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Binet's formula

formula used to find the nth term of the Fibonacci sequence
Intangible Formula Q54539168

Facts

5 properties
Instance of
formula, theorem[2]
Defining formula
F_n = \frac{\phi ^n -(-\phi)^{-n}}{\phi -(-\phi)^{-1}}[5]
Different from
Binet equation[4]
Maintained by WikiProject
WikiProject Mathematics[6]
Named after
Jacques Philippe Marie Binet[3]
🏷️ Also known as
en Binet's Fibonacci number formula en Binet's formula it formula di Binet it formula di Binet per la successione di Fibonacci ro Formula lui Binet ru формула Бине
🔖 Identifiers · 1
MathWorld ID
BinetsFibonacciNumberFormula

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Summary

Binet's formula is a formula[1].

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [2] ↑ . wikidata.org.
  2. [3] ↑ . wikidata.org.
  3. [4] ↑ . wikidata.org.
  4. [5] ↑ . wikidata.org.
  5. [6] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

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Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Binet's formula. Retrieved November 9, 2026, from https://4ort.xyz/entity/binet-s-formula
MLA “Binet's formula.” 4ort.xyz Knowledge Graph, 4ort.xyz, 9 Nov. 2026, https://4ort.xyz/entity/binet-s-formula.
BibTeX @misc{4ortxyz_binet-s-formula_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Binet's formula}}, year = {2026}, url = {https://4ort.xyz/entity/binet-s-formula}, note = {Accessed: 2026-11-09}}
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