# Definitions for geodesicˌdʒi əˈdɛs ɪk, -ˈdi sɪkge·o·des·ic

### Princeton's WordNetRate this definition:0.0 / 0 votes

(mathematics) the shortest line between two points on a mathematically defined surface (as a straight line on a plane or an arc of a great circle on a sphere)

of or relating to or determined by geodesy

### WiktionaryRate this definition:0.0 / 0 votes

1. geodesicnoun

the shortest line between two points on a specific surface

of or relating to geodesy

of or relating to a geodesic dome

### WikipediaRate this definition:0.0 / 0 votes

1. Geodesic

In geometry, a geodesic () is a curve representing in some sense the shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization of the notion of a "straight line". The noun geodesic and the adjective geodetic come from geodesy, the science of measuring the size and shape of Earth, though many of the underlying principles can be applied to any ellipsoidal geometry. In the original sense, a geodesic was the shortest route between two points on the Earth's surface. For a spherical Earth, it is a segment of a great circle (see also great-circle distance). The term has since been generalized to more abstract mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph. In a Riemannian manifold or submanifold, geodesics are characterised by the property of having vanishing geodesic curvature. More generally, in the presence of an affine connection, a geodesic is defined to be a curve whose tangent vectors remain parallel if they are transported along it. Applying this to the Levi-Civita connection of a Riemannian metric recovers the previous notion. Geodesics are of particular importance in general relativity. Timelike geodesics in general relativity describe the motion of free falling test particles.

### ChatGPTRate this definition:0.0 / 0 votes

1. geodesic

A geodesic is the shortest possible line or path between two points on a curved surface or within a curved space. It represents the concept of a straight line in Euclidean geometry extended to curved spaces. In the context of physics and astronomy, particularly in the theory of general relativity, geodesics are trajectories followed by free-falling particles under the effect of gravity.

### Webster DictionaryRate this definition:0.0 / 0 votes

alt. of Geodesical

2. Geodesicnoun

a geodetic line or curve

### WikidataRate this definition:5.0 / 1 vote

1. Geodesic

In mathematics, particularly differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". In the presence of an affine connection, a geodesic is defined to be a curve whose tangent vectors remain parallel if they are transported along it. If this connection is the Levi-Civita connection induced by a Riemannian metric, then the geodesics are the shortest path between points in the space. The term "geodesic" comes from geodesy, the science of measuring the size and shape of Earth; in the original sense, a geodesic was the shortest route between two points on the Earth's surface, namely, a segment of a great circle. The term has been generalized to include measurements in much more general mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph. Geodesics are of particular importance in general relativity, as they describe the motion of inertial test particles.

### Numerology

1. Chaldean Numerology

The numerical value of geodesic in Chaldean Numerology is: 4

2. Pythagorean Numerology

The numerical value of geodesic in Pythagorean Numerology is: 4

### Popularity rank by frequency of use

geodesic#10000#47830#100000

## Translations for geodesic

### From our Multilingual Translation Dictionary

• geodätisch, Geodäte
• geodésica, geodésico
• gagnvegur
• geodetico
• geodetisch
• geodesisk
• geodésico
• trắc địa

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A descant
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