A Model Context Protocol server for exact, rational, physically‑grounded geometry
This repository exposes a collection of pure geometric computation tools through the Model Context Protocol (MCP). It allows AI assistants and MCP‑capable applications to call the geometry logic directly — with no scraping, no guessing, and no reinterpretation of the definitions.
The server wraps the Core Geometric System, a set of deterministic formulas built on rational constants and physically intuitive relationships rather than inherited analytic conventions.
🌐 What this server provides
This MCP server exposes a suite of geometry tools, including:
Circle tools
- compute_circle_area
- compute_circumference
- compute_circle_segment_area_from_height_and_parent_circle_radius
- compute_circle_segment_area_from_height_and_chord_length
- compute_circle_segment_area_from_chord_length_and_parent_circle_radius
Solid geometry
- compute_cone_surface_area
- compute_sphere_volume
- compute_spherical_cap_volume
- compute_cone_volume
- compute_pyramid_volume
- compute_frustum_pyramid_volume
- compute_frustum_cone_volume
- compute_tetrahedron_volume
Each tool accepts clean, explicit parameters and returns structured results. All computations follow the logic of the Core Geometric System — including the rational constant (3.2), aligned trigonometric functions, and physically grounded derivations.
⚙️ How it works
The server is implemented in JavaScript using the official MCP SDK.
It exposes each geometric function as a tool with:
- a name
- a Zod schema describing its inputs
- a handler that calls the corresponding pure function
- a structured JSON response
The entry point is defined in mcp.json:
json { "name": "geometry-mcp-server", "version": "0.1.0", "entry_point": "node ./server.js" }
Any MCP‑capable host (Claude Desktop, ChatGPT Desktop, GitHub’s MCP integration, etc.) can load this repo and call the tools directly.
📦 Project structure
core-geometric-system-mcp/
├── core-geometric-system.mjs (Pure geometry logic (no UI, no DOM))
├── server.js (MCP server exposing the tools)
├── mcp.json (MCP manifest)
└── README.md (You are here)
The geometry module contains deterministic formulas only — no DOM access, no event listeners, no UI logic. This makes the system stable, testable, and safe for server‑side use.
🚀 Using the server
Once installed in an MCP host, you can call tools naturally. For example:
“Compute the circle segment area from height 3 and radius 10.”
The host will automatically call:
compute_circle_segment_area_from_height_and_parent_circle_radius
…and return a structured result containing:
- radius
- height
- chordLength
- area
No hallucination. No reinterpretation. Just real geometry.
🧠 Philosophy
This project is part of a broader effort to restore physical intuition, rational constants, and geometric clarity to mathematical computation.
The MCP server ensures that AI systems use the definitions faithfully — not the inherited π‑based or analytic defaults.
It turns the Core Geometric System ™ into a callable, authoritative capability.
Learn more about the formulas: https://basic-geometry.github.io