18. Proportion and scale

18 - 04 THE FIBONACCI NUMBERS:

Till so far as the thirteenth century, geometry was the only real basis for construction. Decimal fractions and algebra were not in common use, and thus never applied to philosophical and aesthetic pursuits.

Leonardo Fibonacci, an Italian merchant-traveller-mathematician, was the first to realize the advantages of the Arabic (decimal) system of numeration over the Roman, and he proposed a series of numbers, that had a close resemblance to the rule of the Golden Section. This the Fibonacci Series, which begins with the number one, and each successive unit is formed by adding together the two preceding numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on. The higher the series goes, the more closely it resembles the Golden Section ratio. It gives us the nearest whole number approximation to mean and extreme ratios.