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单词 angular defect
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angular defect
angular defect n. Mathematics (a) (in non-Euclidean geometry) the difference between the sum of the interior angles of a given figure and that of the same figure as it would appear in the Euclidean plane (cf. non-Euclidean adj.); (b) the difference between the sum of the angles at any vertex of a regular polyhedron and 360°; cf. defect n. 1c.
ΚΠ
1844 Edinb. New Philos. Jrnl. 36 313 For when the several parts of the areas and of the angular defects are proportional, so must any corresponding sums of such parts.
1971 H. S. M. Coxeter in M. J. Wenninger Polyhedron Models p. xi/1 The angular defect, added up for all the corners, always makes a total of 720°.
2007 Math. in School 36 8/2 Each solid has 20 vertices, each with an angular defect of 36°.
2012 B. H. Lavenda New Perspective Relativity i. 35 The surfaces of negative curvature produce a geometry in which the angular defect is proportional to the area.
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