![]() These numbers, 34 and 21, are numbers in the Fibonacci series, and their ratio 1.6190476 closely approximates Phi, 1.6180339.įollow our Number Sense blog for more math activities, or find a Mathnasium tutor near you for additional help and information. The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. DNA moleculesĮven the microscopic realm is not immune to Fibonacci. When a hawk approaches its prey, its sharpest view is at an angle to their direction of flight - an angle that's the same as the spiral's pitch. And as noted, bee physiology also follows along the Golden Curve rather nicely. Following the same pattern, females have 2, 3, 5, 8, 13, and so on. Thus, when it comes to the family tree, males have 2, 3, 5, and 8 grandparents, great-grandparents, gr-gr-grandparents, and gr-gr-gr-grandparents respectively. Males have one parent (a female), whereas females have two (a female and male). In addition, the family tree of honey bees also follows the familiar pattern. The answer is typically something very close to 1.618. ![]() The most profound example is by dividing the number of females in a colony by the number of males (females always outnumber males). The Fibonacci sequence may simply express the most efficient packing of the seeds (or scales) in the space available.Speaking of honey bees, they follow Fibonacci in other interesting ways. ![]() As each row of seeds in a sunflower or each row of scales in a pine cone grows radially away from the center, it tries to grow the maximum number of seeds (or scales) in the smallest space. That is, these phenomena may be an expression of nature's efficiency. The same conditions may also apply to the propagation of seeds or petals in flowers. ![]() Given his time frame and growth cycle, Fibonacci's sequence represented the most efficient rate of breeding that the rabbits could have if other conditions were ideal. Why are Fibonacci numbers in plant growth so common? One clue appears in Fibonacci's original ideas about the rate of increase in rabbit populations. The number of rows of the scales in the spirals that radiate upwards in opposite directions from the base in a pine cone are almost always the lower numbers in the Fibonacci sequence-3, 5, and 8. ![]() The corkscrew spirals of seeds that radiate outward from the center of a sunflower are most often 34 and 55 rows of seeds in opposite directions, or 55 and 89 rows of seeds in opposite directions, or even 89 and 144 rows of seeds in opposite directions. Similarly, the configurations of seeds in a giant sunflower and the configuration of rigid, spiny scales in pine cones also conform with the Fibonacci series. All of these numbers observed in the flower petals-3, 5, 8, 13, 21, 34, 55, 89-appear in the Fibonacci series. There are exceptions and variations in these patterns, but they are comparatively few. The number 2 stands for a square of 2 by 2 and so on. The number 1 in the sequence stands for a square with each side 1 long. See the picture below which explains the fibonacci spiral. Some flowers have 3 petals others have 5 petals still others have 8 petals and others have 13, 21, 34, 55, or 89 petals. The explanation can be seen if the sequence is depicted visually since then it becomes clear that the sequences describes a growth pattern in nature. For example, although there are thousands of kinds of flowers, there are relatively few consistent sets of numbers of petals on flowers. ![]()
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