recognition /
Geometry /
Geometry.Schlaefli /
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formal statement (Lean)
99 theorem deficit_eq (h : SimplicialHingeData) :
100 h.deficit = 2 * Real.pi - h.totalTheta := rfl
proof body
Term-mode proof.
101
102 end SimplicialHingeData
103
104 /-! ## §2. Variational data
105
106 For Schläfli's identity we need derivatives of `θ_h` with respect to each
107 edge length `L_e`. We package these as a matrix of real numbers, one per
108 (hinge, edge) pair. The identity below constrains this matrix. -/
109
110 /-- A matrix of deficit-angle derivatives: `dThetadL h e` is intended
111 to be `∂(totalTheta h) / ∂(len e)`. -/
depends on (23)
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deficit
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