See angular defect on Wiktionary
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"ref": "1864, Transactions of the Royal Society of Edinburgh, volume 23, page 444:",
"text": "Prop. XVI. If the angular defects of two triangles are equal, the areas of the triangles are equal.",
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"ref": "1995, Arlan Ramsay, Robert D. Richtmyer, Introduction to Hyperbolic Geometry, page 120:",
"text": "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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"ref": "1998, Kappa Mu Epsilon, The Pentagon: A Mathematics Magazine for Students, page 7:",
"text": "In hyperbolic geometry, similar triangles do not exist and the area of a triangle is directly proportional to its angular defect[…].",
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"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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"_dis1": "71 27 2",
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"ref": "2005, Max K. Agoston, Computer Graphics and Geometric Modelling: Mathematics, page 604:",
"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.",
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"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,\nFigure 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."
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"text": "2015, Jan Guichelaar (translator and editor), Alex Van Den Brandhof, Arnout Jaspers (editors), Half a Century of Pythagoras Magazine, page 164,\nTheorem. For a spherical polyhedron the total angular defect equals 720°."
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"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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"ref": "1986, Fermin A. Carranza, Dorothy A. Perry, Clinical Periodontology for the Dental Hygienist, page 62:",
"text": "In most instances angular defects have accompanying infrabony pockets; infrabony pockets always have an underlying angular defect.",
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"ref": "2008, T. Siji Jacob, P. Arunmozhi, Viva Voce in Periodontics, page 74:",
"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.",
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"ref": "2008, Dental Learning Systems, Compendium of Continuing Education in Dentistry, volume 28, numbers 7-11, page 442:",
"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%.",
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"The angular displacement of a tooth from vertical."
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},
{
"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,\nFigure 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,\nTheorem. For a spherical polyhedron the total angular defect equals 720°."
}
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},
{
"ref": "2008, T. Siji Jacob, P. Arunmozhi, Viva Voce in Periodontics, page 74:",
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},
{
"ref": "2008, Dental Learning Systems, Compendium of Continuing Education in Dentistry, volume 28, numbers 7-11, page 442:",
"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%.",
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Download raw JSONL data for angular defect meaning in All languages combined (5.2kB)
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