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A circle divided into a gibbous shape (light grey) and an astronomical crescent shape (dark grey) by a half-ellipse, where the major axis of the ellipse coincides with a diameter of the circle. According to geometry, an illuminated hemisphere of a sphere will appear to take on such gibbous or crescent shapes when viewed from an angle.
PR is the diameter of a circle centered on O; its radius AO is the arithmetic mean of a and b. Using the geometric mean theorem, triangle PGR's altitude GQ is the geometric mean. For any ratio a:b, AO ≥ GQ. A semicircle can be used to construct the arithmetic and geometric means of two lengths using straight-edge and compass.
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This is a list of two-dimensional geometric shapes in Euclidean and other geometries. For mathematical objects in more dimensions, see list of mathematical shapes. For a broader scope, see list of shapes.
That is, the result of moving a shape around, enlarging it, rotating it, or reflecting it in a mirror is the same shape as the original, and not a distinct shape. Many two-dimensional geometric shapes can be defined by a set of points or vertices and lines connecting the points in a closed chain, as well as the resulting interior points.
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.
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