Definition

1. 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

1. a sequence of numbers in which each number equals the sum of the two preceding numbers