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In geometry, the angular defect or simply defect (also called deficit or deficiency) is the failure of some angles to add up to the expected amount of
Angular_defect
How large a sphere or circle appears
The angular diameter, angular width, angular size, apparent diameter, or apparent size is an angular separation (in units of angle) describing how large
Angular_diameter
Topics referred to by the same term
Look up defect in Wiktionary, the free dictionary. Defect or defects may refer to: Angular defect, in geometry Birth defect, an abnormal condition present
Defect
Fundamental result in geometry
must depend on the triangle. Its difference from 180° is a case of angular defect and serves as an important distinction for geometric systems. In Euclidean
Sum_of_angles_of_a_triangle
Polyhedra are determined by surface distance
wedge that was removed is called the angular defect of the vertex; it is a positive number less than 2π. The defect of a polyhedron vertex can be measured
Alexandrov's theorem on polyhedra
Alexandrov's_theorem_on_polyhedra
Shape with four equal sides and angles
quadrilateral has angles whose sum falls short of 360° by an amount called the angular defect, proportional to its surface area. Small hyperbolic squares are approximately
Square
signs Descartes snark Descartes's theorem Descartes's theorem on total angular defect Folium of Descartes Cartesian diver Cartesian vortex theory Snell–Descartes
List of things named after René Descartes
List_of_things_named_after_René_Descartes
Mathematical measure of how much a curve or surface deviates from flatness
for polyhedra, is the (angular) defect; the analog for the Gauss–Bonnet theorem is Descartes' theorem on total angular defect. Because (Gaussian) curvature
Curvature
Supplementary pair of angles at each vertex of a polygon
angle associated with that vertex, also known by other names such as angular defect. The sum of these exterior angles across all vertices of the polyhedron
Internal_and_external_angles
Cheilitis characterized by inflammation of one or both of the corners of the mouth
Angular cheilitis (AC) is inflammation of one or both corners of the mouth. Often the corners are red with skin breakdown and crusting. It can also be
Angular_cheilitis
Theorem in differential geometry
conversely is proportional to its defect, as established by Johann Heinrich Lambert. Descartes' theorem on total angular defect of a polyhedron is the piecewise-linear
Gauss–Bonnet_theorem
Any of the five regular polyhedra
respectively. The angular deficiency at the vertex of a polyhedron is the difference between the sum of the face-angles at that vertex and 2π. The defect, δ, at
Platonic_solid
Topics referred to by the same term
Descartes's theorem may also refer to: Descartes's theorem on total angular defect, on angles in polyhedra Descartes's rule of signs, on roots of polynomials
Descartes's theorem (disambiguation)
Descartes's_theorem_(disambiguation)
Angular defect in a material
In crystallography, a disclination is a line defect in which there is compensation of an angular gap. They were first discussed by Vito Volterra in 1907
Disclination
Algebraic variety
the order of the group PSL(2, p), and D = π − π/2 − π/3 − π/p is the angular defect of the spherical (2,3,p) triangle. This results in a formula g = 1 24
Modular_curve
Polyhedron with 2 faces
locally Euclidean except at a finite number of points with positive angular defect summing to 4π. This characterization holds also for the distances on
Dihedron
Book by Pasquale Joseph Federico
Descartes' theorem on total angular defect, a discrete version of the Gauss–Bonnet theorem according to which the angular defects of the vertices of a convex
Descartes_on_Polyhedra
French philosopher and mathematician (1596–1650)
Descartes's theorem (4 tangent circles) Descartes's theorem on total angular defect Folium of Descartes List of things named after René Descartes Tree of
René_Descartes
Two pentagonal pyramids fused base-to-base
triangulations that, when their triangles are equilateral, have positive angular defect at every vertex. This makes them a combinatorial analogue of the positively
Pentagonal_bipyramid
de Bruijn's theorem (discrete geometry) Descartes's theorem on total angular defect (polyhedra) Erdős–Anning theorem (discrete geometry) Erdős–Nagy theorem
List_of_theorems
Notation for polytopes and tessellations
regarded as similar to a (3-dimensional) polyhedron, but such that the angular defect is zero. Thus, Schläfli symbols may also be defined for regular tessellations
Schläfli_symbol
1950 book on geometry by Aleksandr Danilovich Aleksandrov
set of points of positive angular defect, obeying Descartes's theorem on total angular defect that the total angular defect should be 4π. Chapter 5 considers
Convex_Polyhedra_(book)
Edge-joined polygons which fold into a polyhedron
each vertex of the resulting shape has positive angular defect and such that the sum of these defects is exactly 4π, then there necessarily exists exactly
Net_(polyhedron)
Solid with eight equal triangular faces
triangulations that, when their triangles are equilateral, have positive angular defect at every vertex. This makes them a combinatorial analogue of the positively
Regular_octahedron
Product of the principal curvatures of a surface
1 # f θ j {\displaystyle 2\pi -\sum _{j=1}^{\#f}\theta _{j}} is an angular defect of the vertex A - area of a control volume around vertex x i {\displaystyle
Gaussian_curvature
Flat-sided three-dimensional shape
19th century. One of its contributions was Descartes' theorem on total angular defect, which is closely related to Euler's polyhedral formula. Leonhard Euler
Polyhedron
Convex polyhedron with 14 triangle faces
triangulations that, when their triangles are equilateral, have positive angular defect at every vertex. This makes them a combinatorial analogue of the positively
Triaugmented_triangular_prism
Artery of the face
The angular artery is an artery of the face. It is the terminal part of the facial artery. It ascends to the medial angle of the eye's orbit. It is accompanied
Angular_artery
case, respectively. Euler characteristic Dehn–Sommerville equations Angular defect Gauss–Bonnet theorem Perles, M. A.; Shepard, G. C. (1967). "Angle sums
Gram–Euler_theorem
Excited atomic quantum state with high principal quantum number (n)
shows some of the energy levels of the lowest three values of orbital angular momentum in lithium. The existence of the Rydberg series was first demonstrated
Rydberg_atom
Tetrahedron whose faces are all congruent
all four faces have the same area, and the tetrahedra in which the angular defects of all four vertices equal π {\displaystyle \pi } . They are the polyhedra
Disphenoid
Five crystals arranged around a common axis
mineral Crystal twinning – Phenomenon in crystallization Disclination – Angular defect in a material Icosahedral twins – Structure found in atomic clusters
Fiveling
are four chief types of bone defects that present in the alveolar bone: horizontal defects vertical, or angular, defects fenestrations dehiscences Generalized
Bone destruction patterns in periodontal disease
Bone_destruction_patterns_in_periodontal_disease
Existence of geodesic circles on surfaces
geodesic of a convex polyhedron would necessarily bisect the total angular defect of the vertices, and almost all polyhedra do not have such bisectors
Theorem of the three geodesics
Theorem_of_the_three_geodesics
Structure found in atomic clusters and nanoparticles
constructions – Shapes for crystals with interfaces and twins Disclination – Angular defect in a material Fiveling – Five crystals arranged around a common axis
Icosahedral_twins
Peridontal assessment parameter measuring loss of connective tissue support
alveolar crest height. This bone loss may present as horizontal or angular defects, compromising periodontal ligament support and further accelerating
Clinical_attachment_loss
Depression of the jawbone
Stafne defect is a depression of the mandible (jawbone), most commonly located on the lingual surface (the side nearest the tongue). The Stafne defect is
Stafne_defect
Inflammation of the lips
hence has a good prognosis compared to oral cancer generally. Angular cheilitis (angular stomatitis, also known as cheilosis) is inflammation of one or
Cheilitis
Topics referred to by the same term
characteristic that acts as a barrier to cognitive performance Defect (geometry), angular deficit Déficit, a 2007 Mexican film by Gael García Bernal Wikiquote
Deficit
Surgical procedure to enhance or reconstruct a human nose
trauma caused by blast injury. Reconstructive surgery can also treat birth defects, breathing problems, and failed primary rhinoplasties. Rhinoplasty may
Rhinoplasty
Lithography using 13.5 nm UV light
abrupt the deformation, the narrower the defect edge extension, the greater the loss in reflectivity. EUV mask defect repair is also more complicated due to
EUV_lithography
Fungal infection
raw-looking lesion. Some sources consider denture-related stomatitis, angular stomatitis, median rhomboid glossitis, and antibiotic-induced stomatitis
Oral_candidiasis
Function describing an electron in an atom
respectively correspond to an electron's energy, its orbital angular momentum, and its orbital angular momentum projected along a chosen axis . The orbitals
Atomic_orbital
Vibration analysis of rotating machinery
from the vibrations of other rotating parts. To address this challenge, angular resampling, also known as Order tracking (signal processing), is applied
Condition-based maintenance of rotating machinery by vibration analysis
Condition-based_maintenance_of_rotating_machinery_by_vibration_analysis
Atoms with a single valence electron, so they behave like hydrogen
small orbital angular momentum, the spectrum is still described well by the Rydberg formula with an angular momentum dependent quantum defect, δ l {\displaystyle
Hydrogen-like_atom
Collision causing gamma ray emission
this process is allowed; see examples of annihilation. Conservation of angular momentum. Conservation of total (i.e. net) lepton number, which is the
Electron–positron annihilation
Electron–positron_annihilation
Flaw which compromises a weld's structural integrity
metalworking, a welding defect is any flaw that compromises the usefulness of a weldment. There are many different types of welding defects, which are classified
Welding_defect
Concept in inversive geometry
to Euclidean or hyperbolic metrics on triangulated manifolds with angular defects at their vertices. However, for manifolds with spherical geometry,
Inversive_distance
Unit of information in a quantum computer
dipole-dipole interactions. Solid-state defects (e.g., NV centers in diamond, SiC) Color center qudit / Defect qudit Electron spin states with S > 1/2
Qudit
Medical condition caused by receiving too little or too many nutrients
chronically. Similarly, folate deficiency has been linked to neural tube defects. Iodine deficiency is "the most common preventable cause of mental impairment
Malnutrition
Light energy absorbance and re-emission
becomes trapped in a defect in the lattice of the crystalline or amorphous material. A defect such as a missing atom (vacancy defect) can trap an electron
Phosphorescence
Sebaceous glands that are present in most individuals
v t e Oral and maxillofacial pathology Lips Cheilitis Actinic Angular Plasma cell Cleft lip Congenital lip pit Eclabium Herpes labialis Macrocheilia Microcheilia
Fordyce_spots
Optical phenomenon
spinning carries orbital angular momentum with the wave train, and will induce torque on an electric dipole. Orbital angular momentum is distinct from
Optical_vortex
Breed of cat
to a wrinkled appearance. The Levkoy's peculiar features are: special angular contour of its head and "stepped" profile (dog-face appearance), folded
Ukrainian_Levkoy
Fundamental concept of classical mechanics
"relativists", even at the time of Newton, felt that absolute space was a defect of the formulation, and should be replaced. The expression inertial frame
Inertial_frame_of_reference
Bone marrow defect in Mandible
Osteoporotic bone marrow defect is a condition which may be found in the body of the mandible. It is usually painless and found during routine radiographs
Osteoporotic bone marrow defect
Osteoporotic_bone_marrow_defect
Speculative feature of the early universe
Cosmic strings are hypothetical 1-dimensional topological defects which may have formed during a symmetry-breaking phase transition in the early universe
Cosmic_string
Common human disease caused by a group of viruses
v t e Oral and maxillofacial pathology Lips Cheilitis Actinic Angular Plasma cell Cleft lip Congenital lip pit Eclabium Herpes labialis Macrocheilia Microcheilia
Hand,_foot,_and_mouth_disease
Medical condition
v t e Oral and maxillofacial pathology Lips Cheilitis Actinic Angular Plasma cell Cleft lip Congenital lip pit Eclabium Herpes labialis Macrocheilia Microcheilia
Transient_lingual_papillitis
Autoimmune disease
leading to proteinuria (excess protein in urine), urinary concentrating defect, and distal renal tubular acidosis. Among the complications discussed above
Sjögren's_disease
Medical condition
may be additional signs and symptoms such as pallor, oral ulceration and angular cheilitis. Iron-deficiency anemia is mainly caused by blood loss, such
Glossitis
Automotive concept
these are about equal. Angular inertia determines the rotational inertia of an object for a given rate of rotation. The yaw angular inertia tends to keep
Automobile_handling
Tongue disorder
v t e Oral and maxillofacial pathology Lips Cheilitis Actinic Angular Plasma cell Cleft lip Congenital lip pit Eclabium Herpes labialis Macrocheilia Microcheilia
Geographic_tongue
Medical condition
Lingual cortical defects, also known as idiopathic bone cavity, Stafne defect, static bone cavity, and salivary gland defect, among others, is a benign
Oral and maxillofacial pathology
Oral_and_maxillofacial_pathology
Branch of physics that studies light
22λD where θ is the angular resolution, λ is the wavelength of the light, and D is the diameter of the lens aperture. If the angular separation of the two
Optics
Inflammation of the soft tissues surrounding the crown of a partially erupted tooth
tooth showing chronic pericoronitis, operculum (blue arrow) and bone destruction (red arrow) from chronic inflammation. Tooth is slightly disto-angular.
Pericoronitis
Inflammation of the mouth and lips
Inflammation of the corners (angles) of the lips is termed angular stomatitis or angular cheilitis. In children a frequent cause is repeated lip-licking
Stomatitis
Physical anomaly involving extra fingers or toes
Polydactyly (commonly known as sixth finger and extra finger) is a birth defect that results in extra fingers or toes. The hands are more commonly involved
Polydactyly
Clarity of vision
peripheral vision. The minimum angular resolution of the human eye is 28 arc seconds or 0.47 arc minutes; this gives an angular resolution of 0.008 degrees
Visual_acuity
Inflammation of the gums
v t e Oral and maxillofacial pathology Lips Cheilitis Actinic Angular Plasma cell Cleft lip Congenital lip pit Eclabium Herpes labialis Macrocheilia Microcheilia
Gingivitis
Region in space
Typically, the largest fluctuations of the primordial CMB temperature occur on angular scales of about 1°. Thus a cold region as large as the "cold spot" appears
CMB_cold_spot
Measurement method in nuclear physics
The perturbed γ-γ angular correlation, PAC for short or PAC-Spectroscopy, is a method of nuclear solid-state physics with which magnetic and electric
Perturbed_angular_correlation
Herpes simplex virus infection of the lip
the corner of the mouth and be mistaken for angular cheilitis of another cause. Sometimes termed "angular herpes simplex". A cold sore at the corner of
Cold_sore
Benign lesion on the side of the tongue due to Epstein-Barr virus
v t e Oral and maxillofacial pathology Lips Cheilitis Actinic Angular Plasma cell Cleft lip Congenital lip pit Eclabium Herpes labialis Macrocheilia Microcheilia
Hairy_leukoplakia
Experimental techniques of solid-state physics
Angular Correlation of Electron Positron Annihilation Radiation (ACAR or ACPAR) is a technique of solid state physics to investigate the electronic structure
Angular Correlation of Electron Positron Annihilation Radiation
Angular_Correlation_of_Electron_Positron_Annihilation_Radiation
Photolithography technique
with a liquid medium that has a refractive index greater than one. The angular resolution is increased by a factor equal to the refractive index of the
Immersion_lithography
Medical condition
v t e Oral and maxillofacial pathology Lips Cheilitis Actinic Angular Plasma cell Cleft lip Congenital lip pit Eclabium Herpes labialis Macrocheilia Microcheilia
Eagle_syndrome
Type of external fixation (medical device)
which cannot be surgically resolved. The Ilizarov apparatus corrects angular deformity in a leg, corrects differences in the lengths of the legs of
Ilizarov_apparatus
Defect types include atom vacancies, adatoms, steps, and kinks that occur most frequently at surfaces due to the finite material size causing crystal discontinuity
Carrier_scattering
Spectroscopic technique
approaches for the analysis of Cu2ZnGeSe4: influence of the off-stoichiometry on defect formation and solar cell performance". Journal of Materials Chemistry A
Raman_spectroscopy
Medical condition
v t e Oral and maxillofacial pathology Lips Cheilitis Actinic Angular Plasma cell Cleft lip Congenital lip pit Eclabium Herpes labialis Macrocheilia Microcheilia
Noma_(disease)
Decreased ability to see
visual field defect in which the peripheral field is contracted to such an extent that the widest diameter of the visual field subtends an angular distance
Visual_impairment
alpha (α). Just like angular velocity, there are two types of angular acceleration: spin angular acceleration and orbital angular acceleration, representing
Glossary_of_physics
Rash that is an early sign of measles
v t e Oral and maxillofacial pathology Lips Cheilitis Actinic Angular Plasma cell Cleft lip Congenital lip pit Eclabium Herpes labialis Macrocheilia Microcheilia
Koplik's_spots
Telescope for observations with visible light
marginal rays, proportional to the square of the objective diameter. Coma A defect by which points appear as comet-like asymmetrical patches of light with
Optical_telescope
American chess grandmaster (1943–2008)
Back in 1958, in the Central Chess Club, Vladimir Alatortsev saw a tall, angular 15-year-old youth, who in blitz games, crushed almost everyone who crossed
Bobby_Fischer
Close surroundings of an atom
impurities or defects, which means that a foreign atom resides on a lattice site or in between lattice sites (interstitials). These small defects and impurities
Local_structure
Inflammation of tooth sockets in the jawbones
where the blood clot fails to form or is lost from the socket (i.e., the defect left in the gum when a tooth is taken out). This leaves an empty socket
Alveolar_osteitis
Congenital disorder of tongue mobility
v t e Oral and maxillofacial pathology Lips Cheilitis Actinic Angular Plasma cell Cleft lip Congenital lip pit Eclabium Herpes labialis Macrocheilia Microcheilia
Ankyloglossia
Visible body parts at the mouth
cheilitis (chronically sun damaged lips). Cleft lip is a type of birth defect that can be successfully treated with surgery. Carcinoma (a malignant cancer
Lip
Semiconductor company
light. This product line includes solutions for inspection, metrology, and defect analysis in logic and memory chip manufacturing, including chiplet production
Carl_Zeiss_SMT
Relativistic equation relating total energy to mass and momentum
such as grams (strictly speaking grams·c2), thereby illustrating the mass defect in especially powerful releases of energy. For example, the first atomic
Energy–momentum_relation
Possible shape of human incisor teeth
v t e Oral and maxillofacial pathology Lips Cheilitis Actinic Angular Plasma cell Cleft lip Congenital lip pit Eclabium Herpes labialis Macrocheilia Microcheilia
Shovel-shaped_incisors
Sore on the mucous membrane of the oral cavity
ulcer which specifically occurs on a mucous membrane. An ulcer is a tissue defect which has penetrated the epithelial-connective tissue border, with its base
Mouth_ulcer
Non-local formulation of continuum mechanics
{{\{0\}}\times \mathbb {R} ^{n})}}} . Due to the necessity of satisfying angular momentum conservation, the condition below on the scalar valued function
Peridynamics
Electronic oscillator circuit
are abundant near the crystal seed. Another defect of importance is the hydrogen containing growth defect, when instead of a Si−O−Si structure, a pair
Crystal_oscillator
Law of electrical current and voltage
the s parameter is taken to be jω (with j the imaginary unit and ω the angular frequency of the sinusoid), corresponding to a complex sinusoid Ae jωt
Ohm's_law
Physical theory of the cosmos
shape of the universe to be spatially almost flat by measuring the typical angular size (the size on the sky) of the anisotropies. In early 2003, the first
Big_Bang
Medical condition
v t e Oral and maxillofacial pathology Lips Cheilitis Actinic Angular Plasma cell Cleft lip Congenital lip pit Eclabium Herpes labialis Macrocheilia Microcheilia
Velopharyngeal_inadequacy
Medical condition
v t e Oral and maxillofacial pathology Lips Cheilitis Actinic Angular Plasma cell Cleft lip Congenital lip pit Eclabium Herpes labialis Macrocheilia Microcheilia
Caviar_tongue
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