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[1] If the author of this work was subjected to repression and rehabilitated posthumously, replace the death date by the later rehabilitation date. [2] Amateur films which were first shown on January 1, 1930 or later are subjects of points 1-2 of this template. [3] ROSTA reports created before July 10, 1925 are subjects of points 1-2 of this ...
The region of the plane between two concentric circles is an annulus, and analogously the region of space between two concentric spheres is a spherical shell. [6] For a given point c in the plane, the set of all circles having c as their center forms a pencil of circles. Each two circles in the pencil are concentric, and have different radii.
Slicing with the z = 0 plane produces two concentric circles, x 2 + y 2 = 2 2 and x 2 + y 2 = 8 2, the outer and inner equator. Slicing with the x = 0 plane produces two side-by-side circles, (y − 5) 2 + z 2 = 3 2 and (y + 5) 2 + z 2 = 3 2. Two example Villarceau circles can be produced by slicing with the plane 3y = 4z. One is centered at ...
A circle is an ellipse with two coinciding foci. The limit of hyperbolas as the foci are brought together is degenerate: a pair of intersecting lines. If an orthogonal net of ellipses and hyperbolas is transformed by bringing the two foci together, the result is thus an orthogonal net of concentric circles and lines passing through the circle ...
It consists of a family of real circles, all tangent to each other at a single common point. The degenerate circle with radius zero at that point also belongs to the pencil. A family of concentric circles centered at a common center (may be considered a special case of a hyperbolic pencil where the other point is the point at infinity).
A compact binary circle packing with the most similarly sized circles possible. [7] It is also the densest possible packing of discs with this size ratio (ratio of 0.6375559772 with packing fraction (area density) of 0.910683). [8] There are also a range of problems which permit the sizes of the circles to be non-uniform.
The two given circles α and β touch the n circles of the Steiner chain, but each circle C k of a Steiner chain touches only four circles: α, β, and its two neighbors, C k−1 and C k+1. By default, Steiner chains are assumed to be closed , i.e., the first and last circles are tangent to one another.
Except in the case of a line or circle, the parallel curves have a more complicated mathematical structure than the progenitor curve. [1] For example, even if the progenitor curve is smooth , its offsets may not be so; this property is illustrated in the top figure, using a sine curve as progenitor curve. [ 2 ]