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  2. Circle - Wikipedia

    en.wikipedia.org/wiki/Circle

    Since the diameter is twice the radius, the "missing" part of the diameter is (2r − x) in length. Using the fact that one part of one chord times the other part is equal to the same product taken along a chord intersecting the first chord, we find that (2r − x)x = (y / 2) 2. Solving for r, we find the required result.

  3. Unit circle - Wikipedia

    en.wikipedia.org/wiki/Unit_circle

    In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. [1] Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. In topology, it is often denoted as S 1 because it is a one-dimensional unit n-sphere ...

  4. Roundness - Wikipedia

    en.wikipedia.org/wiki/Roundness

    Having a constant diameter, measured at varying angles around the shape, is often considered to be a simple measurement of roundness.This is misleading. [3]Although constant diameter is a necessary condition for roundness, it is not a sufficient condition for roundness: shapes exist that have constant diameter but are far from round.

  5. Incircle and excircles - Wikipedia

    en.wikipedia.org/wiki/Incircle_and_excircles

    The radius of this Apollonius circle is + where is the incircle radius and is the semiperimeter of the triangle. [ 27 ] The following relations hold among the inradius r {\displaystyle r} , the circumradius R {\displaystyle R} , the semiperimeter s {\displaystyle s} , and the excircle radii r a {\displaystyle r_{a}} , r b {\displaystyle r_{b ...

  6. Equivalent radius - Wikipedia

    en.wikipedia.org/wiki/Equivalent_radius

    as one would expect. This is equivalent to the above definition of the 2D mean diameter. However, for historical reasons, the hydraulic radius is defined as the cross-sectional area of a pipe A, divided by its wetted perimeter P, which leads to =, and the hydraulic radius is half of the 2D mean radius. [3]

  7. Circle packing - Wikipedia

    en.wikipedia.org/wiki/Circle_packing

    The most efficient way to pack different-sized circles together is not obvious. In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap.