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The first 300 Fibonacci numbers are here and some questions for you to answer. But Fibonacci does what mathematicians often do at first, simplify the problem and see what happens - and the series bearing his name does have lots of other interesting and practical applications as we see later.

The Family Tree of humans involves a different sequence to the Fibonacci Numbers. Try searching it to see where you can spot the golden section occurring and the Fibonacci numbers.

4 is not a Fibonacci number!

  • Some species are very precise about the number of petals they have - eg buttercups, but others have petals that are very near those above, with the average being a Fibonacci number.
  • Fibonacci numbers can also be seen in the arrangement of seeds on flower heads.
  • At all stages the Fibonacci Spirals can be seen.

Which plants show Fibonacci spirals on their flowers?

Are there flowers shown with other numbers of petals which are not Fibonacci numbers? Pine cones Pine cones show the Fibonacci Spirals clearly.

Leaf arrangements Also, many plants show the Fibonacci numbers in the arrangements of the leaves around their stems. Leaves per turn The Fibonacci numbers occur when counting both the number of times we go around the stem, going from leaf to leaf, as well as counting the leaves we meet until we encounter a leaf directly above the starting one.

Notice that 2, 3 and 5 are consecutive Fibonacci numbers.

 

The Elliott wave theory is the basis of a technical analysis technique for predicting the behavior and market trends in the stock market, invented by Ralph Nelson Elliott in 1939. It is based on the belief that markets exhibit well-defined wave patterns that can be used to predict market direction: specifically that stock prices are governed by cycles which adhere to the Fibonacci sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, etc. It claims that the stock market, acting as a meter for mob or crowd psychology, displays many of the same geometric features as other organic structures. Proponents of the Elliott wave theory claim that the pattern is exhibited repeatedly in past market price patterns, and that the fractal nature of such patterns creates a repetition of them on varying levels of order and magnitude.


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