angular defect
Language: English
Part of speech: noun
Forms: form: angular defects
Senses: examples: text: Prop. XVI. If the angular defects of two triangles are equal, the areas of the triangles are equal.
ref: 1864, Transactions of the Royal Society of Edinburgh, volume 23, page 444:
text: We have seen that under any reasonable definition of area, the angular defect of a triangle is proportional to its area.
ref: 1995, Arlan Ramsay, Robert D. Richtmyer, Introduction to Hyperbolic Geometry, page 120:
text: In hyperbolic geometry, similar triangles do not exist and the area of a triangle is directly proportional to its angular defect[…].
ref: 1998, Kappa Mu Epsilon, The Pentagon: A Mathematics Magazine for Students, page 7:
topics: geometry
mathematics
sciences
qualifier: non-Euclidean geometry
glosses: 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.
examples: text: The angular defect clearly has something to do with curvature, because the larger it is, the more pointed the surface is at the vertex.
ref: 2005, Max K. Agoston, Computer Graphics and Geometric Modelling: Mathematics, page 604:
text: 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.
text: 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°.
topics: geometry
mathematics
sciences
glosses: The amount by which the total of the angles around a vertex of a polyhedron is less than 360° (2π radians).
examples: text: In most instances angular defects have accompanying infrabony pockets; infrabony pockets always have an underlying angular defect.
ref: 1986, Fermin A. Carranza, Dorothy A. Perry, Clinical Periodontology for the Dental Hygienist, page 62:
text: 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.
ref: 2008, T. Siji Jacob, P. Arunmozhi, Viva Voce in Periodontics, page 74:
text: Without therapy, the positive predictive rate of an angular defect to forecast more bone loss (22 mm) during a 10-year study was 28%.
ref: 2008, Dental Learning Systems, Compendium of Continuing Education in Dentistry, volume 28, numbers 7-11, page 442:
topics: dentistry
medicine
sciences
glosses: The angular displacement of a tooth from vertical.
Synonyms: sense: amount by which the total of the interior angles of a polygon is less than on the Euclidean plane
word: angular deficiency
sense: amount by which the total of the interior angles of a polygon is less than on the Euclidean plane
word: angular deficit
sense: angular deficiency, angular deficit
word: amount by which the total of the total of the angles around a vertex of a polyhedron is less than 360°
sense: angular displacement of tooth
word: vertical defect