edulab

简体中文 · English

A collection of education skills that turn academic problems into interactive lesson web pages.

Install

Recommended — install with skills in one command:

npx skills add wy51ai/edulab

To update to the latest version later:

npx skills update

Or use it as a Claude Code plugin marketplace:

/plugin marketplace add wy51ai/edulab
/plugin install edulab

Once installed, the skills activate on their trigger words, and can also be invoked manually.

Skill: edu-solid-geometry

Solves one solid geometry problem into a self-contained interactive lesson page. Three entry points:

Problem types covered: line-plane angle, dihedral angle, angle between skew lines, point-to-plane distance, volume, and more — on cubes / cuboids, pyramids / prisms, cylinders / cones. All solved uniformly via the "coordinate system + vector method."

Trigger words: solid geometry, line-plane angle, dihedral angle, angle between skew lines, distance to plane, interactive geometry solution page; 立体几何、线面角、二面角、异面直线、点到平面距离、正四棱锥、解这道几何题、随机出一道立体几何题、这张图里的立体几何题, etc.

Dependency

The compute core lib/geometry_kernel.py depends on sympy. Use any python3 that can import sympy:

python3 -m pip install sympy   # if sympy is missing

Generate from the command line (without Claude)

cd skills/edu-solid-geometry
python3 scripts/generate.py cube   ./cube.html     # cube · line-plane angle
python3 scripts/generate.py box    ./box.html      # cuboid · volume
python3 scripts/generate.py random 7 ./random.html # random problem (seed=7)
python3 lib/geometry_kernel.py                     # kernel built-in self-check

If you don't pass an output path, it writes to the current working directory (cwd).

Skill: edu-analytic-geometry

Solves one analytic geometry (conic sections) problem into a self-contained interactive lesson page. Same three entry points as above (text / image / random). Built on a 2D Canvas board + KaTeX with a generic, data-driven interactive engine: a parameter slider drives derived constructions (line∩conic, point-on-conic, central reflection, tangent…) and live readouts, with a theoretical-range bar or a fixed-value indicator.

Problem types covered: standard equation, chord length, dot-product range / fixed value, triangle-area extremum, fixed point, fixed value (slope product), locus, tangent, eccentricity — on ellipses / hyperbolas / parabolas / circles. All solved uniformly via "parametrized line x = my + c + system + Vieta's formulas + substitution."

A correctness note baked into the kernel: open/closed interval endpoints are decided by whether a real line attains them, so the boxed answer always matches what the interactive tool shows (e.g. the ellipse MA·MB range is the closed [-3, 7/4] — slide θ to 0° and you read exactly −3).

Trigger words: analytic geometry, conic sections, ellipse, hyperbola, parabola, chord length, dot product range, fixed point, fixed value, locus, eccentricity, interactive analytic geometry solution page; 解析几何、圆锥曲线、椭圆、双曲线、抛物线、焦点弦、向量数量积取值范围、定点问题、定值问题、斜率之积、三角形面积最值、轨迹方程、离心率, etc.

Dependency

The compute core lib/analytic_kernel.py depends on sympy (same as above).

Generate from the command line (without Claude)

cd skills/edu-analytic-geometry
python3 scripts/generate.py list                          # list registered problem types
python3 scripts/generate.py ellipse_dot_range ./sol.html  # ellipse · MA·MB range [-3, 7/4]
python3 scripts/generate.py parabola_dot_const ./sol.html # parabola focal chord · OA·OB ≡ -3
python3 scripts/generate.py all ./out_dir                 # all registered types
python3 lib/analytic_kernel.py                            # kernel built-in self-check

Like above, no output path → writes to the current working directory (cwd).

How it works

1. Get a problem spec — normalize all three entry points into a structured description (body type and dimensions, given conditions, the quantity asked, language).
2. Exact kernel computation — sympy computes exact coordinates, key vectors, normals, the final answer, and every intermediate value (as LaTeX strings). Never by hand.
3. Assemble and inject the template — feed the lesson / steps / model data into the data-driven template template/lesson.html; 3D vertex coordinates come from kernel.to_three(...), sharing the same source as the solution.
4. Self-check — kernel answer == answer card == final value shown in the last step; a local static server + preview check confirms no console errors and correct formula/highlight rendering.
5. Deliver — the finished page is written to the user's current working directory, named like solution-<short-description>.html.

Project structure

edulab/
├── .claude-plugin/
│   ├── plugin.json              # plugin metadata
│   └── marketplace.json         # marketplace manifest
├── index.html                   # finished sample (quad pyramid · line-plane angle)
└── skills/
    ├── edu-solid-geometry/      # solid geometry — 3D (Three.js) + MathJax
    │   ├── SKILL.md
    │   ├── template/lesson.html # data-driven template (generic 3D renderer + data island)
    │   ├── lib/
    │   │   ├── geometry_kernel.py  # sympy exact-computation core
    │   │   └── bodies.py           # edge-topology library for solids
    │   ├── scripts/generate.py
    │   ├── output/
    │   └── references/          # problem-schema.md · conventions.md
    └── edu-analytic-geometry/   # analytic geometry / conics — 2D (Canvas) + KaTeX
        ├── SKILL.md
        ├── template/board.html  # data-driven template (generic 2D renderer + param engine)
        ├── lib/
        │   ├── analytic_kernel.py  # sympy exact-solver core (system · Vieta · range · fixed value)
        │   └── conics.py           # conic-section definition library
        ├── scripts/generate.py
        ├── output/
        └── references/          # problem-schema.md · conventions.md

Extending

edu-solid-geometry

• Add a problem type: add a solver function in geometry_kernel.py (see the recipe table in references/conventions.md), then add a build_* in generate.py.
• Add a solid: add a coordinate-construction function in geometry_kernel.py, then add its edge topology in bodies.py.

edu-analytic-geometry

• Add a problem type: add a target-quantity function in analytic_kernel.py and reuse range_over_m / is_constant_in_m, then add a build_* in generate.py (pick an interaction: range bar / fixed value / fixed point / locus trace).
• Add a curve: ellipse / hyperbola / parabola / circle are built in; new curves go in conics.py and the board.html engine.

License

Apache-2.0

Author

WY · @akokoi1

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