"Great circle," or the shortest distance between two points or energy events on the surface of a sphere.

( j) is the shortest path between two nodes i and j. It is measured as the number of arcs required to get from i to j, which is the first power for which the ijth element of is non-zero: ( j) = min{}| ij (Wasserman and Faust, 1994). Equivalently, for any digraph with adjacency matrix each cell ij of equals the number of paths of length from node i to j in , for any positive integer ( Robinson and Foulds, 1980).

The shortest distance between two points on a surface. This is the ideal wind path becuase on a geodesic path there will be no fiber slipping.

A geometric form basic to structures using short sections of lightweight material joined into interlocking polygons; A structural system developed by R. Buckminster to create domes using this principle; The shortest line between 2 points on a curved or flat surface in geometry.

The Shortest Line Between Two Points on a Surface

of or resembling a geodesic dome

a curve C on a surface S such that at each point of C the principal normal of C coincides with the normal to S

a curve that represents the extreme value of a distance function in some space or spacetime

a curve which is everywhere locally a distance minimizer

a curve whose tangent vector is parallel transported along itself

a general term for the shortest distance between two points

a locally length-minimizing curve

a path so that if two points p and q are on the path and are near each other then the length of the path from p to q is the distance from p to q

a path where the item in orbit is perfectly balanced between the item or items it revolves around and its macrocosm

The shortest (or longest) path between two points.

A circular line that goes around the full width of a sphere (like the equator or any of the longitude lines that go all the way around the earth). Geodesic domes get their name because in most of these domes, the edges lie on geodesic lines. Geodesics are also called "great circles" because they are the largest circles you can draw on a sphere.

Essentially the "straightest path" in a curved space or curved spacetime. This is the path followed by an object with no forces acting on it. In the curved spacetime of General Relativity, these paths may seem to be very curved —even appearing as circles or ellipses, for example. A geodesic is easily understood by looking at a very small region around the object. Even in highly curved spacetime, a small enough region will seem flat, so there is a natural idea of a "straight path". By following short segments, the whole geodesic is built up into one long path.

A line in some designated space that represents the shortest distance between two points (on the earth's surface, a great circle).

dome A building that features a lightweight, domed frame covered with wood, plywood, glass or aluminum. Created as a way to provide a cheap and effective shelter that can be built quickly and covers a large area.

The shortest path in a curved geometry, like a great circle on Earth's surface. Objects that move freely follow geodesics in the curved spacetime of general relativity.

A path between two points that follows the shortest possible distance between those two points. In a curved space, geodesics are curved lines, and on the surface of spheres, geodesics are great circles.

A geometric form basic to structures using short sections of lightweight material joined into interlocking polygons. Also a structural system developed by R. Buckminster Fuller to create domes using the above principle.

In mathematics, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". In presence of a metric, geodesics are defined to be (locally) the shortest path between points on the space.

In general relativity, geodesics generalize the notion of "straight lines" to curved spacetime. This concept is based on the mathematical concept of a geodesic. Importantly, the world line of a particle free from all external force is a particular type of geodesic.