{
  "$schema": "../../../schemas/mko-v0.3.schema.json",
  "schema_version": "mko-v0.3",
  "id": "mko-right-triangle",
  "semantic_family_id": "sf-right-triangle",
  "type": "definition",
  "version": "0.5.0",
  "language": "zh-Hant",
  "titles": { "zh-Hant": "直角三角形", "en": "Right triangle" },
  "summary": { "zh-Hant": "具有一個內角為直角的三角形。" },
  "statement": { "zh-Hant": "若三角形的一個內角等於九十度，或以弧度表示為 π/2，則此三角形稱為直角三角形。" },
  "formula": {
    "tex": "\\gamma=\\frac{\\pi}{2}",
    "mathml": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>γ</mi><mo>=</mo><mfrac><mi mathvariant=\"normal\">π</mi><mn>2</mn></mfrac></mrow></math>",
    "semantic_ast": {
      "type": "equation",
      "lhs": { "type": "symbol", "name": "gamma", "glyph": "γ" },
      "rhs": {
        "type": "fraction",
        "numerator": { "type": "constant", "name": "pi", "glyph": "π" },
        "denominator": { "type": "number", "value": 2 }
      }
    },
    "compiler": {
      "id": "ocme-formula-core",
      "version": "0.3.0",
      "source_sha256": "20b9e60078ce5a031211422ad449d3a270be3065b34a17bfabafb331e6d0686a"
    }
  },
  "assumptions": [
    { "id": "a1", "zh-Hant": "討論對象是平面中的非退化三角形。" },
    { "id": "a2", "zh-Hant": "角度使用度數或弧度表示，且 90° 與 π/2 表示同一角度。" }
  ],
  "symbols": [
    { "token": "γ", "role": "right_angle", "role_zh": "被指定為直角的內角", "scope": "definition" },
    { "token": "π", "role": "circle_constant", "role_zh": "圓周率", "scope": "definition" }
  ],
  "dependencies": [],
  "explanation": {
    "paragraphs_zh": [
      "三角形最多只能有一個直角，因為三個內角的總和為 180°。",
      "直角所對的邊稱為斜邊，另外兩邊稱為股；斜邊是三邊中最長的一邊。",
      "程式可以檢查三個輸入角是否在容差內加總為 180°，並判斷其中是否存在 90°；這仍只是對具體輸入的檢查。"
    ],
    "common_misconception_zh": "只看到某兩條邊互相垂直，卻沒有確認它們與第三邊構成非退化三角形。"
  },
  "proofs": [],
  "computational_companions": [
    {
      "id": "cc-python-right-triangle-001",
      "language": "python",
      "relation": "finite_angle_definition_checker",
      "status": "reference_only",
      "path": "reference/python/right_triangle.py",
      "warning": "此程式只在有限精度與指定容差下檢查具體角度輸入，不等同於幾何定義本身。",
      "source": "from math import isclose\n\ndef is_right_triangle_angles(alpha, beta, gamma, *, tol=1e-9):\n    angles = (alpha, beta, gamma)\n    if min(angles) <= 0:\n        return False\n    return isclose(sum(angles), 180.0, abs_tol=tol) and any(isclose(x, 90.0, abs_tol=tol) for x in angles)",
      "non_identity": {
        "preserved": ["三個正角度輸入", "內角和為 180°", "其中一角為 90°"],
        "approximated": ["角度比較使用浮點容差"],
        "omitted": ["三角形幾何構造的存在性", "歐幾里得公理背景"]
      }
    }
  ],
  "verification": {
    "computational_status": "finite_cases_passed",
    "warning_zh": "有限角度案例通過只表示參考程式符合所列測試，不等於完成幾何定義的形式化。",
    "evidence_refs": [
      {
        "id": "evidence-sha256-d2f7e95c5eb44099070a59498f1ad1b82c0818327df33683b6e82d8624544ea9",
        "role": "finite_computational_check",
        "producer_id": "ocme-python-suite"
      }
    ],
    "producers": [
      {
        "id": "ocme-python-suite",
        "adapter": "native_python",
        "config_path": "reference/python/verify_all.py",
        "status": "active"
      }
    ]
  },
  "formalization": {
    "status": "not_formalized",
    "target_systems": ["Lean 4"],
    "next_obligation_zh": "對接 Mathlib 的三角形、角度與垂直關係定義。"
  },
  "provenance": {
    "origin": "evemisslab_original_mvp",
    "note_zh": "此定義物件為 OCME v0.2 的原生架構示範。",
    "content_license": "CC-BY-SA-4.0",
    "code_license": "MIT",
    "created_at": "2026-07-25"
  }
}