Fibonacci Series

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Algebra I

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Fibonacci Series

Fibonacci Series

The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric figures such as the pentagon, pentagram, decagon and dodecahedron. It is denoted , or sometimes .

Biography Fibonacci was an Itallian number theorist. It is believed that Leonardo Pisano was born in the 13th century, in 1170 and he died in 1250. He was born in Italy but he had his education in north africa. There is not much known of him and his family. Much of the information about Fibonacci has been gathered by his autobiographical notes which he included in his books.

Golden Ratio

The Fibonacci sequence was the outcome of a mathematical problem about rabbit breeding. The problem was this: Beginning with a single pair of rabbits (one male and one female), how many pairs of rabbits will be born in a year, assuming that every month each male and female rabbit gives birth to a new pair of rabbits, and the new pair of rabbits itself starts giving birth to additional pairs of rabbits after the first month of their birth?

There are 34 spirals that turn clockwise and 21 spirals that turn counterclockwise. The counter-clockwise spirals appear to grow according to the golden ratio.

A slice through a Nautilus shell reveals golden spiral construction principle.

Brocolli/Cauliflower. Each floret is peaked and is an identical but smaller version of the whole thing and this makes the spirals easy to see.

The Fibonacci Sequence is the series of numbers:0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...The next number is found by adding up the two numbers before it.t here



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