# Geodesic > [[PORTAL_Dynamical_system|Dynamical system]] spine. ## Microsims — three.js <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Geodesic_microsim.html" width="100%" height="520" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Geodesic — three.js microsim"></iframe> </div> <p class="wt-pending"><strong>Note:</strong> staged, awaiting CDN deploy.</p> A geodesic is the generalisation of a "straight line" to curved space: the locally shortest path between two points on a given surface or manifold. On a flat plane a geodesic is an ordinary straight line; on a sphere, geodesics are great circles, which is why long-haul flight paths curve on a flat map but are the shortest route on the globe. ## Overview This build renders geodesic paths on several curved surfaces — sphere, torus, and other configurable shapes — live, so the shortest-path property can be checked visually against alternative routes. Geodesics matter to a [[Dynamical_system|dynamical system]] beyond pure geometry: the trajectories of a particle moving under no force but the shape of space itself (as in general relativity, where gravity is curvature rather than a force) are exactly its geodesics, and geodesic flow on a curved [[Manifold|manifold]] is itself a classic example of a dynamical system, one whose long-term behaviour depends sensitively on the manifold's curvature. **On the spine:** [[Dynamical_system]] · [[Manifold]] · [[Physics]]. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Geodesic) : [Wikitube](https://en.wikitube.io/wiki/Geodesic) --- *Repopulated 2026-08-05 · existing three.js asset renamed + wired, Wikipedia-sourced overview · 0 deletions.*