Now that we have the Golden Rectangle to hand it is trivial to create an approximation of the Golden Spiral. This can be done by drawing arcs though the squares with a radius equal to the side of the square. These arcs (with radii) are shown in gold in the images below.
STEP 1: Starting from the centre we draw an arc with radius equivalent to 1.
STEP 2: We draw another arc with radius equivalent to 1 through the second square.
STEP 3: We now draw a third arc through the third circle, this time with radius 2.
STEP 4: We continue this process as we proceed through the squares as shown. This can be continued until we have done this for all the squares we have available.
COMPLETED GOLDEN SPIRAL
Now that we have drawn the arcs through all the available squares, you should now have something similar to the following.
You can, of course, remove the construction lines we have used so far to see the Golden Spiral alone within the Golden Rectangle as below. We are now free to explore the interesting properties of this shape more fully.
