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

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.

Total: 130 registered problem types across 14 skills

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.

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

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).

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.

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

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).

Solves one function & derivative problem into a self-contained interactive lesson page. Built on a 2D Canvas board + MathJax with a parameter slider driving function graphs, tangent lines, extrema, and zeros in real-time.

Problem types covered: tangent line equation, monotonicity & extrema, zero-point discussion, exponential/logarithmic comparison, function symmetry, composite monotonicity, image transform, inverse function, range, abstract function, derivative inequality proof, construct function, hidden zero analysis.

Trigger words: 函数, 导数, 切线, 单调性, 极值, 零点, 奇偶性, 复合函数, 反函数, 值域, 隐零点; function, derivative, tangent line, monotonicity, extzeros, symmetry, composite function, inverse function, interactive function solution page.

cd skills/edu-function
python3 scripts/generate.py list                      # list registered problem types
python3 scripts/generate.py tangent_cubic ./sol.html  # tangent line problem
python3 scripts/generate.py all ./out_dir             # all registered types

Solves one trigonometry problem into a self-contained interactive lesson page. Built on a 2D Canvas board + MathJax with a parameter slider driving waveform changes in real-time.

Problem types covered: sine function image transformation (A/ω/φ), sine law, cosine law, trig evaluation, induction formula, auxiliary angle, trig equation, trig properties, Heron area.

Trigger words: 三角函数, 正弦定理, 余弦定理, 图像变换, 辅助角, 三角形面积, 海伦公式; trigonometry, sine law, cosine law, image transformation, auxiliary angle, interactive trigonometry solution page.

cd skills/edu-trigonometry
python3 scripts/generate.py list                      # list registered problem types
python3 scripts/generate.py sine_transform ./sol.html # sine transform problem
python3 scripts/generate.py all ./out_dir             # all registered types

Solves one sequence problem into a self-contained interactive lesson page. Built on a 2D Canvas board + MathJax with a parameter slider driving bar charts and cumulative sum curves in real-time.

Problem types covered: arithmetic sequence, geometric sequence, recursive sequence, telescoping sum, offset subtraction, Sn-an relation, sequence inequality, comprehensive sum, sequence bound proof.

Trigger words: 数列, 等差数列, 等比数列, 通项公式, 前n项和, 裂项求和, 错位相减; sequence, arithmetic sequence, geometric sequence, general term, sum, interactive sequence solution page.

cd skills/edu-sequence
python3 scripts/generate.py list                      # list registered problem types
python3 scripts/generate.py arithmetic ./sol.html     # arithmetic sequence problem
python3 scripts/generate.py all ./out_dir             # all registered types

Solves one inequality / linear programming problem into a self-contained interactive lesson page. Built on a 2D Canvas board + MathJax with feasible region polygon and objective function contour lines.

Problem types covered: linear programming, AM-GM inequality, quadratic inequality, absolute value inequality, inequality proof, range by inequality.

Trigger words: 不等式, 线性规划, 均值不等式, 可行域, 最值; inequality, linear programming, AM-GM, feasible region, optimization, interactive inequality solution page.

cd skills/edu-inequality
python3 scripts/generate.py list                      # list registered problem types
python3 scripts/generate.py linear_program ./sol.html # linear programming problem
python3 scripts/generate.py all ./out_dir             # all registered types

Solves one line-circle positional relationship problem into a self-contained interactive lesson page. Built on a 2D Canvas board + MathJax with a parameter slider driving line slope changes and real-time positional relationship determination.

Problem types covered: line-circle positional relationship, line from points, two-line relationship, circle equation, circle-circle relationship, tangent to circle, chord length.

Trigger words: 直线与圆, 位置关系, 弦长, 切线长; line and circle, positional relationship, chord length, tangent length, interactive geometry solution page.

cd skills/edu-line-circle
python3 scripts/generate.py list                              # list registered problem types
python3 scripts/generate.py line_circle_position ./sol.html  # line-circle problem
python3 scripts/generate.py all ./out_dir                    # all registered types

Solves one probability & statistics problem into a self-contained interactive lesson page. Built on a 2D Canvas board + MathJax with a parameter slider driving distribution curve changes in real-time.

Problem types covered: normal distribution, classical probability, conditional probability, binomial distribution, geometric distribution, expectation/variance, normal probability, regression, independence test, hypergeometric distribution.

Trigger words: 概率, 统计, 正态分布, 二项分布, 期望, 方差, 超几何分布; probability, statistics, normal distribution, binomial distribution, expectation, variance, interactive probability solution page.

cd skills/edu-probability
python3 scripts/generate.py list                          # list registered problem types
python3 scripts/generate.py normal_distribution ./sol.html # normal distribution problem
python3 scripts/generate.py all ./out_dir                 # all registered types

Solves one plane vector problem into a self-contained interactive lesson page. Built on a 2D Canvas board + MathJax with draggable vector endpoints showing dot product, angle, and projection in real-time.

Problem types covered: dot product, linear combination, basis representation, collinear condition, perpendicular condition, vector projection, vector area.

Trigger words: 向量, 数量积, 夹角, 共线, 垂直, 基底; vector, dot product, angle, collinear, perpendicular, basis, interactive vector solution page.

cd skills/edu-vector
python3 scripts/generate.py list                      # list registered problem types
python3 scripts/generate.py dot_product ./sol.html    # dot product problem
python3 scripts/generate.py all ./out_dir             # all registered types

Solves one set theory problem into a self-contained interactive lesson page. Built on a 2D Canvas board + MathJax with Venn diagram visualization.

Problem types covered: set operations (intersection/union/complement), three-set Venn diagram, set equation, complement, subset condition.

Trigger words: 集合, 交集, 并集, 补集, 韦恩图, 子集; set, intersection, union, complement, Venn diagram, subset, interactive set solution page.

cd skills/edu-set
python3 scripts/generate.py list                      # list registered problem types
python3 scripts/generate.py set_operations ./sol.html # set operations problem
python3 scripts/generate.py all ./out_dir             # all registered types

Solves one combinatorics problem into a self-contained interactive lesson page. Built on a 2D Canvas board + MathJax with step-by-step counting visualization.

Problem types covered: permutation, combination, binomial expansion, binomial coefficient, mixed counting, derangement, grouping, coloring, gap method, inclusion-exclusion.

Trigger words: 排列, 组合, 二项式定理, 错排, 分组, 涂色, 隔板法, 容斥原理; permutation, combination, binomial theorem, derangement, grouping, coloring, interactive combinatorics solution page.

cd skills/edu-combinatorics
python3 scripts/generate.py list                      # list registered problem types
python3 scripts/generate.py permutation_basic ./sol.html # permutation problem
python3 scripts/generate.py all ./out_dir             # all registered types

Solves one parametric equation & polar coordinate problem into a self-contained interactive lesson page. Built on a 2D Canvas board + MathJax with parameter slider driving curve changes in real-time.

Problem types covered: line parametric, ellipse parametric, polar conversion, polar curve, parametric intersection, parametric distance.

Trigger words: 参数方程, 极坐标, 极坐标方程, 心形线, 玫瑰线; parametric equation, polar coordinates, cardioid, rose curve, interactive parametric/polar solution page.

cd skills/edu-parametric-polar
python3 scripts/generate.py list                      # list registered problem types
python3 scripts/generate.py line_parametric ./sol.html # line parametric problem
python3 scripts/generate.py all ./out_dir             # all registered types

Solves one complex number problem into a self-contained interactive lesson page. Built on a 2D Canvas board + MathJax with complex plane visualization.

Problem types covered: basic operations (add/subtract/multiply/divide), modulus, polar form, complex equation, geometry in complex plane, De Moivre's theorem.

Trigger words: 复数, 模, 辐角, 三角形式, 棣莫弗定理; complex number, modulus, polar form, De Moivre, interactive complex number solution page.

cd skills/edu-complex
python3 scripts/generate.py list                      # list registered problem types
python3 scripts/generate.py complex_basic ./sol.html  # complex arithmetic problem
python3 scripts/generate.py all ./out_dir             # all registered types

Solves one logic & proposition problem into a self-contained interactive lesson page. Built on a 2D Canvas board + MathJax with truth tables and proposition structure visualization.

Problem types covered: four propositions (original/converse/inverse/contrapositive), sufficient/necessary conditions, quantifier negation, truth tables, proof by contradiction.

Trigger words: 逻辑, 命题, 充分条件, 必要条件, 量词, 真值表, 反证法; logic, proposition, sufficient condition, necessary condition, quantifier, truth table, proof by contradiction, interactive logic solution page.

cd skills/edu-logic
python3 scripts/generate.py list                          # list registered problem types
python3 scripts/generate.py four_propositions ./sol.html  # four propositions problem
python3 scripts/generate.py all ./out_dir                 # all registered types

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.

edulab/
├── .claude-plugin/
│   ├── plugin.json              # plugin metadata
│   └── marketplace.json         # marketplace manifest
├── index.html                   # finished sample (quad pyramid · line-plane angle)
├── README.md                    # English documentation
├── README.zh-CN.md              # Chinese documentation
└── skills/
    ├── edu-solid-geometry/      # solid geometry — 3D (Three.js) + MathJax
    ├── edu-analytic-geometry/   # analytic geometry / conics — 2D (Canvas) + MathJax
    ├── edu-function/            # functions & derivatives — 2D (Canvas) + MathJax
    ├── edu-trigonometry/        # trigonometry — 2D (Canvas) + MathJax
    ├── edu-sequence/            # sequences — 2D (Canvas) + MathJax
    ├── edu-inequality/          # inequalities — 2D (Canvas) + MathJax
    ├── edu-line-circle/         # line & circle — 2D (Canvas) + MathJax
    ├── edu-probability/         # probability — 2D (Canvas) + MathJax
    ├── edu-vector/              # vectors — 2D (Canvas) + MathJax
    ├── edu-set/                 # sets — 2D (Canvas) + MathJax
    ├── edu-combinatorics/       # combinatorics — 2D (Canvas) + MathJax
    ├── edu-parametric-polar/    # parametric equations & polar — 2D (Canvas) + MathJax
    ├── edu-complex/             # complex numbers — 2D (Canvas) + MathJax
    └── edu-logic/               # logic & propositions — 2D (Canvas) + MathJax

Each skill follows the same structure:

skills/<skill-name>/
├── SKILL.md                    # skill documentation
├── lib/*_kernel.py             # sympy exact-computation core
├── scripts/generate.py         # inject template + build_* + registry
├── template/*.html             # data-driven template (Canvas/Three.js + MathJax)
├── references/                 # conventions.md + problem-schema.md
└── output/                     # generated HTML files

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.

Other skills (edu-function, edu-trigonometry, edu-sequence, edu-inequality, edu-line-circle, edu-probability, edu-vector, edu-set, edu-combinatorics, edu-parametric-polar, edu-complex, edu-logic)

• Add a problem type: add a solver function in the corresponding *_kernel.py, then add a build_* in generate.py.
• Add a function/distribution: extend the kernel with new computation functions.

Apache-2.0

Original skills (edu-solid-geometry, edu-analytic-geometry):

• WY · @akokoi1

Extended skills (edu-function, edu-trigonometry, edu-sequence, edu-inequality, edu-line-circle, edu-probability, edu-vector):

• ofobike

New skills (edu-set, edu-combinatorics, edu-parametric-polar, edu-complex, edu-logic):

• ofobike