# Sacred Geometry

27 26 Some SPeCiaL SPiraLS and how to draw them Spirals are marvellous forms which nature uses at every scale. Three have been selected for this book which give the impression of a spiral from multiple arcs of circles. The first is the Greek Ionic volute shown top left. This is quite hard to draw and the secret lies in the small key shown above it. The dotted lines in the main drawing show the radii of the arcs and give clues to the centres. Its not as hard as it looks Regular spirals such as the one shown top right also need a key. This can simply be two dots, a triangle, a square, a pentagon or a hexagon as shown. The more points you have the more perfect the spiral will be. Simply draw the tiny key and open the compasses wide to draw your first arc until it lines up with the next point of the key. Now move the compass point nearer to the arc, reduce the angle to fit and draw the next section. It sounds much harder than it is if you try it you will soon get the idea. The bigger the key the wider the coils. Now look at the Ionic volute key again can you see what is happening The bottom picture shows a golden section spiral, common throughout the natural world and an example of an exponential spiral. A golden section rectangle has the special property that removing a square from it produces another golden section rectangle, and the golden section spiral is formed by removing successive squares and filling each with a quarter arc. Greek Ionic Volute Spiral with secret key of compass positions above Regular Spiral based on a hexagon of compass positions Golden Section Spiral