angular defect

Definitions

1. 1

   The amount by which the sum of the interior angles of a triangle is less than 180° (π…

   The amount by which the sum of the interior angles of a triangle is less than 180° (π radians); the amount by which the sum of the internal angles of a polygon is less than what would be expected on the Euclidean plane.

   • Prop. XVI. If the angular defects of two triangles are equal, the areas of the triangles are equal.
   • We have seen that under any reasonable definition of area, the angular defect of a triangle is proportional to its area.
   • In hyperbolic geometry, similar triangles do not exist and the area of a triangle is directly proportional to its angular defect[…].
2. 2

   The amount by which the total of the angles around a vertex of a polyhedron is less than…

   The amount by which the total of the angles around a vertex of a polyhedron is less than 360° (2π radians).

   • The angular defect clearly has something to do with curvature, because the larger it is, the more pointed the surface is at the vertex.
   • 2015, Jan Guichelaar (translator and editor), Alex Van Den Brandhof, Arnout Jaspers (editors), Half a Century of Pythagoras Magazine, page 164, Theorem. For a spherical polyhedron the total angular defect equals 720°.
3. 3

   The angular displacement of a tooth from vertical.

   • In most instances angular defects have accompanying infrabony pockets; infrabony pockets always have an underlying angular defect.
   • The base of the angular defect is usually located apical to the surrounding bone and most often accompanied by infrabony pockets.[…]Angular defects are classified on the basis of number of walls.
   • Without therapy, the positive predictive rate of an angular defect to forecast more bone loss (22 mm) during a 10-year study was 28%.

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