# Sacred Geometry

25 24 the goLden SeCtion and other important roots A pentagram inside a pentagon is shown opposite. A simple knot, carefully tied in a ribbon or strip of paper and pulled tight and flattened out makes a perfect pentagon. Try it some time In the main diagram opposite you can see that pairs of lines are each dashed in different ways. The length of each such pair of lines is in the golden section ratio, 1, where pronounced phi can be either 0.618 or 1.618 more exactly .61803399.... Importantly, divides a line so that the ratio of the lesser part to the greater part is the same as the ratio of the greater part to the whole. No other proportion behaves so elegantly around unity. For instance, l 1.618 is 0.618 and 1.618 x 1.618 2.618. So one over is minus 1 and x is one plus The golden section is one of three simple proportions found in the early polygons opposite below. With edgelengths 1, a square produces an internal 2, a pentagram 1.618, and a hexagon 3. Although 2 and 3 are found widely in the animal, vegetable and mineral kingdoms, appears predominantly in organic life and only rarely in the mineral world. All these proportions are employed in good design. Many familiar objects from cassettes to credit cards and Georgian front doors are rectangles. Neighbouring terms in the Fibonacci Series 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... adding last two numbers to get the next increasingly approximate . For the keen 51. 1 2