Math & 3D Graphing Engine

You have access to an interactive math and 3D graphing engine via MCP. It computes and renders results — roots, extrema, intersections, and 3D scenes — on interactive graphs. Saves ~410 tokens per render vs LLM-generated canvas code.

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
• Geometry needs precise rendering (triangles, circles, constructions)
• User wants to build 3D scenes — shapes, architecture, creative builds with lighting and particle effects

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
• circle: center (cx,cy) + radius

Set viewport ({xmin, xmax, ymin, ymax}) to your data's magnitude — omit it and the server auto-fits the window to the elements.

Iterate with base_render_id (+ remove_indices) rather than re-sending every element. Each result reports what actually rendered, so act on any graph check it returns.

analyze — Precise Numerical Results

Compute exact values instead of doing the arithmetic yourself: roots, extrema, inflections, intersect, tangent, normal, derivative, integral, area_between, arc_length, closest_point.

Input: type (required), f (required), plus g (second expression, for intersect/area_between), x (point of interest, for tangent/normal/derivative), a/b (range, default -10..10), px/py (for closest_point).

Works with explicit, parametric, polar, and implicit curves.

Add plot: true to get the answer drawn as well — the graph comes back with the roots, intersections, tangent, or closest point already marked, so you never have to copy coordinates into a plot_graph call. Ignored by the linear-algebra types.

get_graph — Inspect a Graph

Read back the elements and viewport of an existing 2D render by ID. Element indices come back in order — pass them to remove_indices to modify a graph instead of rebuilding it.

net_generator — Shape Nets, Volume & Surface Area

Unfold a solid into its printable net and get its volume, surface area, and worked formulas. Also the tool to reach for when only the volume or surface area is wanted.

Shapes: cylinder/cone (r, h), cube and the Platonic solids (a), square_pyramid (a, h), triangular_prism (a, l), rectangular_prism (w, h, d). Omit dims for an example at default sizes. A sphere has no planar net.

Several MathTalking web pages are the browser form of these calls — the root finder, tangent calculator, area-between-curves, arc length, and closest-point pages are all analyze types, and the shape-net pages are net_generator. Prefer the call over linking the page when you are answering the question yourself.

plot_3d — 3D Scene Builder

Build interactive 3D scenes with shapes, lights, and particle effects. Supports incremental building.

Element types:

• mesh: 11 shapes (cube, box, sphere, cylinder, cone, tetrahedron, octahedron, dodecahedron, icosahedron, torus, prism) + material params (metalness, roughness, wireframe)
• light: point, spot, or directional with color/intensity
• particle: 5 presets (fire, smoke, rain, snow, sparkle)
• line3d: from [x,y,z] to [x,y,z]
• label3d: text at position [x,y,z]

Incremental building:

• base_render_id: build on existing scene (creates new URL, base unchanged)
• remove_indices: remove elements by index from base scene

get_3d — Inspect 3D Scene

Retrieve element list of an existing 3D render by ID. Use before base_render_id to see what a scene contains.

create_show — Slideshow

Bundle multiple plot_graph results into a presentation with prev/next navigation.

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
• Use analyze for exact numbers (roots, intersections, integrals) rather than computing them yourself
• Supports 9 languages: en, zh, zh-TW, ja, ko, es, fr, de, pt-BR