Spiritual+and+Aesthetic+Principles

 Directly related to the Golden Section is the Fibonacci Series, a mathematical concept which was first observed by Leonardo Fibonacci (Leonardo da Pisa) in the thirteenth century. Since his time, biologists have established that it is also a basic principle in nature. The Fibonacci Series is found in numerous natural formations; the leaves on trees, the skins of onions, the arrangement of pads on cats’ feet, the shells of microscopic protozoa, and many organically produced spiral structures. Its production is deceptively simple. The last two numbers in a sequence are added together to give the next number, and so on, i.e. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 etc. It is directly related in geometry to the Golden Section by way of the equiangular spiral, a geometrical form which determines, among other things, the shape of rams’ horns and of nautilus shells. Each section of the spiral relates to the next section in the sequence in the same progression as the Fibonacci Series. As the numbers rise, their ratios correspondingly creep closer and closer to the Golden Section. In recent architecture, this proportional system was applied by Le Corbusier in his modulor, a method of determining harmonious proportion based upon the Golden Section and the Fibonacci Series.
 * The Golden Section** - the pentagram is fundamental to the geometry of harmonious proportion, since it is the figure from which the Golden Section is derived. This is the ratio between the side of the pentagon drawn between the points of a pentagram, and the side of the pentagram itself. The actual figure is 1:1.618014, a ratio which produces shapes both aesthetically pleasing and of mystical importance, and which is found to underlie the proportions of many ancient Greek and Roman temples. Renaissance painters like Leonardo and Raphael constantly used this geometry as a basis for their work, and it has been continued in unbroken tradition through to the present day.

Buckminster Fuller was a man born out of his time. He understood the effects of shape and geometry better than any person of his period, and even today some of his research from the twenties and thirties is only just being recognised and validated. His geodesic dome or bubble would create a very harmonious environment which is easy to engineer, is economical on natural resources and is very strong and cheap to build.