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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.
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.
The rise (height) of a round arch is limited to 1 ⁄ 2 of its span, [7] so it looks more "grounded" than a parabolic arch [3] or a pointed arch. [7] Whenever a higher semicircular arch was required (for example, for a narrow arch to match the height of a nearby broad one), either stilting or horseshoe shape were used, thus creating a stilted arch and horseshoe arch respectively. [8]
The semi-major axis (major semiaxis) is the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. The semi-minor axis (minor semiaxis) of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section.
The salinon (red) and the circle (blue) have the same area. The salinon (meaning 'salt-cellar' in Greek) is a geometrical figure that consists of four semicircles . It was first introduced in the Book of Lemmas , a work attributed to Archimedes .
A stadium is a two-dimensional geometric shape constructed of a rectangle with semicircles at a pair of opposite sides. [1] The same shape is known also as a pill shape, [2] discorectangle, [3] obround, [4] [5] or sausage body. [6] The shape is based on a stadium, a place used for athletics and horse racing tracks.
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.
Semicircle, a geometric shape that forms half of a circle Topics referred to by the same term This disambiguation page lists articles associated with the title Hemicircle .