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For a polyhedron, the defect at a vertex equals 2π minus the sum of all the angles at the vertex (all the faces at the vertex are included). If a polyhedron is convex, then the defect of each vertex is always positive. If the sum of the angles exceeds a full turn, as occurs in some vertices of many non-convex polyhedra, then the defect is ...
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Live Geometry is a free CodePlex project that lets you create interactive ruler and compass constructions and experiment with them. It is written in Silverlight 4 and C# 4.0 (Visual Studio 2010). The core engine is a flexible and extensible framework that allows easy addition of new figure types and features.
Since the result, the sum of all angles, can add up to 0 or (or multiples of ) only, it is sufficient to track through which quadrants the polygon winds, [5] as it turns around the test point, which makes the winding number algorithm comparable in speed to counting the boundary crossings.
The angle at the centre of the Earth that the ray of light passing through the body's GP makes with the line running from the observer's zenith is the same as the zenith distance. This is because they are corresponding angles. In practice it is not necessary to use zenith distances, which are 90° minus altitude, as the calculations can be done ...
Signed binary angle measurement. Black is traditional degrees representation, green is a BAM as a decimal number and red is hexadecimal 32-bit BAM. In this figure the 32-bit binary integers are interpreted as signed binary fixed-point values with scaling factor 2 −31, representing fractions between −1.0 (inclusive) and +1.0 (exclusive).
Walsh diagrams, often called angular coordinate diagrams or correlation diagrams, are representations of calculated orbital binding energies of a molecule versus a distortion coordinate (bond angles), used for making quick predictions about the geometries of small molecules.
According to vector mathematics, the angle of the result of the rational polynomial is the sum of all the angles in the numerator minus the sum of all the angles in the denominator. So to test whether a point in the s-plane is on the root locus, only the angles to all the open loop poles and zeros need be considered. This is known as the angle ...