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Geodesic - Wikipedia 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
Geodesic -- from Wolfram MathWorld 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)
Geodesics in general relativity - Wikipedia 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 In other words, a freely moving or falling particle always moves along a geodesic
Geodesics - ISU Sites 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
Geodesic | mathematics | Britannica 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
5. 8: The Geodesic Equation - Physics LibreTexts 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 ”
Geodesic - definition of geodesic by The Free Dictionary geodesic - (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)