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fibonacci numbers

Low
UK/ˌfɪb.əˈnɑː.tʃi ˈnʌm.bəz/US/ˌfɪb.əˈnɑː.tʃi ˈnʌm.bɚz/

Technical/Academic

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Definition

Meaning

A sequence of integers where each number is the sum of the two preceding ones, typically starting with 0 and 1.

A recursively defined integer sequence with deep mathematical properties, often appearing in nature, art, and computer science.

Linguistics

Semantic Notes

Almost exclusively used in mathematics, computer science, and related technical fields. Often capitalised 'Fibonacci'.

Dialectal Variation

British vs American Usage

Differences

No significant lexical or grammatical differences.

Connotations

Identical technical connotations.

Frequency

Slightly more frequent in American academic discourse due to tech industry prevalence.

Vocabulary

Collocations

strong
generatesequence ofcalculaterecursive formula for
medium
studyapplypattern ofseries of
weak
interestingfamousmathematicalclassic

Grammar

Valency Patterns

The Fibonacci numbers appear in...A function to compute Fibonacci numbers...The ratio of successive Fibonacci numbers...

Vocabulary

Synonyms

Strong

golden ratio sequence

Neutral

Fibonacci sequence

Weak

recursive number series

Vocabulary

Antonyms

random numbersnon-recursive sequence

Phrases

Idioms & Phrases

  • “As predictable as the Fibonacci sequence”

Usage

Context Usage

Business

Rare, except in technical analysis of markets (e.g., Fibonacci retracement levels).

Academic

Common in mathematics, computer science, and biology lectures and papers.

Everyday

Virtually never used.

Technical

Core terminology in algorithms, number theory, and design.

Examples

By Part of Speech

verb

British English

  • The algorithm will fibonacci the initial values.

American English

  • The function is designed to fibonacci the input.

adverb

British English

  • The series increased almost fibonaccially.

American English

  • The population grew Fibonacci-fast.

adjective

British English

  • They studied the fibonacci properties of the spiral.

American English

  • We observed a Fibonacci-like growth pattern.

Examples

By CEFR Level

A2
  • Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8.
B1
  • The next Fibonacci number after 8 is 13.
B2
  • Many plants exhibit patterns related to Fibonacci numbers.
C1
  • The efficiency of the recursive algorithm for generating Fibonacci numbers decreases exponentially.

Learning

Memory Aids

Mnemonic

Start with 0 and 1, then add the last two to get the next one: 0, 1, 1, 2, 3, 5, 8, 13...

Conceptual Metaphor

Growth pattern (natural, organic, spiralling expansion).

Watch out

Common Pitfalls

Translation Traps (for Russian speakers)

  • Avoid literal translation of 'numbers' as 'номера'; use 'числа'.
  • Ensure 'Fibonacci' is transliterated as 'Фибоначчи', not translated.

Common Mistakes

  • Pronouncing 'Fibonacci' with a hard 'c' (/k/) instead of /tʃ/.
  • Using singular 'Fibonacci number' when referring to the whole sequence.

Practice

Quiz

Fill in the gap
The famous rabbit problem is used to explain the sequence.
Multiple Choice

What is the defining property of Fibonacci numbers?

FAQ

Frequently Asked Questions

Typically yes, but some definitions start with 1 and 1. The core recursive rule remains the same.

They are observed in the arrangement of leaves on a stem, the branching of trees, the fruitlets of a pineapple, and the flowering of an artichoke.

As Fibonacci numbers increase, the ratio between successive numbers approximates the golden ratio (approximately 1.618).

They are a classic example for teaching recursion, dynamic programming, and algorithm analysis.