angular defect

Definitions

1. 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.
2. The amount by which the total of the angles around a vertex of a polyhedron is less than 360° (2π radians).
3. The angular displacement of a tooth from vertical.

Examples

“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[…].”

“The angular defect clearly has something to do with curvature, because the larger it is, the more pointed the surface is at the vertex.”

“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°.”

“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%.”

CEFR level