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.

6 天之前 · 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 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.”

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, 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 .

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

In mathematics, a geodesic is the shortest path between 2 points over a curved surface. For example, an aeroplane takes the shortest path to go from one destination to the next. However the earth is not flat, it has the shape of a sphere. Displayed on a map you would see a curved line.