method that you don’t often see referred to these days.  It’s simple and can be extraordinarily precise.  This method can also be very helpful if you’re creating domed framing for any type of construction.

First, establish a horizontal base line then raise a vertical line.

Swing a semi-circle with a diameter based on the minor axis of the ellipse.

Next, open the compass to the length of the major axis and strike a point to the base line.

Draw a diagonal line from the base line to the top of the diameter, as shown.  Then divide the vertical line into any number of equal segments.  (Note, the more segments, the more precise the plan will be.)  Now, draw lines, parallel to the base line, from the semi-circle and extend them to the diagonal line.

Extend the lines at right angles to the diagonal line.  (These lines should be longer than the radius of the semi-circle.)

Set your compass to one of the line segment lengths in the semi-circle.

Transfer this measurement to the corresponding line that has been raised from the diagonal line.

It’s difficult to see in the below illustration, but after you have transferred all of the line measurements, you will have, effectively, created a coordinate map.

Connect the dots and, voila, you have a half or quarter plan based on exact measurements.  (Note that I have “thrown in” a couple of extra lines at the top and bottom of the semi-circle, just to create additional coordinate points.)

Again, there are many ways to draw true ellipses.  But I find this method produces the best results for large work and it is considerably more precise that the string and nail method.

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### 4 Comments on “Another way to create an elliptical 1/2 (or 1/4) plan”

1. Paleotool Says:

Reblogged this on Paleotool's Weblog and commented:
Interesting to learn more of the sacred geometry all the time. Compass and rule work was my favorite bits in high school geometry class. I can’t wait to add this to my layout repertoire!

2. Reblogged this on The Obsession Engine and commented:
I really geek out on stuff like this.

3. I’m having a problem visualizing how to transfer this? What I see is 3 half circles and nothing looking like an ellipsis. Am I missing something obvious?

• D.B. Laney Says:

The left projection is, indeed, an elliptical line. You may be having a little trouble recognizing it as the major axis is not terribly long in reference to the minor axis. The line coming off of the middle of the diagonal line is simply there to demonstrate that the plan can be made as a half or a quarter type. When I get a little time, I’ll draw up a better example. I remember that it took me a little time to fully comprehend what I was seeing. Don’t give up, it’s a very useful method.