Mathgraphs

---
name: mathgraphs
description: >-
  Math & statistics graphing, computation, visualization and validation engine
---

# Math & Statistics Graphing Engine

You have access to an interactive math and statistics graphing engine via MCP. It computes and renders results — roots, extrema, intersections, regression, hypothesis tests — on interactive graphs.

## When to use this skill

- User asks to **graph**, **plot**, or **visualize** any math
- User needs to **verify** a mathematical result visually
- You computed an answer and want to **show** it, not just describe it
- Data needs statistical visualization (histogram, regression, distribution fit)
- Geometry needs precise rendering (triangles, circles, constructions)

## Tools

### `plot_graph` — Math Visualization
Plot functions, points, segments, labels, and shapes. Auto-computes roots, extrema, and intersections.

Element types:
- `function`: expression like "x^2-4", "sin(x)", "x^2+y^2=1", "(cos(t),sin(t))"
- `points`: array of {x, y} coordinates with optional label
- `segment`: line from (x1,y1) to (x2,y2) with optional arrow/dashed
- `label`: text at position (x, y)
- `triangle`: three vertices (x1,y1,x2,y2,x3,y3)
- `box`: edge + height for bar charts

### `compute_stats` — Descriptive Statistics
Input: array of numbers. Returns mean, median, std, min, max, quartiles.

### `add_histogram` — Histogram
Input: array of numbers. Auto-bins and draws bars.

### `add_regression` — Regression
Input: array of {x,y} points. Fits linear/quadratic/exponential/power. Returns R².

### `fit_distribution` — Distribution Fitting
Input: array of numbers. Fits normal/uniform/exponential. Returns best fit.

### `test_hypothesis` — Hypothesis Test
Input: data groups + test type. Returns p-value with visual rejection region.

## Important

- All tools return an **interactive URL** — always share it with the user
- The graph is **live**: user can zoom, pan, add functions, adjust sliders
- Results are **computed from the graph**, not generated — no hallucinated curves
- Supports 9 languages: en, zh, zh-TW, ja, ko, es, fr, de, pt-BR