File size: 618 Bytes
785c727 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | import OAI.Geometry.CylinderCovering.Simplex.ProjectionDefinitions
namespace OAI
noncomputable section
open Set MeasureTheory
namespace CylinderCovering
def RegularMetricNormalizationStatement : Prop :=
∀ v : Fin 4 → Space, AffineIndependent ℝ v →
∀ edge : ℝ, 0 < edge →
(∀ i j : Fin 4, i ≠ j → dist (v i) (v j) = edge) →
Metric.diam (convexHull ℝ (range v)) = edge ∧
volume.real (convexHull ℝ (range v)) = edge ^ 3 / (6 * Real.sqrt 2) ∧
minimumShadowArea (convexHull ℝ (range v)) / 2 = edge ^ 2 / (4 * Real.sqrt 2)
end CylinderCovering
end
end OAI
|