![]() ![]() How often do the Fibonacci numbers occur? Study the spirals occurring in each of the following plants and count the number of leaves or petals in each. Many of these spirals exhibit characteristics described by Fibonacci numbers. Phyllotactic spirals form a distinctive class of patterns in nature. In botany, the word phyllotaxis describes the arrangement of leaves on a plant stem. The image on the right shows the head of a yellow chamomile with the arrangement of 21 and 13 spirals highlighted. Draw an arc connecting opposite corners of each square to create the Fibonacci spiral, shown in the diagram on the right.įibonacci Spiral Natural Occurrences Yellow chamomile head showing the arrangement in 21 (blue) and 13 (aqua) spirals.įibonacci sequences appear in biological settings, such as branching in trees, arrangement of leaves on a stem, the fruitlets of a pineapple, the flowering of artichoke, an uncurling fern and the arrangement of a pine cone, and the family tree of honeybees.The resulting diagram should look like the tile diagram shown here on the right.Continue outlining and labeling adjacent squares of sizes 5, 8, 13, 21, and continue the sequence as long as there is space on the paper.These outlined squares now provide an edge of length three.These two outlined grids now form an edge of length two. Select a grid square near the center of the paper.Begin with a piece of graph paper printed with a grid pattern. ![]() Tiles and Spirals Fibonacci TilesĬreate a series of tiles based on the Fibonacci numbers as follows: Write out the first 15 terms in the sequence. What is the general rule for obtaining the next number in the sequence? (Answer, the next number in the sequence is the sum of the two preceding numbers) What is the next number in the Fibonacci sequence shown above? (Answer, 21) The numbers making up this sequence are now called Fibonacci numbers. Italian mathematician Fibonacci was studying the growth of a rabbit population based on idealized assumptions when he wrote the sequence 0, 1, 1, 2, 3, 5, 8, 13, …. These have many applications in nature and mathematics. These activities introduce the Fibonacci numbers, the golden ratio, and their interrelationship. ![]()
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