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[4] [verification needed] A more complex example is the one at right, the Earth's Hill sphere, which extends between the Lagrange points L 1 and L 2, [clarification needed] which lie along the line of centers of the Earth and the more massive Sun. [not verified in body] The gravitational influence of the less massive body is least in that ...
The generators of any ruled surface coalesce with one family of its asymptotic lines. For developable surfaces they also form one family of its lines of curvature. It can be shown that any developable surface is a cone, a cylinder, or a surface formed by all tangents of a space curve. [5] Developable connection of two ellipses and its development
This last form of the Hill equation is advantageous because a plot of versus [] yields a linear plot, which is called a Hill plot. [ 7 ] [ 8 ] Because the slope of a Hill plot is equal to the Hill coefficient for the biochemical interaction, the slope is denoted by n H {\displaystyle n_{H}} .
The location of L 1 is the solution to the following equation, gravitation providing the centripetal force: = (+) + where r is the distance of the L 1 point from the smaller object, R is the distance between the two main objects, and M 1 and M 2 are the masses of the large and small object, respectively.
When two cells in the Voronoi diagram share a boundary, it is a line segment, ray, or line, consisting of all the points in the plane that are equidistant to their two nearest sites. The vertices of the diagram, where three or more of these boundaries meet, are the points that have three or more equally distant nearest sites.
In geometry, an arrangement of lines is the subdivision of the Euclidean plane formed by a finite set of lines. An arrangement consists of bounded and unbounded convex polygons, the cells of the arrangement, line segments and rays, the edges of the arrangement, and points where two or more lines cross, the vertices of the arrangement.
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. The term also has meaning in any differentiable manifold with a connection.
Shaded relief, or hill-shading, shows the shape of the terrain in a realistic fashion by showing how the three-dimensional surface would be illuminated from a point light source. The shadows normally follow the convention of top-left lighting in which the light source is placed near the upper-left corner of the map.