edulab

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

edulab is a Claude Code plugin (plugin + marketplace). The goal: give it a problem, get back a single self-contained HTML page you can open in any browser — complete with a worked explanation and a visualization, turning "I read it" into "I can rotate it and actually see it."

The first skill, edu-solid-geometry, solves solid geometry problems using the "coordinate system + vector method," driven by exact sympy computation. It outputs a lesson page with step-by-step analysis (MathJax) on the left and an interactive 3D model (Three.js) on the right.

Preview

index.html in the project root is a finished sample (regular quadrilateral pyramid · line-plane angle). Open it directly in a browser:

• Left: problem statement / answer / step-by-step analysis, formulas rendered with MathJax
• Right: the matching 3D model — rotate and zoom, with key elements highlighted per step and the camera moving along
• The answer, the 3D coordinates, and every intermediate value are consistent at the source (all derived from one sympy computation)

More samples live in skills/edu-solid-geometry/output/ (cube / box, etc.).

Install

Use it as a Claude Code plugin marketplace:

/plugin marketplace add wy51ai/edulab
/plugin install edulab

Or install the package from npm:

npm install @wy51ai/edulab

Once installed, the skill activates on its trigger words, and other agents can also invoke it to generate these pages.

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. On some machines the default python3 may be broken — use an interpreter that has sympy, e.g. /opt/homebrew/bin/python3.11:

/opt/homebrew/bin/python3.11 -m pip install --user sympy   # if sympy is missing

Generate from the command line (without Claude)

cd skills/edu-solid-geometry
python3.11 scripts/generate.py cube   ./cube.html     # cube · line-plane angle
python3.11 scripts/generate.py box    ./box.html      # cuboid · volume
python3.11 scripts/generate.py random 7 ./random.html # random problem (seed=7)
python3.11 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).

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/
        ├── SKILL.md             # skill description and workflow
        ├── 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  # template injection + example builders
        ├── output/              # internal development samples
        └── references/
            ├── problem-schema.md   # data format
            └── conventions.md      # coordinate conventions, solution recipes, self-check

Extending

• 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.

License

MIT

Author

WY · @akokoi1

Stars, issues, and PRs are welcome.