fibonacci sequence
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Definition
- Noun:
- A specific integer sequence: The Fibonacci sequence is an infinite sequence of natural numbers where each term after the first two is the sum of the two preceding ones. It typically starts with 0 and 1 (or sometimes 1 and 1).
Usage
- The Fibonacci sequence is a fundamental concept in mathematics and computer science.
- It is used to describe patterns in nature, such as the arrangement of leaves, the flowering of an artichoke, or the spiral of a nautilus shell.
- In mathematics, it is defined by the recurrence relation: F(n) = F(n-1) + F(n-2), with seed values F(0)=0, F(1)=1.
Examples
- Noun:
Advanced Usage
- "Golden Ratio Connection": As the Fibonacci sequence progresses, the ratio of successive terms approximates the golden ratio (φ ≈ 1.618).
- In Programming: Often used in teaching recursion.
Variants and Related Words
- Fibonacci number (n): An individual number within the Fibonacci sequence.
- Fibonacci spiral (n): A logarithmic spiral whose growth factor is related to the golden ratio, often constructed using Fibonacci numbers.
Synonyms
- Fibonacci series: (Often used interchangeably with "Fibonacci sequence," though a "series" technically implies a sum of terms).
- Fibonacci progression: (A less common synonym).
Related Phrases/Idioms
(This term is a technical mathematical concept and is not typically used in idiomatic expressions. However, it appears in descriptive phrases.) - Follows a Fibonacci pattern: Describes a natural or designed object that exhibits growth or structure based on this sequence. The pinecone's scales follow a Fibonacci pattern.
Noun
- a sequence of numbers in which each number equals the sum of the two preceding numbers