Download lean/OAI/Geometry/CylinderCovering/Angular/ApertureDefinitions.lean from roseking/openAI-math-dataset: direct link, hf CLI and curl.
- Browser
- Download file 431 Bytes
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https://huggingface.co/datasets/roseking/openAI-math-dataset/resolve/main/lean/OAI/Geometry/CylinderCovering/Angular/ApertureDefinitions.lean
- Command line
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hf download hf://datasets/roseking/openAI-math-dataset/lean/OAI/Geometry/CylinderCovering/Angular/ApertureDefinitions.lean
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curl -L -o ApertureDefinitions.lean https://huggingface.co/datasets/roseking/openAI-math-dataset/resolve/main/lean/OAI/Geometry/CylinderCovering/Angular/ApertureDefinitions.lean
431 Bytes
| import Mathlib | |
| namespace OAI | |
| noncomputable section | |
| namespace AngularAperture | |
| def transverse (y : ℝ) : ℝ := y ^ 2 / 4 + y ^ 4 | |
| def profile (q : ℝ) : ℝ := (q ^ 2 + q ^ 4) / 16 | |
| def level (τ η q s : ℝ) : ℝ := s - 1 / 2 - τ ^ 2 * (transverse (q * s) + η) | |
| def aperture (τ η b q : ℝ) : Set ℝ := | |
| {s | 0 ≤ s ∧ s ≤ b ∧ s ≤ 1 / 2 + τ ^ 2 * (transverse (q * s) + η)} | |
| end AngularAperture | |
| end | |
| end OAI | |