# Golden Section

8 9 Phi on The Plane pentagrams and golden rectangles Moving from the onedimensional line onto the twodimensional plane, the golden section is not difficult to discover. Starting with a square, an arc centred on the midpoint of its base swung down from an upper corner easily produces a large golden rectangle below left. Importantly, the small rectangle which we have added to the square is also a golden rectangle. Continuing this technique creates a pair of these smaller golden rectangles opposite top left. Conversely, removing a square from a golden rectangle leaves a smaller golden rectangle, and this process can be continued indefinitely to produce a golden spiral opposite lower right, cover. The golden section, which as we have seen unifies parts and whole like no other proportion, is intimately involved with the natural geometry of the pentagram opposite lower left, the very emblem of life. Every point of intersection creates lengths which are in golden relationships to one another. An arm of a pentagram contains the key to another golden section spiral as a continuous series of increasing or shrinking golden triangles opposite top right. The golden cut of a line may be achieved by building a double square on the line and following the diagram below right. The basic operation of the golden section on the plane, showing features of golden rectangles, golden triangles, and the F 1 relation between the diagonal of a pentagram and the edge of its enclosing pentagon. See if you can work out what the two unlabelled measures are in the diagram below. removing squares using rabatment to create a grid finding the occult centre the golden section in the pentagram the Lesser and Greater derived from a square the golden triangle