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785c727 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | import OAI.Geometry.CylinderCovering.Angular.EndpointDefinitions
import OAI.Geometry.CylinderCovering.Angular.FamilyDefinitions
namespace OAI
noncomputable section
namespace CylinderCovering
def AngularEndpointStatement : Prop :=
∀ k : ℕ, 14000 ≤ k →
∃ C : Fin (2*(k^2+1)) → TriangularCovering.TriCylinder,
TriangularCovering.AngularFamily.PrescribedFamily C (1/(k:ℝ))
(fun j => AngularEndpoint.boundary (k^2) j)
(fun j => AngularEndpoint.boundary (k^2) (j+1))
(fun j => AngularEndpoint.alpha (k^2) j)
(fun j => AngularEndpoint.beta (k^2) j)
(fun j => AngularEndpoint.radius (1/(k:ℝ)) (1/1000) (k^2) j) ∧
TriangularCovering.Covers C ∧
|TriangularCovering.totalArea C/TriangularCovering.H -
(1/2-(13/6000:ℝ)*(1/(k:ℝ))^2)| ≤ 14*(1/(k:ℝ))^4 ∧
TriangularCovering.totalArea C < TriangularCovering.A_min/2 ∧
TriangularCovering.relativeCost C < 1/2
end CylinderCovering
end
end OAI
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