Free of Limits > Workshops > The Golden Ratio

The Golden Mean - The Golden Section
The Phi Ratio - The Life Ratio
Construction of the Rectangle and Spiral
A scroll-down lesson from Brian Joseph

Step One	Begin with a square. In this exercise, we will look at the construction (and not the mathematical proof) of the Golden Mean Rectangle and Spiral. To learn the math, refer back to the Mathematical Proof.

Step Two	Open your compass a little over half as wide as a side of the square. Just set the pivot at a corner and eye it. Using light pressure (you will erase these marks later) spin a circle around a corner of the square. Do this for each of the four corners without changing the open-size of the compass.

Step Three	Vertically divide the square into two equal sections. Use your ruler to draw a straight line through points where the circles cross on the up/down axis.

Step Four	Use your ruler to draw a straight line from the center of the bottom side of the square to the upper right-hand corner.

Step Five	Now use your ruler to double the length of the bottom of the square, out to the right (just eye it).

Step Six	Set your compass pivot at the center of the bottom of the square. Open the compass to the top right corner above and swing down to the extended lower line. It is not neccessary to complete as much of the circle as I did.

Step Seven	You've now completed the Golden Ratio. A/B=B/C Go ahead and clean up your work as we'll be adding more soon.

Step Eight	Now create a mirror image of what you did in steps 5 & 6. Set your compass pivot to the center of the top side of the square and open it to the bottom right corner.

Step Nine	Draw a straight line between the points where the arcs meet the extended sides.

Step Ten	We now have a golden rectangle (actually two). If your desire was to create a golden rectangle from a square, simply erase the center vertical line (was the right side of the square) and you are done. If you'd like to construct the spiral, leave that line in there.

Step Eleven	Set your compass pivot at the lower right corner of the rectangle and open it to the bottom of the middle vertical line. Spin an arc that crosses the bottom and right sides of the rectangle. Now create the same arc for the other side without disturbing the width of your compass. Draw a straight line between points where the arcs crossed the sides; you now have a square below and a rectangle above.

Step Twelve	Moving counter-clockwise around your rectangle, continue measuring arcs from corners to sides.

Step Thirteen	After you clean up any unneccessary marks, you should have something that looks like this.

Step Fourteen	Set your pivot a the top right corner of the original square and draw an arc from the top left to the bottom right corners.

Step Fifteen	Now do the same for the square on the lower right.



Step Sixteen	Continue counter-clockwise through each square.

Step Seventeen	Don't rush! Be sure to have your pivot in the right spot before making your arc.

Step Eighteen	Eventually, the squares will become too small for our compass.

Step Twenty	By placing our pivot on the top right corner of our original square, we can extend the spiral outwards from the top left corner.

Complete - use the links at right.