# Golden Section

58 aPPenDix vi More lucas Magic In the early 1990s English researcher Robin Heath observed the strange fact that all of the marriage numbers of the Sun, Moon and Earth can be reduced to combinations of the operation of the Golden Section around the key numbers 18 and 19. The evidence for the favour that the Sun and Moon have for 18 and 19 is indicated both by the Metonic Cycle, which produces full moons at the same calendar dates 19 years later, and the Saros Eclipse Cycle, which results in similar eclipses repeating every 18 years. In addition, the Moons Nodes, the crossing points of the Solar and Lunar orbits as viewed from Earth, take 18.618 years to rotate once around the heavens, or 18 plus the Lesser golden mean. Heath made the startling observation that this same number squared produces 346.63, a highly accurate value for the Eclipse Year in days, which is the length of time it takes for the Sun to return to the same Moons node the nodes of course rotating slowly in the opposite direction to the Sun, Moon, and planets. Adding the magic number 18.618 to this produces 365.25, the number of days in a Solar Year, also 18.618 x 19.618. Finally, adding 18.618 again we obtain 383.87, which is 13 lunations, or the number of days between 13 full moons, also 18.618 x 20.618. Recalling that 18 is a Lucas number 18 F6 F6, we may rephrase the already mentioned expressions thus Eclipse Year 18.618 x 18.618 days F6 F6 F12 days Solar Year 18.618 x 19.618 days 18 F118 F which reduced by Lucas magic F6 F6 F1F6 F6 F days further expressed by Benjamin Bryton as Fn Fn 1 Fn Fn 5, 7, 12 6, 8, 13 note here the structure of the scale 13 Moons 18.618 x 20.618 days F6 F6 F1F6 F6 F2 days aPPenDix vii PhylloTaxis angles 12 180o elm, lime, birch, basswoods, cereals, grapes, some grasses. 13 120o beech, hazel, alder, fiddleneck, blackberry, sedge, tulip, some grasses. 25 144o oak, cherry, apple, holly, plum, apricot, coast live oak, California bay, pepper tree, manzanita, common groundsel, mustard, toyon, madrona. 38 135o poplar, pear, weeping willow, rose, petty spurge, locust thorn phyllotaxy, cabbage, radish, flax, plantains. 513 138.5o almond, bottlebrush, pussy willow, spruce, jasmine, cranberry, leeks. 1334 137.6o pines, magnolia.