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A geodesic dome is a hemispherical thin-shell structure (lattice-shell) based on a geodesic polyhedron. The rigid triangular elements of the dome distribute stress throughout the structure, making geodesic domes able to withstand very heavy loads for their size.
Geodesic domes are typically based on triangular facetings of this geometry with example structures found across the world, popularized by Buckminster Fuller. An example can be found in the model of a buckminsterfullerene, a truncated icosahedron-shaped geodesic dome allotrope of elemental carbon discovered in 1985. [17]
Geodesic polyhedra are a good approximation to a sphere for many purposes, and appear in many different contexts. The most well-known may be the geodesic domes, hemispherical architectural structures designed by Buckminster Fuller, which geodesic polyhedra are named after. Geodesic grids used in geodesy also have the geometry of geodesic polyhedra.
Solving the geodesic equations is a procedure used in mathematics, particularly Riemannian geometry, and in physics, particularly in general relativity, that results in obtaining geodesics.
An example of a spherical cap in blue (and another in red) In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane.It is also a spherical segment of one base, i.e., bounded by a single plane.
An ellipsoidal dome is a dome (also see geodesic dome), which has a bottom cross-section which is a circle, but has a cupola whose curve is an ellipse. [1] There are two types of ellipsoidal domes: prolate ellipsoidal domes and oblate ellipsoidal domes. A prolate ellipsoidal dome is derived by rotating an ellipse around the long axis of the ...
Klein quartic with 28 geodesics (marked by 7 colors and 4 patterns). 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.
There are several ways of defining geodesics (Hilbert & Cohn-Vossen 1952, pp. 220–221).A simple definition is as the shortest path between two points on a surface. However, it is frequently more useful to define them as paths with zero geodesic curvature—i.e., the analogue of straight lines on a curved su
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