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Generalization of Dehn's lemma in the topology of 3-manifolds
mathematics, in the topology of 3-manifolds, the loop theorem is a generalization of Dehn's lemma. The loop theorem was first proven by Christos Papakyriakopoulos
Loop_theorem
Theorem in vector calculus
the surface. The classical theorem of Stokes can be stated in one sentence: The line integral of a vector field over a loop is equal to the surface integral
Stokes'_theorem
Theorem in topology
using his "tower construction". He also generalized the theorem to the loop theorem and sphere theorem. Papakyriakopoulos proved Dehn's lemma using a tower
Dehn's_lemma
Cycles going through a hierarchy
the Peano axioms) in his incompleteness theorem. Gödel showed that mathematics and logic contain strange loops: propositions that not only refer to mathematical
Strange_loop
Theorem about a certain class of control-flow graphs
operates in terms of a while loop. Harel notes that the single loop used by the folk version of the structured programming theorem basically just provides
Structured_program_theorem
Mathematical space
parallel elements. The loop theorem is a generalization of Dehn's lemma and should more properly be called the "disk theorem". It was first proven by
3-manifold
Theorem in quantum physics
In quantum electrodynamics, Furry's theorem states that if a Feynman diagram consists of a closed loop of fermion lines with an odd number of vertices
Furry's_theorem
Limitative results in mathematical logic
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Invariants used to prove properties of loops
In computer science, a loop invariant is a property of a program loop that is true before (and after) each iteration. It is a logical assertion, sometimes
Loop_invariant
Theorem used for studying closed-loop stability
Theorem. Assume two stable systems S 1 {\displaystyle S_{1}} and S 2 {\displaystyle S_{2}} are connected in a feedback loop, then the closed loop system
Small-gain_theorem
Theorem in topology
In topology, the Jordan curve theorem (JCT), formulated by Camille Jordan in 1887, asserts that every Jordan curve (a plane simple closed curve) divides
Jordan_curve_theorem
Klein bottle that is not π1-injective. However, if S is two-sided, the loop theorem implies Kneser's lemma, that if S is incompressible, then it is π1-injective
Incompressible_surface
Formula relating lift on an airfoil to fluid speed, density, and circulation
Kutta-Joukowski theorem, the loop must be chosen outside this boundary layer. (For example, the circulation calculated using the loop corresponding to
Kutta–Joukowski_theorem
Every polynomial has a real or complex root
The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Feynman diagram with only one cycle
In physics, a one-loop Feynman diagram is a connected Feynman diagram with only one cycle (unicyclic). Such a diagram can be obtained from a connected
One-loop_Feynman_diagram
Principle suggesting that time travel paradoxes are inherently impossible
"glancing blow" solution, to evade inconsistencies arising from causality loops. In the revised scenario, the ball from the future emerges at a different
Novikov self-consistency principle
Novikov_self-consistency_principle
Theorem in geometric topology
conjecture (UK: /ˈpwæ̃kæreɪ/, US: /ˌpwæ̃kɑːˈreɪ/, French: [pwɛ̃kaʁe]) is a theorem about the characterization of the 3-sphere (the hypersphere that bounds
Poincaré_conjecture
Greek mathematician (1914–1976)
Papakyriakopoulos is best known for his proofs of Dehn's lemma, the loop theorem, and the sphere theorem, three foundational results for the study of 3-manifolds
Christos_Papakyriakopoulos
Theorems that help decompose a finite group based on prime factors of its order
specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Peter Ludwig Sylow
Sylow_theorems
body Handlebody Incompressible surface Dehn's lemma Loop theorem (aka the Disk theorem) Sphere theorem Haken manifold JSJ decomposition Branched surface
List of geometric topology topics
List_of_geometric_topology_topics
German mathematician (born 1938)
Stud., 113, Princeton Univ. Press, Princeton, NJ, 1987. Graph manifold Loop theorem K-theory of a category Smith conjecture Surface subgroup conjecture Virtually
Friedhelm_Waldhausen
On the loop space of a wedge of spheres
Hilton's theorem, proved by Peter Hilton (1955), states that the loop space of a wedge of spheres is homotopy-equivalent to a product of loop spaces of
Hilton's_theorem
Group that is also a differentiable manifold with group operations that are smooth
Lie group is a Lie group. This is known as the closed subgroup theorem or Cartan's theorem. The quotient of a Lie group by a closed normal subgroup is a
Lie_group
Establishes the concept of stabilization of homotopy groups
homotopy groups, where Ω denotes the loop functor and Σ denotes the reduced suspension functor. The suspension theorem then states that the induced map on
Freudenthal suspension theorem
Freudenthal_suspension_theorem
Pathological embedding of the sphere in 3D space
connected, unlike the exterior of the usual round sphere. The Schoenflies theorem in 2D states that any simple closed curve in the plane can be extended
Alexander_horned_sphere
Theorem implying that no algorithm can optimally perform a task done by humans
science and mathematics, a full employment theorem is a term used, often humorously, to refer to a theorem which states that no algorithm can optimally
Full-employment_theorem
Theorem that every subgroup of a free group is itself free
In group theory, a branch of mathematics, the Nielsen–Schreier theorem states that every subgroup of a free group is itself free. It is named after Jakob
Nielsen–Schreier_theorem
3D motion of fluid near vortex lines
loop, extend to infinity or start/end at solid boundaries. Fluid elements initially free of vorticity remain free of vorticity. Helmholtz's theorems have
Helmholtz's_theorems
2007 book by Douglas Hofstadter
I Am a Strange Loop is a 2007 book by Douglas Hofstadter, examining in depth the concept of a strange loop to explain the sense of "I". The concept of
I_Am_a_Strange_Loop
Theorem in quantum mechanics
The Kinoshita–Lee–Nauenberg theorem or KLN theorem states that perturbatively the Standard Model as a whole is infrared (IR) finite. That is, the infrared
Kinoshita–Lee–Nauenberg theorem
Kinoshita–Lee–Nauenberg_theorem
Evaluates a line integral through a gradient field using the original scalar field
The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated
Gradient_theorem
Commutative group (mathematics)
structure theorem for finitely generated modules over a principal ideal domain. In the case of finitely generated abelian groups, this theorem guarantees
Abelian_group
Problem in computer science
Minsky notes: ...the magnitudes involved should lead one to suspect that theorems and arguments based chiefly on the mere finiteness [of] the state diagram
Halting_problem
Branch of engineering and mathematics
value Krener's theorem Lead-lag compensator – Control system componentPages displaying short descriptions of redirect targets Minor loop feedback – Classical
Control_theory
Concept in differential geometry
closely related to the curvature of the connection, via the Ambrose–Singer theorem. The study of Riemannian holonomy has led to a number of important developments
Holonomy
Theorem in complex analysis
In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard
Cauchy's_integral_theorem
Statistical physics theorem
The fluctuation–dissipation theorem (FDT) or fluctuation–dissipation relation (FDR) is a powerful tool in statistical physics for predicting the behavior
Fluctuation–dissipation theorem
Fluctuation–dissipation_theorem
Both deterministic and nondeterministic machines can solve more problems given more space
In computational complexity theory, the space hierarchy theorems are separation results that show that both deterministic and nondeterministic machines
Space_hierarchy_theorem
Integral criterion for holomorphy
mathematics, Morera's theorem, named after Giacinto Morera, gives a criterion for proving that a function is holomorphic. Morera's theorem states that a continuous
Morera's_theorem
Proof all ranked voting rules have spoilers
Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow. It shows that no procedure for group
Arrow's_impossibility_theorem
Finiteness of sets of forbidden graph minors
In graph theory, the Robertson–Seymour theorem (also called the graph minors theorem) states that the undirected graphs, partially ordered by the graph
Robertson–Seymour_theorem
Theorem in game theory
Aumann's agreement theorem states that two Bayesian agents with the same prior beliefs cannot "agree to disagree" about the probability of an event if
Aumann's_agreement_theorem
Relates the curvature of a Riemannian manifold to its topology
In mathematics, specifically Riemannian geometry, Synge's theorem is a classical result relating the curvature of a Riemannian manifold to its topology
Synge's_theorem
Group theory theorem
In mathematics, the closed-subgroup theorem (sometimes referred to as Cartan's theorem) is a theorem in the theory of Lie groups. It states that if H is
Closed-subgroup_theorem
Ability of a computing system to simulate Turing machines
Computability theory Inner loop Loop (computing) Machine that always halts Rice's theorem S m n theorem Structured program theorem Turing tarpit Virtualization
Turing_completeness
theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem (set theory) Erdős–Rado theorem (set
List_of_theorems
Monster and modular connection
Richard Borcherds for the moonshine module in 1992 using the no-ghost theorem from string theory and the theory of vertex operator algebras and generalized
Monstrous_moonshine
Mathematical group of the homotopy classes of loops in a topological space
first loop, then along the second. Two loops are considered equivalent if one can be deformed into the other without breaking. The set of all such loops with
Fundamental_group
Complete manifolds of non-negative sectional curvature largely reduce to the compact case
In mathematics, the soul theorem is a theorem of Riemannian geometry that largely reduces the study of complete manifolds of non-negative sectional curvature
Soul_theorem
On the number of spanning trees in a graph
mathematical field of graph theory, Kirchhoff's theorem or Kirchhoff's matrix tree theorem is a theorem about the number of spanning trees in a graph.
Kirchhoff's_theorem
Statement about integration on manifolds
generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, is a statement about
Generalized_Stokes_theorem
Relation between genus, degree, and dimension of function spaces over surfaces
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension
Riemann–Roch_theorem
Transformations induced by a mathematical group
known as the orbit–stabilizer theorem. If G is finite then the orbit–stabilizer theorem, together with Lagrange's theorem, gives | G ⋅ x | = [ G : G x
Group_action
Theorem in quantum mechanics
The spin–statistics theorem proves that the observed relationship between the intrinsic spin of a particle (angular momentum not due to the orbital motion)
Spin–statistics_theorem
Grishkov–Zelmanov Theorem. Conjecture: Let L be a finitely generated Moufang loop of exponent 4 or 6. Then L is finite. Proposed: by Alexander Grishkov at Loops '11
List of problems in loop theory and quasigroup theory
List_of_problems_in_loop_theory_and_quasigroup_theory
Theorem in group theory
mathematical subject of group theory, the Grushko theorem or the Grushko–Neumann theorem is a theorem stating that the rank (that is, the smallest cardinality
Grushko_theorem
On degree sums and Hamiltonian cycles
Ore's theorem is a result in graph theory proved in 1960 by Norwegian mathematician Øystein Ore. It gives a sufficient condition for a graph to be Hamiltonian
Ore's_theorem
Gauge symmetry cannot be spontaneously broken
the theorem requires constructing nonlocal gauge invariant operators, whose expectation values need not be zero. The most common ones are Wilson loops and
Elitzur's_theorem
Parametrization used for loop integrals
parametrization is a technique for evaluating loop integrals which arise from Feynman diagrams with one or more loops. However, it is sometimes useful in integration
Feynman_parametrization
implies that it may only be renormalized at one-loop. In the 1994 article Nonrenormalization Theorem for Gauge Coupling in 2+1D the authors find the renormalization
Supersymmetry nonrenormalization theorems
Supersymmetry_nonrenormalization_theorems
Theorem in graph theory
indegree-outdegree pairs of a labeled directed graph with at most one loop per vertex? The theorem can easily be adapted to this formulation, because there does
Gale–Ryser_theorem
Theory of quantum gravity merging quantum mechanics and general relativity
fewer degrees of freedom than the classical theory. Theorems establishing the uniqueness of the loop representation as defined by Ashtekar et al. (i.e.
Loop_quantum_gravity
Describes a periodicity in the homotopy groups of classical groups
In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by Raoul Bott (1957, 1959)
Bott_periodicity_theorem
Mathematical group of loops in a Lie group
These holomorphic subgroups enter the Birkhoff factorization theorem, according to which a loop in G\mathbf C can, on suitable strata, be written in the form
Loop_group
Theorem classifying finite simple groups
classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every finite simple group is
Classification of finite simple groups
Classification_of_finite_simple_groups
On coloring the edges of graphs
necessary. A more general version of Vizing's theorem states that every undirected multigraph without loops can be colored with at most Δ+µ colors, where
Vizing's_theorem
Algebraic structure
algebra and alternative algebra). Moufang's theorem states that when three elements x, y, and z in a Moufang loop obey the associative law: (xy)z = x(yz)
Moufang_loop
Group of 𝑛 × 𝑛 invertible matrices
subspace and dividing into the formula just given, by the orbit-stabilizer theorem. These formulas are connected to the Schubert decomposition of the Grassmannian
General_linear_group
Theorem on the orders of subgroups
In the mathematical field of group theory, Lagrange's theorem states that if H is a subgroup of any finite group G, then | H | {\displaystyle |H|} is
Lagrange's theorem (group theory)
Lagrange's_theorem_(group_theory)
Branch of mathematics that studies abstract algebraic structures
over fields of characteristic zero) include finite groups (see Maschke's theorem), compact groups, and semisimple Lie algebras. In cases where complete
Representation_theory
Algebraic curve in mathematics
geometry) Modularity theorem Moduli stack of elliptic curves Nagell–Lutz theorem Riemann–Hurwitz formula Wiles's proof of Fermat's Last Theorem Sarli, J. (2012)
Elliptic_curve
Existence of group elements of prime order
In mathematics, specifically group theory, Cauchy's theorem states that if G is a finite group and p is a prime number dividing the order of G (the number
Cauchy's theorem (group theory)
Cauchy's_theorem_(group_theory)
Basic law of electromagnetism
electromotive force (emf) around a closed conducting loop to the time rate of change of magnetic flux through the loop. This rule can be derived from the first in
Faraday's_law_of_induction
Assemblage of connected electrical elements
capacitances). An electrical circuit is a network consisting of a closed loop, giving a return path for the current. Thus all circuits are networks, but
Electrical_network
Group of unitary complex matrices with determinant of 1
serve as unit vectors for the description of our 3 spatial dimensions in loop quantum gravity. They also correspond to the Pauli X, Y, and Z gates, which
Special_unitary_group
In board games that cannot end in a draw, one of the two players has a winning strategy
In game theory, Zermelo's theorem is a theorem about finite two-person games of perfect information in which the players move alternately and in which
Zermelo's theorem (game theory)
Zermelo's_theorem_(game_theory)
Class of theorems about Nash equilibrium payoff profiles in repeated games
In game theory, folk theorems are a class of theorems describing an abundance of Nash equilibrium payoff profiles in repeated games (Friedman 1971). The
Folk_theorem_(game_theory)
Theorem in differential topology
topology, there are two Whitney embedding theorems, named after Hassler Whitney: The strong Whitney embedding theorem states that any smooth real m-dimensional
Whitney_embedding_theorem
Mathematical group
algebras Representations of classical Lie groups Theorem of the highest weight Borel–Weil–Bott theorem Lie groups in physics Particle physics and representation
Symplectic_group
Numerical measure of program structure
into a loop, branching out of a loop, and their if-then-else counterparts) which he uses to formulate a theorem analogous to Kuratowski's theorem, and thereafter
Essential_complexity
Group that is a topological space with continuous group operations
Hewitt & Ross 1970, Theorem 27.40. Mackey 1976, section 2.4. Banaszczyk 1983. Hatcher 2001, Theorem 4.66. Hatcher 2001, Theorem 3C.4. Edwards 1995, p
Topological_group
How software progresses through its implementation
(indefinite iteration), or infinitely. A loop inside the loop body is called a nested loop. Early exit from a loop may be supported via a break statement
Control_flow
Construction analogous to that of a dual vector space
is used in the statement of the Poisson summation formula, transference theorems provide connections between the geometry of a lattice and that of its dual
Dual_lattice
Pictorial representation of the behavior of subatomic particles
x = e i k x {\displaystyle A_{kx}=e^{ikx}\,} and the Fourier inversion theorem tells you the inverse: A k x − 1 = e − i k x {\displaystyle A_{kx}^{-1}=e^{-ikx}\
Feynman_diagram
Process of creating equivalent circuits
The Miller theorem refers to the process of creating equivalent circuits. It asserts that a floating impedance element, supplied by two voltage sources
Miller_theorem
Bartlett's bisection theorem is an electrical theorem in network analysis attributed to Albert Charles Bartlett. The theorem shows that any symmetrical
Bartlett's_bisection_theorem
Describes the fundamental group in terms of a cover by two open path-connected subspaces
Seifert–Van Kampen theorem of algebraic topology (named after Herbert Seifert and Egbert van Kampen), sometimes just called Van Kampen's theorem, expresses the
Seifert–Van_Kampen_theorem
Branch of mathematics that studies the properties of groups
is known that V above decomposes into irreducible parts (see Maschke's theorem). These parts, in turn, are much more easily manageable than the whole
Group_theory
Solution concept of a non-cooperative game
Kakutani fixed-point theorem in his 1950 paper to prove existence of equilibria. His 1951 paper used the simpler Brouwer fixed-point theorem for the same purpose
Nash_equilibrium
Type of group in mathematics
} with a2 + b2 = 1. This results from the spectral theorem by regrouping eigenvalues that are complex conjugate, and taking into account
Orthogonal_group
Mathematics concept
with topology, and obtained the first proof of the full Nielsen–Schreier theorem. Otto Schreier published an algebraic proof of this result in 1927, and
Free_group
Pairing where no unchosen pair prefers each other over their choice
and hybrid CPU–GPU execution to reduce overhead. The rural hospitals theorem concerns a more general variant of the stable matching problem, like that
Stable_matching_problem
On zeros of derivatives of cubic polynomials
In mathematics, Marden's theorem, named after Morris Marden but proved about 100 years earlier by Jörg Siebeck, gives a geometric relationship between
Marden's_theorem
Group of unitary matrices
Quaternionic, Fermionic". Retrieved 1 February 2012. Grove (2002), Theorem 10.3. Grove (2002), Theorems 11.22 and 11.26. Milne, Algebraic Groups and Arithmetic Groups
Unitary_group
Theorem in cybernetics
The good regulator theorem is a theorem conceived by Roger C. Conant and W. Ross Ashby that is central to cybernetics. It was originally stated as "every
Good_regulator_theorem
Group without normal subgroups other than the trivial group and itself
eventually arrives at uniquely determined simple groups, by the Jordan–Hölder theorem. The complete classification of finite simple groups, completed in 2004
Simple_group
Subset of a group that forms a group itself
H is called the index of H in G and is denoted by [G : H]. Lagrange's theorem states that for a finite group G and a subgroup H, [ G : H ] = | G | |
Subgroup
Topic in group theory
. This is also known as the Krasner–Kaloujnine embedding theorem. The Krohn–Rhodes theorem involves what is basically the semigroup equivalent of this
Wreath_product
Mathematical group that can be generated as the set of powers of a single element
Golubitsky 2010, pp. 47–48). (Cox 2012, p. 294, Theorem 11.1.7). (Cox 2012, p. 295, Corollary 11.1.8 and Theorem 11.1.9). (Aluffi 2009, pp. 82–84, 6.4 Example:
Cyclic_group
Two equalities that deal with the current and potential difference
voltage drop around any loop is zero. This includes imaginary loops arranged arbitrarily in space – not limited to the loops delineated by the circuit
Kirchhoff's_circuit_laws
LOOP THEOREM
LOOP THEOREM
Boy/Male
Dutch, German, Hebrew
God will Multiply; God will Add
Boy/Male
Indian, Sanskrit
Natural; Original; Innate; Simply; Loop
Surname or Lastname
English
English : metonymic occupational name for a cooper, from Middle English coupe ‘tub’, ‘container’ (see Cooper). In some cases the surname may have been derived from a pub or house sign.Dutch : from koop ‘purchase’, ‘bargain’, hence a nickname for a haggler or a metonymic occupational name for a merchant.
Surname or Lastname
North German
North German : habitational name from any of several places called Loose or Loosey.North German : from a short form of Nikolaus, German form of Nicholas.Dutch : nickname from the adjective loos ‘cunning’, ‘artful’, ‘guileful’.English : variant spelling of Loose.
Boy/Male
Hindu
Flower
Girl/Female
Gujarati, Hindu, Indian
Look
Male
Dutch
, Jehovah's gift (or grace).
Male
French
French form of Latin Lupus, LOUP means "wolf."
Surname or Lastname
Dutch
Dutch : from a short form of the Germanic personal name Robrecht.Altered spelling of German Rupp.English : variant spelling of Roope.
Boy/Male
Hindu, Indian
Look
Boy/Male
Hindu, Indian, Rajasthani, Sindhi, Traditional
Look; Beauty; Appearance
Surname or Lastname
English (Somerset)
English (Somerset) : habitational name from Look in Puncknowle, Dorset, named in Old English with lūce ‘enclosure’.English : possibly a variant of Luck 3.Northern English and Scottish : from a vernacular pet form of Lucas.Dutch (van Look) : topographic name from look ‘enclosure’ or habitational name from a place named with this word.Thomas Look (b. c. 1622) was in Lynn, MA, by 1646. His son, also called Thomas (b. 1646), moved to Martha’s Vineyard about 1670.
Boy/Male
Bengali, Indian
Loop; Autumn
Surname or Lastname
English
English : possibly from the Old Norse personal name Tópi, Túpi, a short form of a personal name formed with þórr, name of the Norse god of thunder (see Thor) + a second element with initial b-, for example björn ‘bear’, ‘warrior’. On the other hand, the name is found mainly in Dorset and Devon, which are far from areas of Scandinavian settlement.
Boy/Male
Hebrew
God will multiply.
Boy/Male
Arabic
The Biblical Lot is the English Language Equivalent
Girl/Female
Hindu
Look, Blessed with beauty, Shape, Beauty
Boy/Male
British, English
Barrel Maker
Girl/Female
Arabic, Muslim
Look
Girl/Female
Tamil
Look, Blessed with beauty, Shape, Beauty
LOOP THEOREM
LOOP THEOREM
Boy/Male
Hindu, Indian
Seperation
Boy/Male
Tamil
Immortal
Female
Norwegian
Norwegian form of Icelandic IngifrÃður, INGFRID means "Ing-beautiful."
Boy/Male
Australian, Dutch, French, German, Greek
Superior; Best of Thinkers; Diminutive of Aristotle
Boy/Male
Tamil
Boy/Male
Gaelic Russian Teutonic
Noble warrior.
Girl/Female
Arabic
Great
Female
Native American
Native American Algonquin name OOTA DABUN means "day star."
Boy/Male
Arabic, Indian, Muslim
Chosen
Boy/Male
Dutch Anglo Saxon
Tall.
LOOP THEOREM
LOOP THEOREM
LOOP THEOREM
LOOP THEOREM
LOOP THEOREM
pl.
of Trou-de-loup
v. t.
To break over the poop or stern, as a wave.
v. i.
To seem; to appear; to have a particular appearance; as, the patient looks better; the clouds look rainy.
n.
Any one of several aquatic, wed-footed, northern birds of the genus Urinator (formerly Colymbus), noted for their expertness in diving and swimming under water. The common loon, or great northern diver (Urinator imber, or Colymbus torquatus), and the red-throated loon or diver (U. septentrionalis), are the best known species. See Diver.
v. t.
To influence, overawe, or subdue by looks or presence as, to look down opposition.
n.
Hence; Appearance; aspect; as, the house has a gloomy look; the affair has a bad look.
v. t.
To confine in a coop; hence, to shut up or confine in a narrow compass; to cramp; -- usually followed by up, sometimes by in.
v. i.
To direct the attention (to something); to consider; to examine; as, to look at an action.
n.
The act of looking; a glance; a sight; a view; -- often in certain phrases; as, to have, get, take, throw, or cast, a look.
n.
Expression of the eyes and face; manner; as, a proud or defiant look.
v. t.
To look at; to turn the eyes toward.
n.
See 1st Loop.
n.
A curve of any kind in the form of a loop.
v. t.
To express or manifest by a look.
v. t.
To bind or fasten with hoops; as, to hoop a barrel or puncheon.
n.
See Loon, the bird.
v. t.
To let hang down; as, to lop the head.
v. t.
To make a loop of or in; to fasten with a loop or loops; -- often with up; as, to loop a string; to loop up a curtain.
v. t.
To beat in the game of loo by winning every trick.
n.
A ring; a circular band; anything resembling a hoop, as the cylinder (cheese hoop) in which the curd is pressed in making cheese.