fibonacci sequence
LowTechnical/Academic
Definition
Meaning
An infinite sequence of numbers in which each number (after the first two) is the sum of the two preceding numbers, typically starting with 0 and 1.
The sequence (0, 1, 1, 2, 3, 5, 8, 13, ...), named after the Italian mathematician Leonardo Fibonacci, which appears in many biological settings and mathematical phenomena.
Linguistics
Semantic Notes
While a proper noun, it is not capitalised in general technical writing, except when 'Fibonacci' is used as a modifier (e.g., Fibonacci numbers). It denotes both the specific mathematical sequence and the concept applied in broader contexts.
Dialectal Variation
British vs American Usage
Differences
No significant lexical differences; standard term in both varieties.
Connotations
Identical technical, mathematical connotations.
Frequency
Equally low-frequency and specialised in both dialects.
Vocabulary
Collocations
Grammar
Valency Patterns
[the] Fibonacci sequence + [verb: appears, recurs, grows]to + [verb: calculate, generate] + the Fibonacci sequencethe Fibonacci sequence + in + [noun: nature, art, mathematics]Vocabulary
Synonyms
Neutral
Weak
Usage
Context Usage
Business
Rare, except in quantitative finance or technical analysis where Fibonacci retracements are used.
Academic
Common in mathematics, computer science, and certain life sciences.
Everyday
Very rare outside specific educational or hobbyist contexts.
Technical
Standard term in mathematics, computer algorithms, and design theory.
Examples
By Part of Speech
adjective
British English
- The algorithm uses a Fibonacci-style recursion.
- A Fibonacci-based retracement level was identified.
American English
- The pattern followed a Fibonacci-type progression.
- He applied a Fibonacci-esque approach to the design.
Examples
By CEFR Level
- A sunflower often has seeds in a Fibonacci sequence.
- The rabbits in the famous problem produce a Fibonacci sequence.
- Computer scientists study the Fibonacci sequence to understand recursive algorithms.
- The apparent ubiquity of the Fibonacci sequence in phyllotaxis continues to fascinate biologists and mathematicians alike.
Learning
Memory Aids
Mnemonic
Think: 'FIBO' - 'First I, Before Others' - the next number is the sum of the two before it.
Conceptual Metaphor
A SELF-GENERATING PATH (each step builds on the previous two).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Do not translate 'Fibonacci' as 'фибоначчиевый' (calque). Use the established term 'последовательность Фибоначчи'.
- Avoid interpreting 'sequence' as 'секвенция' (rare in Russian mathematics); 'последовательность' is correct.
Common Mistakes
- Incorrect capitalisation: 'fibonacci Sequence' (should be 'Fibonacci sequence').
- Mispronunciation: /faɪˈboʊnɑːtʃi/ instead of /ˌfɪbəˈnɑːtʃi/.
- Incorrect starting numbers: stating it begins with 1,1 instead of 0,1 (both conventions exist, but 0,1 is standard in mathematics).
Practice
Quiz
What are the first three numbers (starting with 0) of the Fibonacci sequence?
FAQ
Frequently Asked Questions
In modern mathematics, it standardly begins with F_0 = 0 and F_1 = 1. Some older or applied texts may start with 1, 1.
It is often observed in the arrangement of leaves (phyllotaxis), the branching of trees, the fruitlets of a pineapple, and the spirals of sunflower seeds and pinecones.
The ratio of consecutive Fibonacci numbers (e.g., 8/5, 13/8) approximates the Golden Ratio (φ ≈ 1.618), and the approximation becomes more precise as the numbers increase.
Leonardo Fibonacci was a 13th-century Italian mathematician who introduced the sequence to Western European mathematics in his book Liber Abaci, though it was known earlier in Indian mathematics.