`bandgapFrequency`

definition

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module: IndisputableMonolith.Physics.PhotonicsMetamaterialFromPhi
domain: Physics
line: 27 · github
papers citing: none yet

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IndisputableMonolith.Physics.PhotonicsMetamaterialFromPhi on GitHub at line 27.

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formal source

  24
  25theorem metamaterialTypeCount : Fintype.card MetamaterialType = 5 := by decide
  26
  27noncomputable def bandgapFrequency (k : ℕ) : ℝ := phi ^ k
  28
  29theorem bandgapRatio (k : ℕ) :
  30    bandgapFrequency (k + 1) / bandgapFrequency k = phi := by
  31  unfold bandgapFrequency
  32  have hpos := pow_pos phi_pos k
  33  rw [pow_succ, div_eq_iff hpos.ne']
  34  ring
  35
  36structure PhotonicsMetamaterialCert where
  37  five_types : Fintype.card MetamaterialType = 5
  38  phi_ratio : ∀ k, bandgapFrequency (k + 1) / bandgapFrequency k = phi
  39
  40noncomputable def photonicsMetamaterialCert : PhotonicsMetamaterialCert where
  41  five_types := metamaterialTypeCount
  42  phi_ratio := bandgapRatio
  43
  44end IndisputableMonolith.Physics.PhotonicsMetamaterialFromPhi

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