angular defect

Noun

angular defect (plural angular defects)

1. (non-Euclidean geometry) 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

   Synonyms:

   angular deficiency, angular deficit

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, page 604
   • 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.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
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 Hygienist, page 62
   • 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, P. Arunmozhi, Viva Voce in Periodontics, page 74

   Synonyms:

   amount by which the total of the total of the angles around a vertex of a polyhedron is less than 360°, vertical defect