Theorems · Theorem · number theory
Real.coe_fib_eq
∀ (n : ℕ), ↑(Nat.fib n) = (Real.goldenRatio ^ n - Real.goldenConj ^ n) / √5
Binet's formula as a dependent equality.
- Defined in
- Mathlib.NumberTheory.Real.GoldenRatio
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Real.sqrtstatement and proof · cited by 545
- Nat.fibstatement · cited by 74
- Real.goldenRatiostatement and proof · cited by 25
- Real.goldenConjstatement and proof · cited by 23
- Real.coe_fib_eq'proof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- tendsto_fib_succ_div_fib_atTopproof · cited by 1
- Real.fib_succ_sub_goldenRatio_mul_fibproof · cited by 0
- Real.coe_intFib_eqproof · cited by 0