In geometry, a geodesic (/ ˌ dʒ iː. ə ˈ d ɛ s ɪ k,-oʊ-,-ˈ d iː s ɪ k,-z ɪ k /) [1] [2] is a curve representing in some sense the locally [a] shortest [b] path between two points in a surface, or more generally in a Riemannian manifold.

2025年4月3日 · A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight lines. On the sphere, the geodesics are great circles (like the equator).

The meaning of GEODESIC is geodetic. How to use geodesic in a sentence.

A geodesic, the shortest distance between any two points on a sphere, is an arc of the great circle through the two points. The formula for determining a sphere’s surface area is 4π r 2 ; its volume is determined by ( 4 / 3 )π r 3 .

In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational forces is a particular type of geodesic.

A geodesic is a generalization of the notion of a “straight line” from a plane to a surface, on which it represents in some sense the shortest path between two points. We will begin with a definition of geodesics, then present various method for finding geodesics on surfaces, and later reveal their relationships to shortest paths.

A geodesic can be defined as a world-line that preserves tangency under parallel transport, Figure \(\PageIndex{1}\). This is essentially a mathematical way of expressing the notion that we have previously expressed more informally in terms of “staying on course” or moving “inertially.”

In this article, we'll look at the mathematics that lies behind geodesic domes, but we'll also talk a little about why they make good engineering sense and how they might be constructed from real materials.

Illustrated definition of Geodesic: The shortest line segment between two points on a sphere or other curved surface. A Geodesic Dome is made with...

GEODESIC definition: 1. relating to the shortest possible line between two points on a sphere or other curved surface 2…. Learn more.