# Golden Section

10 11 The fibonacci sequence stepping stones to gold Nature widely expresses the golden section through a very simple series of whole numbers. The astounding Fibonacci number series 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377... is both additive, as each number is the sum of the previous two, and multiplicative, as each number approximates the previous number multiplied by the golden section. The ratio becomes more accurate as the numbers increase. Inversely, any number divided by its smaller neighbor approximates , alternating as more or less than , forever closing in on the divine limit opposite lower right. Each Fibonacci number is the approximate geometric mean of its two adjacent numbers see Cassini formula, page 53. Although officially recognised later, the series appears to have been known to the ancient Egyptians and their Greek students. Ultimately Edouard Lucas in the 19th century named the series after Leonardo of Pisa c. 11701250, also known as Fibonacci son of the bull, who made the series famous through his solution of a problem regarding the breeding of rabbits over a years time right. Fibonacci numbers occur in the family trees of bees, stock market patterns, hurricane clouds, selforganising DNA nucleotides, and in chemistry as with the uranium oxide compounds U2O5, U3O8, U5O13, U8O21, and U13O34 intermediate between UO2 UO3. A turtle has 13 horn plates on its shell, 5 centred, 8 on the edges, 5 paw pins, and 34 backbone segments. There are 144 vertebrae in a Gabon snake, a hyena has 34 teeth, and a dolphin 233. Many spiders have 5 pairs of extremities, 5 parts to each extremity, and a belly divided into 8 segments carried by its 8 legs.