Lo que nadie sabe de la sucesión de Fibonacci 🤫
Derivando・2 minutes read
The Fibonacci sequence is a series of numbers starting with 1 and 1, found in nature and related to the golden ratio. Variants like tribonacci and tetran numbers, as well as concepts like Fibonacci polynomials and Lucas numbers, provide further insights and applications in mathematics.
Insights
- The Fibonacci sequence, known for its appearance in nature and relation to the golden ratio, has extensions such as negative numbers and generalizations like tribonacci and tetran numbers.
- Lucas numbers, a variant of Fibonacci numbers, possess unique properties that intrigue mathematicians due to their close association with the golden ratio, providing a deeper understanding of this numerical phenomenon.
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Recent questions
What is the Fibonacci sequence?
A series starting with 1, 1, with each number being the sum of the previous two.
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Summary
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"Fibonacci Sequence: Nature, Numbers, and Applications"
- The Fibonacci sequence starts with 1 and 1, with each subsequent number being the sum of the previous two, leading to 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on.
- The Fibonacci sequence is famous for its appearance in nature and its relation to the golden ratio.
- A magazine dedicated to the Fibonacci sequence is published by the Fibonacci association in Canada, along with an international conference on Fibonacci numbers and their applications.
- Generalizations of the Fibonacci sequence exist, such as tribonacci numbers (starting with three numbers) and tetran numbers (starting with four numbers).
- The Fibonacci sequence has been extended to negative numbers, with a formula (Binet formula) allowing for the extension to real numbers.
- Fibonacci polynomials have been studied, with each polynomial's value at x=1 corresponding to the Fibonacci number.
- Lucas numbers, a variant of Fibonacci numbers, have properties that make them interesting to mathematicians, with a closer relationship to the golden ratio.
