angular defectの例文

例文

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1. Its difference from 180?is a case of " angular defect " and serves as an important distinction for geometric systems.
2. The discrete analog of curvature, corresponding to curvature being concentrated at a point and particularly useful for polyhedra, is the Descartes'theorem on total angular defect.
3. Topologically, a regular 2-dimensional tessellation may be regarded as similar to a ( 3-dimensional ) polyhedron, but such that the angular defect is zero.
4. The polyhedron can be thought of as being folded from a sheet of paper ( a homeomorphic ( topologically equivalent ) to a sphere, and locally Euclidean except for a finite number of cone points whose angular defect sums to 4.
5. A converse to this theorem is given by Alexandrov's uniqueness theorem, according to which a metric space that is locally Euclidean except for a finite number of points of positive angular defect, adding to 4?, can be realized in a unique way as the surface of a convex polyhedron.