Geodesic - Wikipedia
In geometry, a geodesic (/ ˌdʒiː.əˈdɛsɪk, - oʊ -, - ˈdiːsɪk, - zɪk /) [1][2] is a curve representing in some sense the shortest [a] 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.
Geodesic -- from Wolfram MathWorld
2024年11月7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).
Geodesic Definition & Meaning - Merriam-Webster
: made of light straight structural elements mostly in tension. a geodesic dome. geodesic. 2 of 2. noun. : the shortest line between two points that lies in a given surface. Examples of geodesic in a Sentence. Recent Examples on the Web. Adjective.
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.”
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.
Geodesics on an ellipsoid - Wikipedia
A geodesic is the shortest path between two points on a curved surface, analogous to a straight line on a plane surface. The solution of a triangulation network on an ellipsoid is therefore a set of exercises in spheroidal trigonometry (Euler 1755).
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.
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 .
Geodesic line - Encyclopedia of Mathematics
2012年3月5日 · The notion of a geodesic line (also: geodesic) is a geometric concept which is a generalization of the concept of a straight line (or a segment of a straight line) in Euclidean geometry to spaces of a more general type.
Lecture 9: Geodesics | General Relativity - MIT OpenCourseWare
Lecture 9: Geodesics. Description: The kinematics of bodies in spacetime. Free fall described by geodesics: trajectories that parallel transport their tangents through spacetime, and extremize the experienced proper time.
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