Download lean/OAI/Geometry/CylinderCovering/Angular/CubicAreaDefinitions.lean from roseking/openAI-math-dataset: direct link, hf CLI and curl.
- Browser
- Download file 532 Bytes
-
https://huggingface.co/datasets/roseking/openAI-math-dataset/resolve/main/lean/OAI/Geometry/CylinderCovering/Angular/CubicAreaDefinitions.lean
- Command line
-
hf download hf://datasets/roseking/openAI-math-dataset/lean/OAI/Geometry/CylinderCovering/Angular/CubicAreaDefinitions.lean
-
curl -L -o CubicAreaDefinitions.lean https://huggingface.co/datasets/roseking/openAI-math-dataset/resolve/main/lean/OAI/Geometry/CylinderCovering/Angular/CubicAreaDefinitions.lean
532 Bytes
| import OAI.Geometry.CylinderCovering.Angular.MarginsDefinitions | |
| namespace OAI | |
| noncomputable section | |
| namespace CylinderCovering.Cubic | |
| def speedSq (l r : ℝ) : ℝ := alpha l r ^ 2 + 2 * beta l r ^ 2 | |
| def areaTerm (eps l r : ℝ) : ℝ := | |
| (r - l) * cap eps l r ^ 2 / Real.sqrt (1 + eps ^ 2 * speedSq l r) | |
| def areaDensity (q : ℝ) : ℝ := -(1 / 8 : ℝ) - q ^ 2 / 4 + 7 * q ^ 4 / 8 | |
| def areaSum (eps : ℝ) (N : ℕ) : ℝ := | |
| ∑ j : Fin N, areaTerm eps (node N j) (node N (j + 1)) | |
| end CylinderCovering.Cubic | |
| end | |
| end OAI | |