Crate monge_rs 

monge-rs

A Rust implementation of Monge’s theorem for fleet mathematics, designed to integrate with Forgemaster’s constraint theory (jc1-ct-bridge).

Overview

Monge’s theorem states that for three circles in the plane, the three external homothetic centers are collinear. This crate implements the theorem and its generalizations, providing:

• Homothetic centers — external and internal for pairs of circles
• Radical axes — as 1-cocycles in Čech cohomology
• Zero Holonomy Consensus — a Lyapunov-based distributed consensus protocol
• Pythagorean48 — zero-drift verification using 48 lattice directions
• nD Lassak generalization — Monge’s theorem in higher dimensions

Quick Start

use nalgebra::Vector2;
use monge_rs::geometry::Circle;
use monge_rs::homothetic::{external_homothetic_center, monge_collinear_area};

let c1 = Circle::new(Vector2::new(0.0, 0.0), 1.0);
let c2 = Circle::new(Vector2::new(4.0, 0.0), 2.0);
let c3 = Circle::new(Vector2::new(2.0, 3.0), 1.5);

// External homothetic centers
let s12 = external_homothetic_center(&c1, &c2).unwrap();
let s23 = external_homothetic_center(&c2, &c3).unwrap();
let s31 = external_homothetic_center(&c3, &c1).unwrap();

// Verify Monge collinearity (area should be ≈ 0)
let area = monge_collinear_area(&c1, &c2, &c3).unwrap();
assert!(area < 1e-10);

Modules

• geometry — foundational types (Circle, Sphere, 3D lifting, nD generalization)
• homothetic — external and internal homothetic centers
• radical_axis — radical axis as 1-cocycle, radical center
• consensus — zero holonomy consensus protocol
• p48 — Pythagorean48 verification framework

Modules

consensus

Zero-holonomy consensus — a Lyapunov-based distributed consensus protocol using Monge’s theorem geometry.

geometry

Foundational types for Monge geometry — circles in ℝ², spheres in ℝⁿ, 3D lifting (paraboloid map), and n-dimensional Lassak generalization.

homothetic

External and internal homothetic centers of circles.

p48

Pythagorean48 — a verification framework for zero-drift Monge consistency in 48 lattice directions derived from 6 primitive Pythagorean triples.

radical_axis

Radical axis as a 1-cocycle in the Čech cohomology of circle covers.