angular defect

Noun

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.
   • Prop. XVI. If the angular defects of two triangles are equal, the areas of the triangles are equal. - 1864, Transactions of the Royal Society of Edinburgh, volume 23, page 444:
   • We have seen that under any reasonable definition of area, the angular defect of a triangle is proportional to its area. - 1995, Arlan Ramsay, Robert D. Richtmyer, Introduction to Hyperbolic Geometry, page 120:
   • In hyperbolic geometry, similar triangles do not exist and the area of a triangle is directly proportional to its angular defect[…]. - 1998, Kappa Mu Epsilon, The Pentagon: A Mathematics Magazine for Students, page 7:
2. 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. - 2005, Max K. Agoston, Computer Graphics and Geometric Modelling: Mathematics,...
   • 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...
   • 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. 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. - 1986, Fermin A. Carranza, Dorothy A. Perry, Clinical Periodontology for the Dental...
   • 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. - 2008, T. Siji Jacob,...
   • Without therapy, the positive predictive rate of an angular defect to forecast more bone loss (22 mm) during a 10-year study was 28%. - 2008, Dental Learning Systems, Compendium of Continuing Education in Dentistry,...