Nomina
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.
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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.
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In hyperbolic geometry, similar triangles do not exist and the area of a triangle is directly proportional to its angular defect[…].
The amount by which the total of the angles around a vertex of a polyhedron is less than 360° (2π radians).
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The angular defect clearly has something to do with curvature, because the larger it is, the more pointed the surface is at the vertex.
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2014, C. R. Calladine, The Static-geometric Analogy in the Equations of Thin Shell Structures, W. Olszak, Thin Shell Theory: New Trends and Applications, page 294, Figure 4(c) shows a flattened view of a small part of the undeformed polygonalized S-surface, consisting of the triangles surrounding a particular vertex. When the S-surface is strained there will be a consequent change of angular defect, which we wish to calculate.
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°.
The angular displacement of a tooth from vertical.
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In most instances angular defects have accompanying infrabony pockets; infrabony pockets always have an underlying angular defect.
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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%.