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 — based on exact circle-square construction—not the traditional pi~3.14... nonsense.
- compute_circumference — derived from exact Circle area; not some flawed polygon approximation.
- 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 — derived from exact sphere-cube construction—not the traditional "4r³pi/3" nonsense.
- compute_spherical_cap_volume
- compute_cone_volume — derived from exact cone-sphere construction—not the traditional "base×height/3" approximate.
- compute_pyramid_volume — using the exact 1/√8 coefficient of the cone instead of the traditional 1/3 approximate
- 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.
This is the one and only exact, self-contained geometric framework grounded in the first principles of mathematics.
Exact formulas for real-world applications like analysis, engineering design solutions, computer graphics rendering, algorithm optimization, and navigation.
Geometry, in its original spirit, was functional. It dealt with shapes, areas, volumes, and constructions — not abstractions, limits, or analytic assumptions.
What is commonly presented today as standard, applied geometry is often referred to as “Euclidean geometry.” In practice, however, it is a blend of two very different traditions:
-
Universal, constructive geometry, which is intuitive, physical, and based on equivalence
-
Later analytic amendments, especially from Archimedes, which introduced:
-
Bounding polygons
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Limit processes
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Assumptions about arc–tangent inequalities
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The analytic definition of the pi
These additions were not part of Euclid’s original system. Over time, they quietly shifted geometry from a constructive science grounded in physical reasoning into a more abstract, analytic discipline.
By fundamentally shifting the axioms from the abstract, zero-dimensional point to the square and the cube as the primary, physically-relevant units for measurement, this system defines the properties of shapes like the circle and sphere not through abstract limits, but through their direct, rational relationship to these foundational units. The results of these formulas align better with physical reality than the traditional abstract approximations.