`SolarWindType`

definition

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module: IndisputableMonolith.Astrophysics.SolarWindFromPhiLadder
domain: Astrophysics
line: 23 · github
papers citing: none yet

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IndisputableMonolith.Astrophysics.SolarWindFromPhiLadder on GitHub at line 23.

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formal source

  20namespace IndisputableMonolith.Astrophysics.SolarWindFromPhiLadder
  21open Constants
  22
  23inductive SolarWindType where
  24  | quiet | slow | intermediate | fast | extreme
  25  deriving DecidableEq, Repr, BEq, Fintype
  26
  27theorem solarWindTypeCount : Fintype.card SolarWindType = 5 := by decide
  28
  29/-- Adjacent solar wind speeds at phi-ladder rungs. -/
  30noncomputable def solarWindSpeed (k : ℕ) : ℝ := phi ^ k
  31
  32theorem solarWindSpeedRatio (k : ℕ) :
  33    solarWindSpeed (k + 1) / solarWindSpeed k = phi := by
  34  unfold solarWindSpeed
  35  have hpos := pow_pos phi_pos k
  36  rw [pow_succ, div_eq_iff hpos.ne']
  37  ring
  38
  39structure SolarWindCert where
  40  five_types : Fintype.card SolarWindType = 5
  41  phi_ratio : ∀ k, solarWindSpeed (k + 1) / solarWindSpeed k = phi
  42
  43noncomputable def solarWindCert : SolarWindCert where
  44  five_types := solarWindTypeCount
  45  phi_ratio := solarWindSpeedRatio
  46
  47end IndisputableMonolith.Astrophysics.SolarWindFromPhiLadder

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