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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 | import OAI.Geometry.CylinderCovering.Physical.Minimum
namespace OAI
namespace RadialPhysical.PhysicalMinimum
theorem minimum_edge_one_model : CylinderCovering.Similarity.minimumArea (modelBody false (1/2)) =
Real.sqrt 2 / 4 := by
rw [minimum_modelBody false (by norm_num : (0:ℝ) < 1/2)]
simp only [Bool.false_eq_true, ite_false, height]
ring
theorem minimum_unit_centered_model : CylinderCovering.Similarity.minimumArea (modelBody true 1) =
4 * Real.sqrt 2 := by
rw [minimum_modelBody true (by norm_num : (0:ℝ) < 1)]
simp [height]
end RadialPhysical.PhysicalMinimum
end OAI
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