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If a physical particle of unit mass were to move from x to y, it would have a moment about the origin of the coordinate system. The geometric equivalent to this moment is a vector whose direction is perpendicular to the plane containing the line L and the origin, and whose length equals twice the area of the triangle formed by the displacement ...
The first known trigonometric table, compiled by Hipparchus in the 2nd century BC, is no longer extant but tabulated the value of the chord function for every 7 + 1 / 2 degrees. In the 2nd century AD, Ptolemy compiled a more extensive table of chords in his book on astronomy , giving the value of the chord for angles ranging from 1 / ...
These turn out to be "tamer" than the projective planes since the extra degrees of freedom permit Desargues' theorem to be proved geometrically in the higher-dimensional geometry. This means that the coordinate "ring" associated to the geometry must be a division ring (skewfield) K, and the projective geometry is isomorphic to the one ...
Here algebraic varieties over a field k are considered as a special class of schemes over k. When k is algebraically closed , one can also think of a projective variety in a more elementary way, as a subset of P N ( k ) = ( k N + 1 − 0 ) / k ∗ {\displaystyle {\mathbf {P} }^{N}(k)=(k^{N+1}-0)/k^{*}} defined by homogeneous polynomial ...
It is a standard exercise of ... and in the coordinate approach have an exact parallel in the ... Discrete & Computational Geometry, 29 (3): 323–374. doi:10.1007 ...
Example of true position geometric control defined by basic dimensions and datum features. Geometric dimensioning and tolerancing (GD&T) is a system for defining and communicating engineering tolerances via a symbolic language on engineering drawings and computer-generated 3D models that describes a physical object's nominal geometry and the permissible variation thereof.
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