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The connector consists of a hub, usually of aluminium, with up to twelve slots into which tubes (the axial members) can be inserted. The assemblage is stabilized by a central bolt with a washer (through the middle of the hub). It is generally used with aluminium tubes, but stainless steel was introduced in 1966.
A geodesic dome is a hemispherical thin-shell structure ... This type of dome is often called a hub-and-strut dome because of the use of steel hubs to tie the struts ...
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.
This is analogous to the Earth's surface, where the geodesic between two points along a great circle is the shortest route only up to the antipodal point; beyond that, there are shorter paths. Beyond a conjugate point, a geodesic in Lorentzian geometry may not be maximizing proper time (for timelike geodesics), and the geodesic may enter a ...
The geodesic oscillates north and south of the equator; on each oscillation it completes slightly less than a full circuit around the ellipsoid resulting, in the typical case, in the geodesic filling the area bounded by the two latitude lines β = ±β 1. Two examples are given in Figs. 18 and 19.
In Riemannian geometry, a Jacobi field is a vector field along a geodesic in a Riemannian manifold describing the difference between the geodesic and an "infinitesimally close" geodesic. In other words, the Jacobi fields along a geodesic form the tangent space to the geodesic in the space of all geodesics.
Cut locus C(P) of a point P on the surface of a cylinder. A point Q in the cut locus is shown with two distinct shortest paths , connecting it to P.. In the Euclidean plane, a point p has an empty cut locus, because every other point is connected to p by a unique geodesic (the line segment between the points).
In Riemannian geometry, Gauss's lemma asserts that any sufficiently small sphere centered at a point in a Riemannian manifold is perpendicular to every geodesic through the point. More formally, let M be a Riemannian manifold , equipped with its Levi-Civita connection , and p a point of M .