Theratio between one number and its predecessor in the seriesapproaches 1.6180 as the numbers increase (5/3=1.667,8/5=1.600, 13/8=1.625, 21/13=1.615, 34/21=1.619, 55/34=1.618).This magical ratio turns out to be a universal measure ofbeauty, which the Greeks called the 'golden section' or 'divineproportion.' Most of the ancient Greek temples, including theParthenon in Athens, obey this law of divine proportion. In fact, such a law seems to govern the Fibonacci numbers. There must be a general law of symmetry,aesthetics and beauty. Although exceptions tothe Fibonacci rule are not difficult to find, the 'numbers oflife' occur so frequently in nature that they cannot beexplained by chance. On average, daisieswill have 21, 34, 55 or 89 petals, chrysanthemums 21, and somesenecio species either 13 or 21 petals. Pick some randomflowers and count their colored petals. Yet, Fibonacci numbers appear not only in the leaves and conesof plants, but also in flower blossoms. The cones of pines, in contrast, use 34 scales in 13windings. In the cones ofspruce and fir trees, 21 scales turn eight times for oneperiod. In cabbage, asters or hawkweeds, for example, eightleaves complete a period after three circles. Other plants show widely varyingperiodicities that are nevertheless consistent with the numbersof life. In other words, the periodicity consists of twowindings and five leaves. In willows, roses, and many other plants, consecutiveleaves follow each other by an average angle of 144*.Therefore, five leaves account for 720* or two completecircles. The leaves of many plant speciessprout in well-defined geometrical arrays spirally from thestem. Interestinglyenough, the 'numbers of life' appear throughout biology. It wouldn't be a marvel, though, if these numbers were foundonly in the growth of a rabbit population. Rabbits helped Fibonacci to discover one of the greatmarvels of nature. One month later, the count was threeand five, then five and eight, eight and 13, 13 and 21, and soforth. After three months, there were two adult pairsand three juvenile pairs. After twomonths, the count was one adult pair (the original) and twojuvenile pairs. He wrote in the Book of the Abacus, in 1202: 'Someone placed apair of rabbits in a certain place, enclosed on all sides by awall, to find out how many pairs will be born in the course ofone year, it being assumed that every month a pair of rabbitsproduces another pair, and that rabbits begin to bear young twomonths after their own birth.' When Fibonacci checked after onemonth, he found one adult pair and one juvenile pair. Pisano, the first greatmathematician of medieval Europe, discovered these magicalnumbers by analyzing the birth rate of rabbits. This looks likea simple pattern, yet it determines the shape of a mollusk'sshell and a parrot's beak, or the sprouting of leaves from thestem of any plant-a revelation as surprising to me, at 16, asit probably was to Leonardo Pisano-later known asFibonacci-almost 800 years ago. Inthe Fibonacci sequence, every number (after the first two) isthe sum of the two preceding numbers: 0, 1, 1, 2, 3, 5, 8, 13,21, 34, 55, 89, 144, 233, 377, 610, and so on. The pattern of the 'numbers of life' is elegantly simple. Yet, when I was about 16, one such law, the'numbers of life' or Fibonacci sequence, awakened my interestin biology-an interest that carried me all the way through aPh.D. It was hard forme to grasp at that time-and somehow still is today-that thestructures of plants and animals alike seem to obeymathematical laws. More important, I realizedthat mathematical beauty exists not only in mere numbers-it isalso an intrinsic feature of the living world. Withhis help, I started to recognize that abstract mathematicalfigures can have an inherent beauty. But he aroused mycuriosity for the obscure world of numbers and equations. I was determined to become a cartographer, until my highschool mathematics teacher forever changed that plan.

I knew every valley, every mountain and everytown. I spent countless hours under a dimlight bent over unfolded maps from all over my nativeSwitzerland.

Fibonacci sequence in nature video