The Fibonacci sequence begins with 1, 1. From there on, each term is the sum of the previous two terms. The first few terms of the sequence are:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, …
The Fibonacci sequence appears often in nature. The sequence is found in the spiral patterns of pine cones and flowers. The number of spirals traced one way will usually be a Fibonacci number. The number of spirals traced the other way will be an adjacent Fibonacci number. Count the spirals in this pine cone:
and in this flower:
The ratios of adjacent terms of the fibonacci sequence are also interesting.
1 / 1 = 11 / 2 = .52 / 3 = .6666673 / 5 = .65 / 8 = .6258 / 13 = .61538513 / 21 = .61904721 / 34 = .61764734 / 55 = .61818255 / 89 = .61797789 / 144 = .618056144 / 233 = .618025233 / 377 = .618037377 / 610 = .618033…approaching | 1 / 1 = 12 / 1 = 23 / 2 = 1.55 / 3 = 1.6666678 / 5 = 1.613 / 8 = 1.62521 / 13 = 1.61538534 / 21 = 1.61904755 / 34 = 1.61764789 / 55 = 1.618182144 / 89 = 1.617977233 / 144 = 1.618056377 / 233 = 1.618025610 / 377 = 1.618037…approaching |