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Regular

Regular is an adjective denoting conformity to a rule, standard, or pattern. It has multiple meanings across various fields, including language and grammar, mathematics, science and social science, military terminology, organizations, people, and arts and entertainment. For specific uses, see the sections below.

Language

Grammar

In linguistics, a regular verb is one that follows a predictable pattern of conjugation, typically by adding a suffix such as -ed to form the past tense and past participle in English.^[1] For example, the verb "walk" conjugates as "walked" in both the simple past and past participle forms, adhering to this standard rule without alteration to the stem.^[2] In contrast, irregular verbs deviate from this pattern, often involving vowel changes or entirely different stems, as seen in "go" becoming "went" in the past tense.^[3] Regular inflection refers to the systematic modification of words to indicate grammatical categories like tense, number, person, case, or gender, following consistent rules across a language's lexicon.^[4] In English, nouns typically form plurals by adding -s or -es, as in "cat" to "cats" or "box" to "boxes," while adjectives may add -er or -est for comparatives and superlatives, such as "big," "bigger," and "biggest."^[5] Verb inflections include third-person singular present tense markers like -s in "walks," and across languages, similar patterns appear in adjective agreements; for instance, in Spanish, adjectives inflect for gender and number to match nouns, as in "casa roja" (red house, feminine singular) becoming "casas rojas" (red houses, feminine plural).^[6] These predictable rules facilitate language acquisition and processing by minimizing exceptions.^[7] Regular syntax encompasses the adherence to fixed structural patterns in sentence construction, particularly in analytic languages where word order conveys grammatical relationships rather than inflection alone.^[8] English exemplifies this with its canonical subject-verb-object (SVO) order, as in "The dog chased the cat," where altering the sequence disrupts meaning unless marked by other cues.^[9] This regularity contrasts with more flexible orders in synthetic languages and supports clarity in communication by relying on position over morphological changes.^[10] The historical development of regular forms traces back to Proto-Indo-European (PIE), which featured complex inflectional systems that gradually simplified in descendant languages.^[11] In Latin, an Italic branch of PIE, verbs followed four regular conjugations based on thematic vowels, such as the first conjugation in "amō, amāre" (to love), which influenced Romance languages through Vulgar Latin.^[12] As Latin evolved into modern Romance tongues like French and Spanish, verbal inflections persisted but streamlined; for example, Latin's multiple tenses consolidated into analytic periphrastic forms (e.g., French "j'ai aimé" for perfect tenses), while regular patterns like stem + -er/-ir endings became dominant for new verbs.^[13] Noun and adjective inflections, however, eroded more extensively, shifting Romance languages toward analytic syntax with fixed word orders inherited from Latin's emerging SVO preference.^[14]

Lexicography and general usage

The word "regular" derives from the Late Latin regularis, meaning "of a bar or ruler," which itself stems from the Latin regula, referring to a straight piece of wood or rule used for measuring or guiding.^[15] This etymological root underscores the term's core connotation of conformity to a standard or pattern. As an adjective in English, "regular" primarily describes something that conforms to a rule, standard, or expected norm, often implying consistency, uniformity, or even spacing; for instance, it can denote a usual occurrence, such as a regular schedule, or a symmetrical arrangement, like regular features in design.^[16]^[17] In noun form, "regular" refers to a habitual or frequent participant in an activity, most commonly a loyal customer or patron in commercial contexts, such as a "regular" at a coffee shop who visits daily and receives personalized service.^[16] This usage extends to everyday life, where it highlights reliability and familiarity, as in a gym "regular" who maintains a consistent routine, fostering community ties in social or service-oriented settings.^[18] While it can also denote a steady soldier in non-specialized senses, the term's everyday application emphasizes patronage and habit rather than formal roles.^[19] Synonyms for "regular" as an adjective include "steady," "constant," "periodic," and "customary," which convey reliability in contexts like schedules (e.g., regular meetings) or physical forms (e.g., regular shapes).^[20] Antonyms such as "irregular," "infrequent," or "erratic" highlight deviations from norms, often used to contrast unpredictable events against routine ones.^[21] In linguistic terms, the adjective briefly relates to grammatical regularity, where verb forms follow predictable patterns without exceptions. Cross-linguistically, "regular" translates to French as régulier, which similarly applies to temporal consistency (e.g., livraisons régulières for regular deliveries) and spatial evenness (e.g., rythme régulier for a steady rhythm). A common idiomatic expression in French, régulier comme une horloge, equates to "regular as clockwork," emphasizing punctuality or unwavering precision in daily habits. This mirrors English usage but adds a cultural nuance of mechanical reliability, often invoked in discussions of work or personal discipline.

Mathematics

Algebra and number theory

In group theory, the regular representation of a finite group G is the representation induced by left multiplication on the group algebra \mathbb{C}[G], where the action is defined by \rho(g)(f)(h) = f(g^{-1}h) for g, h \in G and functions f: G \to \mathbb{C}.^[22] This representation is faithful, meaning its kernel is trivial, and it decomposes as a direct sum of all irreducible representations of G, each appearing with multiplicity equal to its dimension.^[23] In commutative algebra, a regular sequence in a Noetherian ring R is a sequence of elements x_1, \dots, x_n \in R such that each x_i is a non-zero-divisor on R/(x_1, \dots, x_{i-1})R and the ideal (x_1, \dots, x_n) is proper.^[24] An ideal generated by such a sequence is called a regular ideal, and these ideals play a central role in resolutions and homological dimensions, as they allow for Koszul complexes that are projective resolutions.^[24] A regular local ring is a Noetherian local ring (R, \mathfrak{m}) whose maximal ideal \mathfrak{m} is generated by a regular sequence of length equal to the Krull dimension of R.^[25] Such rings are characterized by having finite global dimension equal to their Krull dimension, and they are domains of unique factorization.^[26] The Cohen structure theorem states that a complete Noetherian local ring of characteristic zero with maximal ideal generated by a regular sequence is isomorphic to a power series ring over a complete discrete valuation ring.^[27] A regular ring in the commutative sense is a Noetherian ring whose localization at every prime ideal is a regular local ring; this differs from the non-commutative von Neumann regular ring, where every principal ideal is generated by an idempotent.^[25] Regular rings exhibit strong homological properties, such as all finitely generated modules having finite projective dimension, and they localize to regular local rings, preserving dimension under flat extensions.^[25] In number theory, a regular prime is an odd prime p such that the class number of the p-th cyclotomic field \mathbb{Q}(\zeta_p) is 1.^[28] Kummer's criterion provides a computational test: p is regular if and only if p does not divide the numerator of any even-indexed Bernoulli number B_k for $2 \leq k \leq p-3. The first few regular primes are 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43, 47, ...; the first irregular prime is 37. Heuristics suggest that approximately 60% of odd primes are regular, and all odd primes up to at least $10^{12} have been classified. It remains unknown whether there are infinitely many regular primes.^[29]^[30]

Geometry

In geometry, a regular polygon is a convex polygon with all sides of equal length and all interior angles equal, ensuring rotational symmetry about its center.^[31] For an n-sided regular polygon, the measure of each interior angle is \frac{(n-2)\pi}{n} radians, derived from the total sum of interior angles (n-2)\pi divided equally among the vertices.^[31] Representative examples include the equilateral triangle (n=3), with interior angles of \pi/3 radians each, and the square (n=4), with right angles of \pi/2 radians.^[31] A regular polyhedron, also known as a Platonic solid, is a convex three-dimensional polyhedron where all faces are congruent regular polygons and the same number of faces meet at each vertex, maximizing symmetry.^[32] There are exactly five such solids: the tetrahedron (4 triangular faces), cube (6 square faces), octahedron (8 triangular faces), dodecahedron (12 pentagonal faces), and icosahedron (20 triangular faces).^[32] These satisfy Euler's formula for convex polyhedra, V - E + F = 2, where V is the number of vertices, E the edges, and F the faces, confirming their topological consistency.^[32] Regular polytopes generalize Platonic solids to higher dimensions, defined as convex polytopes with regular polygonal facets meeting uniformly at each vertex.^[33] In four dimensions, there are six convex regular polytopes, including the tesseract (hypercube, with 8 cubic cells), the 16-cell (cross-polytope, with 16 tetrahedral cells), the 24-cell (with 24 octahedral cells), the 120-cell (with 120 dodecahedral cells), the 600-cell (with 600 tetrahedral cells), and the 5-cell (4D simplex).^[33] Beyond four dimensions, only three infinite families exist: the hypercubes, cross-polytopes, and simplices, reflecting constraints on symmetry in higher Euclidean spaces.^[33] Regular tilings, or tessellations, cover the Euclidean plane (or space) without gaps or overlaps using congruent regular polygons, with identical arrangements at each vertex.^[34] In the plane, three regular tessellations exist: the triangular tiling (equilateral triangles), square tiling (squares), and hexagonal tiling (regular hexagons).^[34] In three dimensions, regular polyhedra like the cube tile space periodically.^[34] Archimedean tilings, as semi-regular variants, employ two or more types of regular polygons while maintaining vertex transitivity, yielding eight distinct plane tilings such as the snub square tiling.^[34] A regular curve in differential geometry is a smooth parametrized curve \alpha: I \to \mathbb{R}^n where the derivative \alpha'(t) \neq 0 for all t \in I, ensuring a well-defined tangent vector without singular points.^[35] Such curves admit an arc-length parametrization \beta(s), where s measures distance along the curve and \|\beta'(s)\| = 1, facilitating the study of intrinsic properties like curvature \kappa(s) = \|\beta''(s)\|.^[35] Non-vanishing curvature \kappa > 0 further implies the curve is nowhere straight, distinguishing it from line segments in applications like trajectory analysis.^[35]

Combinatorics, discrete math, and mathematical computer science

In combinatorics and graph theory, a regular graph is an undirected graph in which every vertex has the same degree r, denoted as an r-regular graph.^[36] This uniformity implies that the sum of all vertex degrees equals n r, where n is the number of vertices; by the handshaking lemma, which states that the sum of degrees is twice the number of edges, the graph has exactly \frac{n r}{2} edges.^[36] The Petersen graph provides a classic example of a 3-regular (cubic) graph with 10 vertices and 15 edges, notable for its role as a counterexample in graph coloring problems and as the smallest (3,5)-cage graph.^[37] In mathematical computer science and formal language theory, a regular language is a formal language that can be recognized and accepted by a finite automaton, capturing sets of strings over a finite alphabet with finite memory requirements.^[38] A key property distinguishing regular languages is the pumping lemma, which asserts that for any regular language L, there exists a pumping length p such that any string w \in L with |w| \geq p can be divided as w = xyz where |xy| \leq p, |y| > 0, and xy^i z \in L for all integers i \geq 0.^[39] This lemma, originally proved using properties of finite automata, enables proofs that certain languages (like \{ a^n b^n \mid n \geq 0 \}) are non-regular by contradiction.^[38] Regular expressions provide a formal algebraic notation for denoting regular languages, built from basic symbols using three operations: union (denoted | or +), concatenation, and Kleene star (denoted *), which applies to any expression R to form R^* representing zero or more repetitions of strings matching R. Introduced by Stephen Kleene in his foundational work on nerve nets and automata, regular expressions are equivalent to finite automata via constructive proofs. Thompson's construction algorithm converts a regular expression to a nondeterministic finite automaton (NFA) by recursively building sub-automata for literals and composing them for operations: for union, create parallel branches; for concatenation, chain start and accept states; for star, add loops with epsilon transitions. This method ensures the resulting NFA has O(1) states per symbol in the expression, facilitating efficient implementation in compilers and text processing tools. In discrete mathematics and computer science, a regular tree is an infinite rooted tree where every node has the same finite degree k \geq 2, forming a uniform branching structure often called a k-ary tree.^[40] These trees model infinite state spaces in algorithms, such as breadth-first search in infinite domains or as acceptance structures in tree automata for verifying properties of recursive data like XML documents.^[40] Their regularity ensures predictable growth, with the number of nodes at depth d exactly k^d, enabling analytical bounds on search complexity in areas like artificial intelligence planning.^[41] Matroid theory, a branch of combinatorial optimization, defines a regular matroid as one that is representable over every field, equivalently, one arising from a totally unimodular matrix where all subdeterminants are -1, 0, or $1.^[42] Introduced in the context of graphic and linear matroids, regular matroids unify structures like cycle matroids of graphs and vector matroids over rationals, with applications in integer linear programming due to their integral polyhedra.^[42] W.T. Tutte characterized them via excluded minors, showing that the non-Pappus and non-Fano matroids are the only binary obstructions, ensuring computational tractability in optimization problems.^[42]

Analysis

In complex analysis, a function is termed regular at a point if it is holomorphic there, possessing a convergent power series expansion in a neighborhood of that point and thus free from singularities.^[43] This contrasts with singular points, where the function fails to be holomorphic, such as at poles or essential singularities, and underscores the smoothness inherent in regular functions as approximations to polynomials locally.^[43] Entire functions exemplify global regularity, being holomorphic across the whole complex plane without any singularities, enabling uniform approximation properties on compact sets via Runge's theorem extensions.^[43] Within distribution theory, a regular distribution corresponds to a locally integrable function f, defined by its action on test functions \phi \in C_c^\infty(\mathbb{R}^n) as T_f(\phi) = \int_{\mathbb{R}^n} f(x) \phi(x) \, dx, thereby extending classical functions to generalized ones while preserving convolution operations.^[44] Convolution of a regular distribution with a test function \phi yields a smooth function T_f * \phi, which approximates the original distribution and facilitates analysis of singularities through mollification, highlighting the role of regular distributions in bridging pointwise functions to broader approximation frameworks.^[44] This structure ensures that derivatives of regular distributions remain representable by functions, avoiding the need for higher-order generalized derivatives in many applications. Regular variation describes functions f: (0, \infty) \to (0, \infty) satisfying \lim_{x \to \infty} f(tx)/f(x) = t^\rho for some index \rho \in \mathbb{R} and all t > 0, capturing asymptotic scaling behaviors essential for approximation in large-variable limits.^[45] Karamata's theorem establishes that such functions factor as f(x) = x^\rho L(x), where L is slowly varying with \lim_{x \to \infty} L(tx)/L(x) = 1, enabling precise tail approximations in integrals and series via uniform convergence on compact sets.^[45] These properties facilitate smoothness in asymptotic analysis, such as in Tauberian theorems, where regular variation approximates divergent behaviors by slower-varying components. Regular summability methods assign values to divergent series while preserving convergence for ordinary sums, with Cesàro means of order \alpha > -1 defined as the limit of weighted averages of partial sums using binomial coefficients.^[46] Higher-order Cesàro means iteratively apply averaging, enhancing approximation for oscillatory or slowly convergent sequences, as in the case where the (\mathrm{C}, \alpha) method sums series like the Fourier expansion of a square wave to its mean value.^[46] This regularity ensures consistent limits, providing a smooth transition from finite partial sums to generalized totals in analytic continuation. Sobolev regular solutions to partial differential equations (PDEs) are weak solutions in Sobolev spaces W^{k,p}(\Omega) that achieve higher regularity, such as membership in W^{m,p} for m > k, through bootstrapping based on the equation's structure and data smoothness.^[47] For elliptic PDEs like \Delta u = f with f \in L^\infty, interior regularity theory yields u \in C^{1,1-\varepsilon} for any \varepsilon > 0, with further gains to C^{k+2,\alpha} if f \in C^{k,\alpha}, emphasizing approximation by classical smooth solutions.^[47] In divergence-form equations, the De Giorgi–Nash theorem guarantees Hölder continuity u \in C^{0,\alpha} for H^1 solutions, paving the way for higher Sobolev embeddings and C^\infty smoothness under analytic coefficients.^[47]

Topology

In topology, a regular space, also denoted as a T3 space, is a topological space that satisfies a separation axiom allowing points to be separated from closed sets not containing them. Specifically, for every point x in the space and every closed set F not containing x, there exist disjoint open sets U containing x and V containing F.^[48] This property implies that singletons are closed if the space is also T1 (Hausdorff in the weak sense), but some definitions of regularity incorporate T0 or T1 directly; for instance, in the Bourbaki tradition, regularity aligns precisely with the T3 axiom without additional assumptions.^[49] Variants include preregular spaces (T0 plus the separation condition) and completely regular spaces (T3.5 or Tychonoff, where continuous functions separate points from closed sets), which strengthen the axiom for embedding into Hausdorff spaces.^[50] A regular open set in a topological space is an open set U such that U equals the interior of its closure, denoted U = \operatorname{int}(\operatorname{cl}(U)).^[51] These sets form a complete Boolean algebra under the operations of union, intersection, and complement (relative to the whole space), providing a foundational structure in pointless topology, or locale theory, where spaces are described solely by their lattices of open sets without reference to points.^[52] In this framework, the algebra of regular open sets serves as a basis for constructing locales, enabling the study of continuous functions as frame homomorphisms and generalizing classical topological properties like compactness and connectedness algebraically.^[52] Regular homotopy refers to a homotopy between two immersions of manifolds that remains an immersion throughout, ensuring transverse intersections and avoiding singularities.^[53] This concept is central to immersion theory, where René Thom's transversality theorem guarantees that generic perturbations yield regular homotopies, classifying immersion classes in high codimensions.^[54] Thom's work further establishes that stable regular homotopy classes of immersions correspond to elements in stable homotopy groups via the Pontryagin-Thom construction, linking differential topology to algebraic topology for dimensions where the codimension exceeds the manifold's dimension.^[55] In knot theory, regular isotopy is an equivalence relation on link diagrams generated solely by the second and third Reidemeister moves (R2 and R3), excluding the first move (R1) to preserve framing or ribbon structure.^[56] This corresponds to ambient isotopy in three-dimensional space that maintains the knot type without introducing twists, making it suitable for studying framed links and Vassiliev invariants.^[57] Louis Kauffman's development of invariants under regular isotopy, such as the Kauffman polynomial, distinguishes knots beyond classical ambient isotopy by capturing framing information through diagrammatic Reidemeister equivalence.^[56] A free regular set is a subset of a topological space on which a group acts freely (no fixed points, i.e., only the identity element fixes any point) and discontinuously (properly, meaning the action map is proper, ensuring quotients are Hausdorff).^[50] Such sets arise in the construction of covering spaces and orbifolds, where the free and discontinuous action guarantees that the quotient topology yields a manifold or similar structure without singularities from stabilizers.^[58]

Logic, set theory, and foundations

In set theory, a regular cardinal is defined as an infinite cardinal number \kappa such that its cofinality \mathrm{cf}(\kappa) = \kappa, meaning \kappa cannot be expressed as the union of fewer than \kappa many sets each of cardinality less than \kappa. This property distinguishes regular cardinals from singular cardinals, where \mathrm{cf}(\kappa) < \kappa, and positions them as weak limit cardinals that are not successors of smaller cardinals. Examples include \aleph_0 and all successor cardinals \kappa^+ under the axiom of choice, though the existence of uncountable regular cardinals beyond successors is independent of ZFC. A regular ultrafilter on a set of cardinality \kappa, where \kappa is a regular cardinal, is a non-principal ultrafilter that is \kappa-complete, meaning it is closed under intersections of fewer than \kappa many sets.^[59] Such ultrafilters play a key role in constructing ultrapowers and embedding theorems, particularly for measurable cardinals, where the existence of a \kappa-complete non-principal ultrafilter on \kappa implies \kappa is measurable and hence regular.^[59] The regularity of \kappa ensures that the ultrafilter's completeness aligns with the cardinal's closure under small unions, facilitating applications in forcing and inner model theory.^[60] An inaccessible cardinal, or strongly inaccessible cardinal, is an uncountable regular cardinal \kappa that is also a strong limit cardinal, satisfying $2^\lambda < \kappa for all \lambda < \kappa. This combines regularity with a power set closure property, making \kappa unreachable from smaller cardinals via standard set-theoretic operations like exponentiation or unions. The existence of inaccessible cardinals cannot be proved in ZFC and implies the consistency of ZFC itself, as V_\kappa models ZFC. Vopěnka's principle, which asserts that for any proper class of structures of the same type there is an elementary embedding from one member to another, is a stronger large cardinal axiom equivalent to the existence of a proper class of Vopěnka cardinals—inaccessibles \kappa such that V_\kappa satisfies the principle—and implies a proper class of inaccessible cardinals.^[61] In mathematical logic, regular logic refers to an abstract logic extending first-order logic that is closed under unions of formulas of cardinality less than some regular cardinal \kappa, incorporating infinitary conjunctions and disjunctions while preserving key properties like the Löwenheim-Skolem theorem.^[62] Lindström's theorem characterizes such logics: if a regular logic satisfies both compactness (every consistent set of sentences has a model) and the Löwenheim-Skolem property, then it is equivalent to first-order logic.^[63] Compactness in regular logics holds under the regularity of the bounding cardinal, enabling the logic to handle infinite theories without collapsing to finitary expressiveness, as seen in applications to infinitary logics like L_{\kappa,\omega}.^[62] Regular categories provide a foundational framework in category theory for interpreting regular logic, defined as finitely complete categories (with all finite limits) that have coequalizers of finite families of parallel arrows and in which every morphism factors as a regular epimorphism followed by a monomorphism, with the property stable under pullback. This structure captures the existential-conjunctive fragment of first-order logic internally, where regular epimorphisms correspond to surjections and monomorphisms to injections. Seminal work by Barr and Diaconescu establishes that regular categories support the semantics of regular logic, allowing proofs of coherence theorems and equivalences with coherent categories under additional conditions like exactness.^[64] Thus, regular categories form the categorical foundation for the logical operations of conjunction and existential quantification without negation or universal quantification.

Probability and statistics

In probability theory, a regular conditional probability refers to a disintegration of a probability measure P on a product space (\Omega \times \mathcal{Y}, \mathcal{F} \times \mathcal{G}) into a family of conditional measures P_y on \Omega for each y \in \mathcal{Y}, such that P(A \times B) = \int_B P_y(A) \, Q(dy) for probability measures Q on \mathcal{Y} and sets A \in \mathcal{F}, B \in \mathcal{G}.^[65] This construction ensures the conditional measures are proper probability measures almost surely with respect to Q.^[65] Existence of such regular conditional probabilities is guaranteed when the spaces are Polish (separable complete metric spaces), under which the disintegration theorem applies, allowing representation via Radon-Nikodym derivatives with respect to a dominating measure.^[66] Equivalence between regular conditional properties and Radon spaces has been established, where Radon spaces are those admitting such disintegrations for every probability measure.^[67] A regular stochastic matrix, in the context of Markov chains, is a row-stochastic transition matrix P (non-negative entries with rows summing to 1) such that there exists some integer k \geq 1 where P^k has all strictly positive entries.^[68] This property implies the chain is irreducible and aperiodic, leading to a unique stationary distribution. By the Perron-Frobenius theorem for positive matrices, P has a dominant eigenvalue of 1 (simple, with spectral radius 1), associated with a unique positive eigenvector (up to scaling) that serves as the stationary distribution, normalized to sum to 1.^[68] For such matrices, the powers P^n converge to a matrix with identical rows equal to the stationary distribution as n \to \infty. In statistics, regular variation describes the tail behavior of a distribution function F, where the survival function \overline{F}(x) = 1 - F(x) satisfies \overline{F}(tx)/\overline{F}(x) \to t^{-\rho} as x \to \infty for t > 0 and \rho > 0, often modulated by a slowly varying function L(x) such that \overline{F}(x) \sim x^{-\rho} L(x). The Pareto distribution exemplifies this with exact power-law tails \overline{F}(x) = (x/\sigma)^{-\rho} for x > \sigma > 0. To estimate the tail index \rho, the Hill estimator uses the spacings of order statistics: for a sample X_1, \dots, X_n with top k order statistics X_{n-i+1:n} (i=1,\dots,k), \hat{\rho}_k = k / \sum_{i=1}^k \log(X_{n-i+1:n}/X_{n-k:n}), which is consistent as k \to \infty and k/n \to 0 under regular variation.^[69] Absolute regularity, also known as \beta-mixing, quantifies dependence in stochastic processes as a coefficient between \sigma-algebras \mathcal{A} and \mathcal{B} defined by \beta(\mathcal{A}, \mathcal{B}) = \sup_{A \in \mathcal{A}} \| P(\cdot | A) - P(\cdot) \|_{1}/2, where \| \cdot \|_1 is the total variation norm.^[70] For a stationary process \{X_t\}, the process is absolutely regular if \beta(\mathcal{F}_m, \mathcal{F}_{m+k}) \to 0 as k \to \infty for each m, measuring asymptotic independence between past and future \sigma-algebras \mathcal{F}_m = \sigma(X_s : s \leq m) and \mathcal{F}_{m+k} = \sigma(X_s : s > m+k-1). This condition, stronger than \alpha-mixing, facilitates central limit theorems and large deviation results for dependent sequences. In Bayesian statistics, regular priors are chosen to ensure the posterior distribution is proper (integrable to 1) even when the likelihood is improper or the model is complex, often by selecting non-informative priors with sufficient weight in the parameter space.^[71] The Jeffreys prior, derived as \pi(\theta) \propto \sqrt{\det \mathcal{I}(\theta)} where \mathcal{I}(\theta) is the Fisher information matrix, provides an objective choice that is invariant under reparameterization and typically yields proper posteriors under regularity conditions like asymptotic normality.^[72] For example, in normal models with unknown mean and variance, the Jeffreys prior \pi(\mu, \sigma^2) \propto 1/\sigma^2 ensures posterior propriety.^[71]

Natural sciences

In chemistry, a regular solution refers to a mixture where the entropy of mixing follows ideal solution behavior, but the enthalpy of mixing is non-zero due to intermolecular interactions, often modeled using a lattice-based approach assuming random distribution of components. This theory, developed by Joel H. Hildebrand, predicts solubility based on the similarity of cohesive energy densities between solute and solvent. The Hildebrand solubility parameter, denoted as δ, quantifies this and is calculated as δ = √(ΔH_v / V_m), where ΔH_v is the enthalpy of vaporization and V_m is the molar volume, providing a practical tool for estimating miscibility in non-polar systems.^[73] In astronomy, a regular moon is defined as a natural satellite exhibiting a prograde orbit—aligned with the planet's rotation—with low eccentricity (nearly circular path) and minimal inclination relative to the planet's equatorial plane, typically indicating formation within the planet's circumplanetary disk. Prominent examples include the four Galilean moons of Jupiter—Io, Europa, Ganymede, and Callisto—which maintain such stable, low-eccentricity orbits, contrasting with irregular moons captured later from external sources.^[74] In solid-state physics and crystallography, a regular crystal lattice describes the periodic, repeating arrangement of atoms or ions in a crystalline solid, forming an infinite array of points that maintain translational symmetry throughout the structure. These lattices are classified into 14 distinct types known as Bravais lattices, grouped under seven crystal systems (cubic, tetragonal, orthorhombic, hexagonal, trigonal, monoclinic, and triclinic), each defined by unique combinations of lattice parameters and symmetry operations that dictate the material's physical properties like density and elasticity.^[75] Biological systems often display regular symmetry as an adaptive trait for efficient function and development, particularly in radial or bilateral patterns that enhance stability and resource distribution. In marine invertebrates like sea urchins (class Echinoidea), regular species exhibit pentaradial symmetry, with a central mouth and five-fold repetition of skeletal plates and tube feet, as seen in the globular test of the common purple sea urchin (Strongylocentrotus purpuratus), which supports locomotion and feeding on ocean floors. This symmetry evolves from bilateral larval stages to radial adult forms, reflecting echinoderm phylogeny.^[76] In human physiology, a regular heartbeat, or normal sinus rhythm, is the standard cardiac cycle initiated by the sinoatrial node, producing a consistent ventricular rate of 60-100 beats per minute in adults at rest. On an electrocardiogram (ECG), it appears as a sequence of waveforms: an upright P wave (atrial depolarization, duration 80-100 ms), followed by a QRS complex (ventricular depolarization, <120 ms wide with Q, R, and S deflections), a ST segment (ventricular repolarization plateau), a T wave (ventricular recovery), and occasional U waves, all occurring at regular intervals without premature beats.^[77] Molecular geometries in chemistry frequently incorporate regular polygonal arrangements, such as the trigonal planar structure of boron trifluoride (BF₃), where three fluorine atoms form an equilateral triangle around the central boron.^[78] In economics, a regular economy refers to a state in general equilibrium theory where the aggregate excess demand function has a non-zero slope at equilibrium price vectors, ensuring that each Walrasian equilibrium is locally unique.^[79] This property implies that small perturbations in endowments or preferences do not lead to multiple nearby equilibria, facilitating the Walrasian auctioneer's price adjustment process toward stability.^[79] Such economies are generic, meaning non-regular cases have measure zero in the parameter space, as established by seminal work in the field.^[80] In sociology, regular employment denotes stable, full-time positions with consistent hours, benefits, and long-term contracts, contrasting sharply with the gig economy's short-term, task-based work often mediated by digital platforms.^[81] The rise of gig work has contributed to labor market instability, with contingent workers comprising 4.3% (6.9 million) of the U.S. workforce and independent contractors 7.4% (11.9 million) as of July 2023, leading to income volatility and reduced access to health insurance or paid leave.^[82] This shift exacerbates inequality, as gig workers—particularly those in low-wage sectors—face higher mental distress and economic precarity compared to those in traditional roles, with studies showing negative employment impacts on working-age individuals.^[83]^[84] Regular migration patterns describe predictable human movements, such as seasonal labor flows or daily commutes, which follow demographic models like the gravity equation in migration analysis.^[85] The gravity model posits that migration volumes between origins and destinations vary positively with their population sizes or economic masses and negatively with distance, capturing routine patterns influenced by factors like job opportunities and transport costs.^[85] For instance, visa policies can reduce such flows by 40-47% while redirecting migrants to alternative destinations by 2.8-16.9%, highlighting the model's utility in forecasting stable, recurring migrations in demography.^[85] Regular social norms encompass consistent behavioral expectations within groups, reinforced through shared values that promote cohesion, as conceptualized by Émile Durkheim in his theory of mechanical solidarity.^[86] In mechanical solidarity, prevalent in traditional societies, individuals conform to a collective conscience of uniform beliefs and sentiments, with deviations punished by repressive sanctions to maintain societal regularity.^[86] This form of solidarity arises from homogeneity in roles and experiences, fostering predictable interactions without the differentiation seen in more complex, organic societies.^[86] Regular voting systems involve periodic elections governed by fixed rules, which shape party structures according to principles like Duverger's law, a foundational observation in political sociology.^[87] Duverger's law states that single-member district plurality voting (first-past-the-post) tends to produce two-party systems by disadvantaging third parties, as seen in the UK's 1964 election where Liberals garnered 11.2% of votes but only 1.4% of seats.^[87] In contrast, proportional representation encourages multiparty systems by ensuring fairer seat allocation, while two-ballot majority systems allow initial multiplicity but promote strategic alliances, influencing the regularity of electoral outcomes over time.^[87] In statistical modeling of social data, regular variation captures consistent distributional patterns, such as tail behaviors in income or network ties, aiding predictions of societal trends without delving into extreme value specifics.^[88]

Military

Armed forces

In military contexts, "regular" refers to professional standing armed forces that are permanently maintained by a state, consisting of full-time personnel who are trained, uniformed, and funded through national budgets, distinguishing them from temporary levies, reserves, or ad hoc militias.^[89] These forces emerged prominently in the 18th century as standing armies became a hallmark of modern nation-states, replacing feudal obligations with centralized, professional institutions capable of sustained operations. For instance, the British Regular Army during the Napoleonic Wars exemplified this model, serving as a core expeditionary force in campaigns like the Peninsular War (1808–1814), where the overall army numbered around 250,000 at its peak in 1813 and the British contingent in the Peninsular theater reached approximately 70,000 by 1814, relying on voluntary enlistment supplemented by limited conscription to maintain cohesion against French forces.^[90] In contemporary terms, the United States Army represents a modern regular force, operating as an all-volunteer professional entity since the end of conscription in 1973, with over 450,000 active-duty soldiers (as of June 2025) focused on global readiness and funded annually through federal appropriations of $185.9 billion for FY2025.^[91]^[92] Regular forces are differentiated from irregulars under international humanitarian law, where regulars are defined as members of organized armed forces under responsible command, openly carrying arms, and adhering to the laws of war, thereby qualifying as combatants entitled to prisoner-of-war status if captured.^[93] Irregulars, such as guerrillas or militias not integrated into state structures, must meet additional criteria—like wearing fixed distinctive signs and conducting operations in compliance with the laws of war—to gain similar protections, as outlined in Article 4 of the Third Geneva Convention (1949); failure to do so risks classification as unlawful combatants.^[94] This distinction underscores the emphasis on uniformity, discipline, and accountability in regular units, which prioritize conventional tactics over asymmetric warfare employed by irregular groups.^[95] Regular military service typically involves either voluntary enlistment or conscription into these standing forces, with terms varying by nation but often ranging from 2 to 4 years of active duty followed by reserve obligations.^[96] In voluntary systems like the U.S. Army, enlistees commit to an initial 2–6 years active followed by inactive reserves, receiving benefits such as comprehensive healthcare, education assistance via the GI Bill, and retirement pensions after 20 years.^[97] Conscription-based regulars, as seen in countries like Israel or South Korea, mandate 32–36 months in Israel (for men, extended in 2024 amid security needs) and 18–21 months in South Korea (depending on branch), as of 2025, offering post-service incentives like tuition subsidies to encourage participation and retention.^[98]^[99] The evolution of regular armies traces from medieval feudal levies—temporary assemblies of vassals and peasants summoned for short campaigns—to professionalized standing forces by the early modern period, driven by gunpowder warfare and state centralization in 15th–17th century Europe.^[100] Post-World War II, this professionalization accelerated with the decline of mass conscription in Western nations, shifting toward smaller, highly trained volunteer forces equipped with advanced technology, as evidenced by NATO allies' emphasis on interoperability and specialization since the 1950s.^[101] This transition enhanced operational efficiency but raised debates on sustainability amid reduced public involvement in defense.

Ranks and terminology

In military contexts, a regular officer refers to a commissioned officer serving full-time in a standing army, distinct from reserve or militia officers who serve part-time or on a temporary basis. These officers undergo rigorous training at dedicated academies, such as the United States Military Academy at West Point, where graduates are commissioned as second lieutenants in the active-duty component of the U.S. Army. Promotion paths for regular officers follow a structured merit-based system, typically advancing from lieutenant to captain after about two years, then to major and beyond based on performance evaluations, command experience, and selection boards, ensuring a professional cadre for sustained operations.^[102]^[103] Regular enlistment denotes the standard term of service for non-commissioned personnel in the active-duty forces, usually an initial commitment of four years of full-time service followed by four years in the Individual Ready Reserve, totaling an eight-year military service obligation. This contrasts with short-term enlistments, which are limited and often tied to specific incentives like college funding programs, or specialist roles such as those in cyber or medical fields that may require longer commitments of six years or more due to advanced training needs. Enlistees under regular terms receive comprehensive basic training and assignment to standard units, fostering a core of experienced personnel for ongoing readiness.^[96] In military terminology, "regular" often describes standard-issue equipment, procedures, or formations essential to disciplined operations. For instance, regular march involves synchronized stepping at a 30-inch pace and 120 steps per minute in quick time, maintaining alignment and cadence for ceremonial or tactical movement, whereas route step allows a relaxed, unsynchronized pace over uneven terrain without counting steps or swinging arms, used for endurance marches to conserve energy. Standard-issue gear, such as the M4 carbine rifle or ACH helmet, is termed "regular" to denote the baseline equipment provided to all personnel, ensuring uniformity and logistical efficiency across units. Historically, the term "regular" has denoted established ranks within professional armies. In colonial American forces during the Revolutionary War, a regular captain was a commissioned leader in the Continental Army, responsible for commanding a company of about 100 men in the standing national force, unlike militia captains who led local volunteers; figures like Captain Benjamin Bartholomew exemplified this role in sustained campaigns. Similarly, in the Roman legions, regular cohorts formed the core tactical units of approximately 480 legionaries each, organized into ten per legion for heavy infantry operations, distinguishing them from auxiliary or irregular contingents recruited from provinces. These structures emphasized professional, full-time service to maintain imperial cohesion.^[104]^[105]

Organizations

Religious organizations

In ecclesiastical contexts, the term "regular" refers to clergy who live according to a formal religious rule, distinguishing them from secular clergy who serve dioceses without such communal vows. Regular clergy, including priests and monks, profess vows of poverty, chastity, and obedience while adhering to a specific rule, such as the Rule of St. Benedict, which emphasizes monastic discipline, prayer, and manual labor in community settings.^[106]^[107] In contrast, secular clergy are incardinated into a diocese, focus on pastoral duties like parish administration, and take only the promise of celibacy without belonging to a religious institute.^[106] This distinction originated in early Christianity to organize clerical life, with regular clergy often residing in monasteries or convents to pursue a more contemplative existence.^[107] Regular canons, particularly the Augustinian canons, played a pivotal role in medieval European religious and social life by combining clerical duties with communal monasticism under the Rule of St. Augustine, which stressed apostolic poverty, chastity, and common life. Emerging in the 11th century as part of the Gregorian Reform, these canons regular established numerous houses across Europe, serving as educators, administrators of cathedrals, and missionaries who bridged monastic seclusion with active pastoral engagement.^[108] In regions like the British Isles and Ireland, Augustinian canons proliferated during the 12th century, founding over 200 priories and abbeys that supported church reform, managed pilgrimage sites, and contributed to cultural developments such as scriptoria and legal scholarship.^[109] Their adaptability allowed them to staff urban chapters and rural foundations, influencing the transition from feudal to centralized ecclesiastical structures until the Reformation diminished their presence.^[110] The Regular Baptists emerged in 18th-century America as a Calvinist denomination within the Baptist tradition, emphasizing adherence to confessional standards like the Philadelphia Confession of Faith over revivalist emotionalism. Formed in contrast to the Separate Baptists, who split from New England Congregationalists in 1751 under leaders like Shubal Stearns to prioritize immediate spiritual experiences and lay preaching, the Regular Baptists maintained a more structured, creed-bound approach rooted in the Philadelphia Baptist Association established in 1707.^[111] This division highlighted tensions between doctrinal orthodoxy and enthusiastic piety, with Regular Baptists focusing on educated ministry and associational governance to preserve Calvinist soteriology amid the Great Awakening.^[111] By the late 18th century, mergers in states like Kentucky began reconciling the groups, though the "Regular" label persisted among confessional Baptists.^[111]

Secular organizations

In secular organizations, the concept of "regular" status emphasizes adherence to established constitutional rules, formal membership criteria, and governance structures that ensure standardized operations and mutual recognition among affiliated groups. This usage parallels, but remains distinct from, organizational parallels in religious clergy hierarchies, where regularity might involve doctrinal compliance rather than civic or professional frameworks.^[112] In Freemasonry, "regular" jurisdictions denote Grand Lodges recognized by the United Grand Lodge of England (UGLE) for upholding ancient landmarks, including a requirement for members to profess belief in a Supreme Being, which aligns with deistic religious principles. UGLE's recognition criteria, codified since 1929, mandate regularity of origin through lawful establishment by recognized bodies, exclusive adherence to Masonic rituals without political discussion, and the absence of women or irregular affiliations.^[113] These standards ensure mutual visitation rights among approximately 50 recognized Grand Lodges worldwide, preserving a theistic framework that echoes religious organizational discipline.^[114] Regularity denotes lodges and members that conform to the constitutional principles of recognized Grand Lodges, including regularity of origin (traceable establishment from a sovereign body), conduct (such as requiring belief in a Supreme Being and prohibiting political or religious discussions in lodge), and autonomy in overseeing the three Craft degrees. These frameworks, as outlined in the United Grand Lodge of England's Basic Principles for Grand Lodge Recognition (1929), enable inter-lodge visitation and mutual support, distinguishing regular bodies from irregular ones that deviate from these standards. Beyond any theological elements, the emphasis lies on administrative and jurisdictional governance to maintain organizational integrity.^[112]^[113] Employee associations, such as trade unions, define regular membership as full participation for individuals employed within a recognized bargaining unit, entitling them to voting rights, representation, and access to union resources. For instance, in the Service Employees International Union (SEIU), a regular member is any worker in a bargaining unit where the union serves as the official agent, paying standard dues and engaging in governance through local meetings.^[115] Fraternal orders like the Independent Order of Odd Fellows and the Benevolent and Protective Order of Elks use chartered lodges that operate under the sovereign grand body's constitution, conducting standard rituals, meetings, and charitable activities. In the Odd Fellows, lodges form the core network for fellowship and service, with membership requiring initiation and adherence to principles of friendship, love, and truth, as governed by the Sovereign Grand Lodge.^[116] Similarly, Elks lodges achieve status through formal chartering, enabling full participation in national programs and local governance.^[117] Professional organizations, such as bar associations, designate regular members as licensed practitioners with active status, granting them full privileges like voting and committee service. The Ohio State Bar Association, for example, defines regular membership for any attorney admitted to practice in Ohio who is not otherwise restricted, subject to annual dues and ethical compliance. This accreditation ensures standardized professional conduct and peer recognition across jurisdictions.^[118]^[119]

People

Real people

In military history, the term "regular" denotes professional soldiers serving in a standing army, distinct from temporary militia or volunteers. During the American Revolutionary War, British regulars formed the backbone of the Crown's forces, comprising enlisted men from regiments like the 4th, 10th, and 23rd Foot, who were recruited primarily from urban poor and rural laborers in Britain and Ireland. These soldiers, often facing harsh discipline and low pay, participated in key engagements such as the Battles of Lexington and Concord in 1775, where approximately 700 regulars under Lieutenant Colonel Francis Smith marched to seize colonial arms, igniting the war. Accounts from survivors and officers highlight their role as disciplined but weary professionals, embodying the archetype of the "regular soldier" in colonial resistance narratives.^[120]^[121] In the U.S. Civil War, the Union Regular Army included career officers and enlisted men who provided continuity and expertise amid the influx of volunteers. Their contributions underscored the value of trained professionals in sustaining prolonged campaigns. The nickname "Regular Joe" or "regular guy" has been applied to modern public figures to emphasize their approachable, working-class personas. Former U.S. President Joe Biden, raised in Scranton, Pennsylvania, has long been portrayed as a "regular Joe" for his emphasis on middle-class roots, personal tragedies like the loss of his first wife and daughter, and unpretentious habits such as biking and ice cream outings, which contrast with elite political norms. This image helped define his 2020 campaign, appealing to voters seeking relatability amid national divisions.^[122] Samuel Joseph Wurzelbacher, famously known as "Joe the Plumber," emerged as an icon of the everyday American during the 2008 presidential election when he questioned Barack Obama on economic policies at a Ohio rally. A self-employed plumber from Toledo, Wurzelbacher symbolized the "regular guy" struggling with taxes and small-business aspirations, becoming a Republican talking point on fiscal issues despite later revelations that he was not licensed and earned under the tax threshold he criticized. His brief fame influenced campaign rhetoric but faded as he pursued conservative activism until his death in 2023 from pancreatic cancer.^[123]^[124] In sports, John Madden, legendary NFL coach and broadcaster, was cherished in his Pleasanton, California community as a "regular guy" who maintained a modest lifestyle post-fame, frequently spotted at local eateries like Round Table Pizza without fanfare. Despite leading the Oakland Raiders to a Super Bowl victory in 1977 and revolutionizing football commentary, Madden's unassuming demeanor—rooted in his working-class upbringing—made him a relatable figure until his passing in 2021.^[125]

Fictional characters

In the animated television series Regular Show (2010–2017), the protagonists Mordecai, a blue jay, and Rigby, a raccoon, are portrayed as ordinary groundskeepers at a local park, embodying the "regular" archetype through their slacker lifestyles and everyday slights that escalate into surreal escapades.^[126] Their dynamic highlights the tension between mundane responsibilities and chaotic interruptions, with Mordecai often serving as the more level-headed counterpart to Rigby's impulsive nature, reflecting relatable young adult struggles in a fantastical framework.^[127] This setup underscores the show's title, positioning the duo as quintessential "regular guys" thrust into extraordinary situations.^[128] The "regular guy" archetype in American literature represents the ordinary individual navigating societal pressures, often serving as a relatable lens for themes of alienation and authenticity. In J.D. Salinger's The Catcher in the Rye (1951), Holden Caulfield exemplifies this through his portrayal as a disillusioned teenager from a middle-class background, critiquing phoniness while yearning for genuine connection amid everyday adolescent turmoil.^[129] His narrative voice captures the everyman experience of feeling out of place in a conformist world, influencing subsequent depictions of youthful normalcy in fiction.^[130] In comic books, Archie Andrews from the Archie series (debuting in 1941) stands as the quintessential regular teen, depicted as an average high schooler in the idyllic town of Riverdale, balancing school, friendships, and romantic entanglements without superhuman traits.^[131] Originally billed as "America's Typical Teenager," Archie's character arc revolves around relatable dilemmas like juggling affections for Betty and Veronica, embodying the everyman ideal of wholesome, unremarkable youth in mid-20th-century American culture.^[132] This archetype has sustained the series' popularity by mirroring the aspirations and faux pas of ordinary adolescence.^[133] Film portrayals of the regular character often emphasize resilience amid life's unpredictability, as seen in Forrest Gump (1994), where the titular protagonist, an Alabama man with an IQ of 75, navigates historical events through sheer perseverance and simple decency.^[134] Forrest's journey from bench-sitting observer to unwitting participant in major 20th-century moments illustrates the everyman archetype's capacity for quiet heroism, grounded in everyday moral choices rather than exceptional abilities. His story, inspired by Winston Groom's 1986 novel, highlights how ordinary struggles like loss and loyalty can intersect with broader narratives.

Arts, entertainment, and media

Music

In music theory, regular meter refers to a consistent rhythmic structure where beats are organized into measures of fixed length, providing a steady pulse that underpins much of Western classical and popular music.^[135] This contrasts with irregular or changing meters, as regular meter maintains uniform beat durations throughout a piece, facilitating predictable phrasing and ensemble coordination. For instance, the common 4/4 time signature exemplifies regular meter, dividing each measure into four quarter-note beats, which is prevalent in sonata form compositions by composers like Mozart and Beethoven.^[136] In Beethoven's Piano Sonata No. 8 in C minor, Op. 13 ("Pathétique"), the first movement employs a regular 4/4 meter to establish a dramatic yet structured rhythmic foundation, emphasizing thematic development through consistent pulse.^[137] Regular harmony denotes predictable and conventional chord progressions that create a sense of stability and familiarity, often rooted in diatonic scales and common tonal relationships. In folk music traditions, such harmonies typically revolve around simple cycles like the I-IV-V progression, which reinforces melodic lines without complex modulations. This approach is evident in traditional Appalachian folk tunes, where guitar or banjo accompaniments follow these patterns to support narrative ballads. The circle of fifths, a foundational harmonic sequence progressing through keys in fifth intervals (e.g., C to G to D), exemplifies regular harmony by providing a logical, resolving flow that is widely used in folk and classical contexts to build tension and release predictably.^[138] Historically, regular canons represent a sophisticated form of polyphony where a single melody is imitated at fixed intervals by additional voices, creating interlocking lines in strict rhythmic alignment. Johann Sebastian Bach's The Musical Offering, BWV 1079 (1747) includes several such canons, composed in response to a theme by Frederick the Great, showcasing intricate yet regular imitative structures. For example, the "Canon 1 a 2" in the collection features two voices entering at regular two-measure intervals, demonstrating Bach's mastery of contrapuntal regularity to achieve harmonic density without deviation. These works highlight the canon's role in Baroque polyphony as a pedagogical and artistic device for exploring melodic permutation within consistent temporal frameworks.^[139] Several musical compositions bear the title "Regular," often exploring themes of everyday routine or normalcy through varied genres. Queens of the Stone Age's "Regular John" from their 1998 debut album Queens of the Stone Age is a gritty rock track that uses driving rhythms to evoke mundane yet intense daily experiences, blending garage rock with stoner influences. In K-pop, NCT 127's "Regular" (2018) from the album Regular-Irregular delivers an upbeat electronic pop sound, with lyrics reflecting on consistent personal identity amid chaos.^[140] Indie artist Shamir's "On the Regular" (2014) from Northtown employs falsetto vocals and synth-pop elements to celebrate habitual joy in ordinary life, marking an early highlight in their career. These tracks illustrate how "regular" as a title can musically frame the ordinary as a source of rhythm and repetition.

Other media

In television, Regular Show is an American animated sitcom that aired on Cartoon Network from September 6, 2010, to January 16, 2017, spanning eight seasons and 261 episodes.^[141] Created by J.G. Quintel, the series follows the surreal misadventures of two best friends—Mordecai, a blue jay, and Rigby, a raccoon—who work as groundskeepers at a park and often escalate ordinary tasks into fantastical crises involving supernatural elements, time travel, and bizarre antagonists.^[142] Episodes typically run about 11 minutes and follow a structure where mundane workplace conflicts spiral into high-stakes adventures resolved through teamwork and absurdity, blending comedy, action, and sci-fi tropes.^[141] In literature, The Regulars: A Novel (2016) by Georgia Clark is an urban fantasy story centered on three ordinary young women—Evie, Krista, and Willow—navigating life in New York City until they discover a magical potion called Everlasting Youth that grants them supermodel beauty, leading to empowering yet chaotic explorations of identity, friendship, and desire.^[143] Published by Atria/Emily Bestler Books, an imprint of Simon & Schuster, the book uses the "regulars" motif to contrast the protagonists' initial averageness with their transformed lives, emphasizing themes of self-acceptance amid societal pressures. Films often feature "regular" protagonists—everyday individuals thrust into extraordinary circumstances—to highlight relatable heroism in comedies. A prominent example is The Hangover (2009), directed by Todd Phillips, where three unassuming friends (played by Bradley Cooper, Ed Helms, and Zach Galifianakis) embark on a Las Vegas bachelor party that devolves into amnesia-fueled chaos as they retrace their steps to rescue the groom, underscoring the humor in ordinary men's resilience. This setup, common in buddy comedies, portrays "regular" characters as accidental heroes whose flaws and normalcy drive the narrative without relying on superhuman traits.^[144] In video games, "regular" modes typically refer to standard difficulty or play styles that provide baseline accessibility and focus on core storytelling, contrasting with specialized variants like hard or classic modes. For instance, in Final Fantasy VII Remake (2020) by Square Enix, Normal Mode allows real-time action combat where players manually control attacks, magic, and abilities to progress through the narrative, suitable for balanced engagement without automated assistance.^[145] This regular approach emphasizes strategic depth in an RPG context, differing from Classic Mode (which automates party actions for a turn-based feel) or Hard Mode (unlocked post-game, restricting items and increasing enemy toughness for replay value).^[145]

References

[1]
Regular Polygon -- from Wolfram MathWorld
A regular polygon is an n-sided polygon in which the sides are all the same length and are symmetrically placed about a common center.
[2]
Euclid's Elements, Book I, Definition 19 - Clark University
Euclid names polygons by the number of their angles. For example, Book IV includes constructions of regular pentagons, hexagons, and pentadecagons (15 ...
[3]
[PDF] Tilings by Regular Polygons - University of Washington
Aug 3, 2005 · called tiles. A tiling of the plane is a family of sets that cover the plane without gaps or overlaps. ("Without overlaps" means that the ...
[4]
[PDF] Regular Verbs and Irregular Verbs. These - LAVC
Regular Verbs are verbs that add –d or –ed to their present form to change the tense from present to past. For example: The dog jumped toward the squirrel.
[5]
Forms of regular verbs - How to Use Verbs - Gallaudet University
Verbs can be regular or irregular. Regular verbs all follow the same conjugation pattern. Irregular verbs don't follow the normal conjugation pattern. You will ...Missing: definition | Show results with:definition
[6]
2.3 Verb Tense – Writing for Success
Regular verbs follow regular patterns when shifting from present to past tense. Irregular verbs do not follow regular, predictable patterns when shifting from ...Missing: grammar | Show results with:grammar
[7]
Inflection | morphology, syntax & phonology - Britannica
Inflection, in linguistics, the change in the form of a word (in English, usually the addition of endings) to mark such distinctions as tense, person, number, ...
[8]
Section 4: Inflectional Morphemes - Analyzing Grammar in Context
An inflection is a change that signals the grammatical function of nouns, verbs, adjectives, adverbs, and pronouns (e.g., noun plurals, verb tenses).Missing: languages | Show results with:languages
[9]
Regular and Irregular Inflection - The Free Dictionary
This is known as regular inflection. For example, we usually create the past simple tense of verbs by adding “-d” or “-ed” (as in ...
[10]
The processing of English regular inflections: Phonological cues to ...
The central issue is whether the representation and processing of regular past tense forms, involving the combination of stems and affixes (e.g., play + /d/ = ...
[11]
Basic Language Structures
Isolating languages are ones that use invariable words, but have strict rules of word order to keep the grammatical meanings of things clear.
[12]
Analytic language versus synthetic: grammar, examples & uses
Jan 17, 2025 · Analytic languages, like English, rely heavily on word order and auxiliary words to express meaning. In contrast, synthetic languages, such as Latin or Russian ...
[13]
Simplifying some linguistics terminology - The Language Closet
Mar 23, 2024 · The common features of more analytic languages include a more rigid basic word order. ... language learning languages linguistics ...
[14]
§4. The Indo-European Family of Languages – Greek and Latin ...
The Indo-European family of languages has two main divisions, Western and Eastern. The Western division includes Hellenic, Italic, Germanic, and Celtic ...
[15]
https://www.etymonline.com/word/regular
[16]
[PDF] From Latin to Romance - HAL-SHS
Oct 22, 2015 · This article provides a succinct overview of the evolution of central aspects of word- formation from Latin to Romance, in particular Romanian, ...
[17]
[PDF] A Developmental History of the Hispano-Romance Verb Conjugations
The Hispano-Romance family of languages includes the languages which developed from Latin as it was spoken in the Iberian Peninsula, the geographic location of ...
[18]
Regular - Etymology, Origin & Meaning
Originating c. 1400 from Latin regula meaning "rule," regular means "subject to a religious rule," a "member of a religious order," and later "soldier" or ...
[19]
REGULAR Definition & Meaning - Merriam-Webster
2025 See All Example Sentences for regular. Word History. Etymology. Adjective. Middle English reguler, from Anglo-French, from Late Latin regularis regular ...
[20]
REGULAR Definition & Meaning | Dictionary.com
adjective usual; normal; customary: To stay tidy, always put things back in their regular place immediately. evenly or uniformly arranged; symmetrical.
[21]
REGULAR | definition in the Cambridge English Dictionary
REGULAR meaning: 1. happening or doing something often: 2. existing or happening repeatedly in a fixed pattern…. Learn more.
[22]
REGULAR definition in American English - Collins Dictionary
21 senses: 1. normal, customary, or usual 2. according to a uniform principle, arrangement, or order 3. occurring at fixed or.
[23]
REGULAR Synonyms: 349 Similar and Opposite Words
Synonyms for REGULAR: frequent, periodic, steady, repeated, periodical, constant, continual, habitual; Antonyms of REGULAR: infrequent, occasional, ...
[24]
1174 Synonyms & Antonyms for REGULAR | Thesaurus.com
regular · constant · efficient · formal · periodic · routine · standardized · steady · systematic.
[25]
[PDF] Finite Groups and Character Theory - Columbia Math Department
(π(g1)(π(g2)f))(m)=(π(g2)f)(g−1. 1 m) = f(g−1. 2 g−1. 1 m) = f((g1g2)−1m)=(π(g1g2)f)(m) . One space that the group G always acts on is itself, and the ...
[26]
[PDF] The Regular Representation
Oct 28, 2019 · Definition 1. Let G be a finite group. The regular representation of G is the homo- morphism L : G −→ GL(CG) defined by. Lg.
[27]
Section 10.68 (0AUH): Regular sequences—The Stacks project
10.68 Regular sequences. In this section we develop some basic properties of regular sequences. Definition 10.68.1. Let R be a ring. Let M be an R-module.
[28]
Section 10.106 (00NN): Regular local rings—The Stacks project
Regular local rings are defined in Definition 10.60.10. It is not that easy to show that all prime localizations of a regular local ring are regular. In fact, ...
[29]
regular local ring in nLab
Jun 25, 2024 · 2. Definition. A regular local ring R is a Noetherian commutative unital local ring whose Krull dimension agrees with the minimal number of ...
[30]
10.160 The Cohen structure theorem - Stacks Project
Hence the Cohen structure theorem implies that any Noetherian complete local ring is a quotient of a regular local ring. In particular we see that a Noetherian ...
[31]
[PDF] Kummer, Regular Primes, and Fermat's Last Theorem
Abstract. This paper rephrases Kummer's proof of many cases of Fermat's last theorem in contemporary notation that was in fact derived from his work.
[32]
[PDF] Kummer's Special Case of Fermat's Last Theorem - William Stein
May 18, 2005 · A prime p is regular if and only if p does not divide the numerators of the Bernoulli numbers B2,B4,...,Bp−3. It is not hard to see with a ...
[33]
Platonic Solid -- from Wolfram MathWorld
The Platonic solids, also called the regular solids or regular polyhedra, are convex polyhedra with equivalent faces composed of congruent convex regular ...
[34]
Polytope -- from Wolfram MathWorld
, there are only three regular convex polytopes: the hypercube, cross polytope, and regular simplex, which are analogs of the cube, octahedron, and tetrahedron ...
[35]
Tessellation -- from Wolfram MathWorld
A tessellation is a tiling of regular polygons (2D), polyhedra (3D), or polytopes (n dimensions). It can also refer to breaking up self-intersecting polygons.
[36]
[PDF] Differential geometry of curves and surfaces
DEFINITION. A parametrized differentiable curve a: I→ R³ is said to be regular if a'(t) = 0 for all t = I.
[37]
Graph Theory
This standard textbook of modern graph theory, now in its sixth edition, combines the authority of a classic with the engaging freshness of style.
[38]
Petersen Graph -- from Wolfram MathWorld
The Petersen graph is a cubic graph with 10 vertices and 15 edges, introduced as a counterexample to an edge coloring problem. It has a girth of 5 and diameter ...
[39]
[PDF] Introduction to Automata Theory, Languages, and Computation
Hopcroft, John E., 1939-. Introduction to automata theory, languages, and computation / John E. Hopcroft, Rajeev Motwani, Jeffrey D. Ullman.-2nd ed. p. cm. ISBN ...
[40]
Formal parsing systems | Communications of the ACM
BAR-HILLEL, Y., PERLES, M., AND SHAMIR, E. On formal properties of simple phrase structure grammars. Zeit. Phonet. Spraehwiss. Kommunik. Forsch. 15, 2 (1961), ...
[41]
[PDF] Exploring the Regular Tree Types - University of Nottingham
Abstract. In this paper we use the Epigram language to define the universe of regular tree types—closed under empty, unit, sum, product and least fixpoint.
[42]
Tree generating regular systems - ScienceDirect.com
Trees are defined as mappings from tree structures (in the graph-theoretic sense) into sets of symbols. Regular systems are defined in which the production ...
[43]
[PDF] Briefly, what is a matroid? - Math@LSU
Definition 1.12. A matroid M is regular if M is representable over every field. The examples above illustrate two results that hold in general. Theorem 1.13 ...
[44]
Math 246A, Notes 4: singularities of holomorphic functions - Terry Tao
Oct 11, 2016 · . A general rule of thumb in complex analysis is that holomorphic functions behave like generalisations of polynomials, and meromorphic ...
[45]
[PDF] Chapter 11: Distributions and the Fourier Transform
A distribution is a continuous linear functional on a space of test functions. Dis- tributions provide a simple and elegant extension of functions that ...
[46]
Karamata Theory (Chapter 1) - Regular Variation
1 - Karamata Theory. Published online by Cambridge University Press: 05 July 2013. N. H. Bingham ,.Missing: original | Show results with:original
[47]
1.15 Summability Methods
Summability methods include Abel, Cesàro, and Borel summability. These methods are regular and consistent with conventional summation.
[48]
[PDF] Regularity Theory for Elliptic PDE - UB
One of the most basic and important questions in PDE is that of regularity. It is also a unifying problem in the field, since it affects all kinds of PDEs.
[49]
[PDF] R. Engelking: General Topology Introduction 1 Topological spaces
Jan 1, 2012 · A topological space X is called a T3-space or regular space, if X is a T1-space and for every x ∈ X and every closed set F ⊂ X such that x /∈ F ...
[50]
[PDF] MA651 Topology. Lecture 6. Separation Axioms.
• ”Elements of Mathematics: General Topology” by Nicolas Bourbaki ... (especially in Russian textbooks) refer to our T3 space as a ”regular” space and vice versa, ...
[51]
[PDF] A note on properly discontinuous actions - UC Davis Math
Jun 18, 2024 · Question 14. Suppose that G is a discrete group, G × X → X is a free continuous action on an n-dimensional topological manifold X such that ...
[52]
[PDF] Regular open or closed sets
We consider regular open (or closed) sets in a topological space and possible generaliza- tions for algebraic openings and closings in a complete lattice.<|separator|>
[53]
[PDF] the point of pointless topology1 - by peter t. johnstone
The minimal projective cover of a space, first constructed by Gleason [18] for (locally) compact Hausdorff spaces and subsequently extended by other authors to ...
[54]
[PDF] REGULAR HOMOTOPY CLASSES OF IMMERSED SURFACES
It is easy to see that regular homotopy defines an equivalence relation on the set of all immersed surfaces in Iw” of type M2.
[55]
[PDF] Regular Homotopies and the Sphere Eversion
Jun 13, 2021 · This theorem, named after the French mathematician René Thom, tells us that transversality is a generic property. Then by turning the immersion ...
[56]
Geometric approach towards stable homotopy groups of spheres ...
Jan 9, 2008 · Abstract: In this paper a geometric approach toward stable homotopy groups of spheres, based on the Pontrjagin-Thom construction is proposed ...
[57]
[PDF] An Invariant of Regular Isotopy - University of Illinois Chicago
Knot theory as the study of the formal diagrammatic system generated by the link diagrams and the Reidemeister moves is a long-standing approach to the subject.
[58]
AMS :: Transactions of the American Mathematical Society
... regular isotopy for classical unoriented knots and links. This invariant is ... Kauffman, New invariants in the theory of knots, Amer. Math. Monthly 95 ...
[59]
[PDF] 1 Discrete group actions
The action of Γ is free and properly discontinuous if and only if X/Γ is a mani- fold quotient (Hausdorff) and X → X/Γ is a covering map. • Γ a discrete ...
[60]
Regular Ultrapowers at Regular Cardinals - Project Euclid
for a regular (ultra)filter D at a singular strong limit cardinal relative to ... [5] Jech, T., Set Theory, 3rd edition, Springer, Berlin, 2003. 420. [6] ...
[61]
Constructing regular ultrafilters from a model-theoretic point of view
Feb 18, 2015 · We apply this to prove that for any n < ω, assuming the existence of n measurable cardinals below λ, there is a regular ultrafilter D on λ such ...
[62]
[PDF] 13 Lecture 06.11.21 - 13.1 Lindstrom's Theorem - UPenn CIS
Lindstrom's Theorem: Let L be a regular logic extending first-order logic. If L satisfies the Compactness and Löwenheim-Skolem properties, then L has the same ...
[63]
[PDF] Lindström's Theorem
Let L be a regular logic satisfying LöSko(L) and Comp(L). Assume that. Lωω < L. Then there exists a ψ ∈ L(S) not equivalent to any first order sentence.
[64]
[PDF] Regular Categories and Regular Logic - BRICS
3 Regular Logic. Regular logic is roughly speaking the ∃–∧–fragment of many-sorted first- order logic. Although we do not prove this here we mention that ...
[65]
[PDF] Conditioning as disintegration - Yale Statistics and Data Science
One way to engage in rigorous, guilt-free manipulation of conditional distributions is to treat them as disintegrating measures–families of probability measures ...Missing: Polish | Show results with:Polish
[66]
[PDF] Pills of measure theory on Polish spaces - cvgmt
Jul 24, 2025 · - In probability theory the disintegration theorem is often used to speak about conditional expectations. In this case, rather than having a ...
[67]
REGULAR CONDITIONAL PROBABILITY, DISINTEGRATION OF ...
Accepted : November 2003. Abstract. We establish equivalence of several regular conditional probability properties and Radon space. In addition, we introduce ...Missing: Polish derivative key
[68]
[PDF] Lecture 17 Perron-Frobenius Theory
• any positive matrix is regular. •. 1 1. 0 1 and. 0 1. 1 0 are not regular ... in other words: the distribution of a regular Markov chain always converges.
[69]
[PDF] A REVIEW OF MORE THAN ONE HUNDRED PARETO-TAIL INDEX ...
The most popular estimator of tail indexes is the Hill estimator (Hill, 1975). Hill sug- gested approximating the k-th largest observations with a Pareto ...<|separator|>
[70]
[PDF] Inferring the mixing properties of a stationary ergodic process from a ...
It is said to be β-mixing or absolutely regular if limm→∞ β(m)=0. It is straightforward to check that β(U, V) ≥ α(U, V) so that absolute regularity implies.
[71]
[PDF] Default priors for Bayesian and frequentist inference
Welch and Peers (1963) derived Jeffreys's prior by a probability matching argument based on Edgeworth expansions. In extending these results to problems ...
[72]
[PDF] Lecture 7: Jeffreys Priors and Reference Priors - People @EECS
Feb 17, 2010 · One might ask, how can we choose a prior to maximize the divergence between the posterior and prior, without having seen the data first ...
[73]
SOLUBILITY. XII. REGULAR SOLUTIONS 1 - ACS Publications
Large decrease in the melting point of benzoquinones via high-n eutectic mixing predicted by a regular solution model.
[74]
The moons of Jupiter - Phys.org
Jun 10, 2015 · Jupiter's Regular Satellites are so named because they have prograde orbits – i.e. they orbit in the same direction the rotation of their planet ...Missing: definition | Show results with:definition
[75]
6.3: Bravais Lattices - Chemistry LibreTexts
May 3, 2023 · In three-dimensional crytals, these symmetry operations yield 14 distinct lattice types which are called Bravais lattices.Missing: arrangement | Show results with:arrangement
[76]
Echinoderms: Sea Stars, Urchins, Sand Dollars, and Relatives
“Regular” urchins show five-part symmetry with a skeleton which is typically round but with long spines that project away from its body. Spines can vary in ...
[77]
Normal Sinus Rhythm - ECG Library Basics - LITFL
Oct 8, 2024 · Regular rhythm at a rate of 60-100 bpm (or age-appropriate rate in children); Each QRS complex is preceded by a normal P wave; Normal P wave ...Missing: physiology | Show results with:physiology
[78]
Geometry of Molecules - Chemistry LibreTexts
Jan 29, 2023 · Molecular geometry, also known as the molecular structure, is the three-dimensional structure or arrangement of atoms in a molecule.
[79]
[PDF] Advanced Microeconomics Partial and General Equilibrium
A regular economy is an economy characterized by an excess demand function which has the property that its slope at any equilibrium price vector is non-zero.
[80]
Smooth preferences and the regularity of equilibria - ScienceDirect
We call an economy regular if its excess demand is transversal to zero. A regular economy has locally unique equilibria. It is shown that regular economies ...
[81]
Working in a gig economy : Career Outlook - Bureau of Labor Statistics
The BLS Occupational Outlook Handbook (OOH) covers about 83 percent of the jobs in the U.S. economy. Its 329 detailed profiles of occupations are sorted by ...Missing: sociology | Show results with:sociology
[82]
National survey of gig workers paints a picture of poor working ...
Jun 1, 2022 · A survey of gig workers in the spring of 2020 revealed that their jobs provided poor working conditions, even relative to other service-sector workers.
[83]
https://www.epi.org/publication/gig-worker-survey/
[84]
Gravity models: A tool for migration analysis - IZA World of Labor
Gravity models provide an intuitive framework to understand the determinants of flows between countries, in particular: trade, migration, or capital.
[85]
The Division of Labor in Society (1893) - Emile Durkheim
Durkheim had thus postulated two distinct types of social solidarity (mechanical and organic), each with its distinctive form of juridical rules (repressive ...
[86]
Duverger: The Electoral System
I expressed its effects in 1946 in the formulation of three sociological laws: (1) a majority vote on one ballot is conducive to a two-party system; (2) ...
[87]
Full article: Testing the Multivariate Regular Variation Model
Apr 15, 2020 · In this article, we propose a test for the multivariate regular variation (MRV) model. The test is based on testing whether the extreme value indices of the ...<|control11|><|separator|>
[88]
What's the Difference between a Standing Army and a Mercenary ...
Sep 7, 2016 · The opponents of standing armies equate professional forces with mercenary forces because, following Machiavelli in The Art of War, they assume the existence ...
[89]
Peninsular War | National Army Museum
Between 1808 and 1814, the British Army fought a war in the Iberian Peninsula against the invading forces of Napoleon's France.Corunna · Torres Vedras · Albuera And Badajoz
[90]
The U.S. Army's Command Structure
The operational Army consists of numbered armies, corps, divisions, brigades, and battalions that conduct full spectrum operations around the world.Missing: modern | Show results with:modern
[91]
Customary IHL - Rule 3. Definition of Combatants
Rule 3. All members of the armed forces of a party to the conflict are combatants, except medical and religious personnel.
[92]
https://www.ausa.org/news/army-unveils-1859-billion-budget-fiscal-2025
[93]
[PDF] Unlawful Combatancy - U.S. Naval War College Digital Commons
Just as regular forces wear uniforms, so must irregular forces use a fixed emblem which will distinguish them—in ordi- nary circumstances and in a reasonable ...
[94]
Service Commitment | U.S. Army
Before Basic Training, you'll agree to an initial eight-year service commitment, which typically works out to about four years of active duty and four years of ...Missing: conscription | Show results with:conscription
[95]
Selective Service: Before the All-Volunteer Force
Voluntary enlistment in the Regular Army was for three or four years, whereas drafted soldiers served initially for twenty-one months, later extended to two ...
[96]
Countries with Mandatory Military Service 2025
6-12 months for males at age 20 (6 months for privates and non-commissioned officers and 12 months for reserve officers); an exemption can be purchased ...
[97]
Caste, Skill, and Training: The Evolution of Cohesion in European ...
Jul 2, 2014 · This essay proposes to examine the structure of medieval Europe's military systems – and the factors that held medieval armed forces together in battle and on ...<|control11|><|separator|>
[98]
[PDF] The Professionalisation of The Armed Forces | Finabel
In the last decades the Western world has grown accustomed to perceiving the partaking in war and active combat as the trade of a select few professionals.
[99]
Cadet Journey | U.S. Military Academy West Point
After graduation, all cadets become second lieutenants in the U.S. Army. But before moving to their first unit, they attend a basic officer leader course and ...Plebe Year · Day in the Life of a Cadet · Cadet housing · Firstie Year
[100]
Path for Army Officers | U.S. Army
As a commissioned Officer, you're not only a leader who guides, problem-solves, and plans for upcoming missions, but you're also empowered to make decisions ...
[101]
Captain Benjamin Bartholomew's Diary
Benjamin Bartholomew (1752-1812) was born in Chester County, Pennsylvania on January 16, 1752. Initially, Bartholomew joined the 4th Pennsylvania Battalion ...
[102]
The Roman Legion
Six centuries of eighty men formed a cohort, and ten cohorts made up a legion. Nine of the cohorts were divided into six centuries. The first cohort, which was ...
[103]
What Is the Difference between Secular Priests and Religious Priests?
Answer: Secular—or better, diocesan—priests are priests who are ordained for a particular diocese and who serve ordinarily in parishes. This is their main work ...
[104]
CATHOLIC ENCYCLOPEDIA: Secular Clergy - New Advent
The secular clergy, in which the hierarchy essentially resides, always takes precedence of the regular clergy of equal rank; the latter is not essential to the ...
[105]
CATHOLIC ENCYCLOPEDIA: Canons and Canonesses Regular
The road along which Canons Regular walk in order to reach the heavenly Jerusalem is the rule of Blessed Augustine. Further lest Canons Regular should ...
[106]
https://www.catholic.com/qa/what-is-the-difference-between-secular-priests-and-religious-priests
[107]
Households of God: the regular canons and canonesses of St ...
Jun 7, 2022 · The canons and canonesses of St Augustine, in their various guises, were the most widespread of all of the religious orders in medieval Ireland.<|control11|><|separator|>
[108]
Regular and Separate Baptists in Kentucky
The Separate Baptists appeared as a result of the great Spiritual awakening in the New England Colonies in 1740-42 under the ministry of George Whitefield and ...
[109]
Regularity and Recognition according UGLE Constitutions
Regularity of origin; i.e. each Grand Lodge shall have been established lawfully by a duly recognised Grand Lodge or by three or more regularly constituted ...Missing: criteria | Show results with:criteria
[110]
[PDF] information for the guidance of members of the craft - UGLE
Mar 13, 2024 · Only Brethren who are members of Lodges under recognised jurisdictions may visit English Lodges. They must produce a certificate (i.e. a Grand ...
[111]
REGULARITY AND RECOGNITION by W.Bro. Tony POPE, editor of ...
The terms 'regular' and irregular' are used to describe individual Masons, their lodges, and their Grand Lodges or other ruling bodies.
[112]
Constitution and Bylaws - SEIU 2015
A. Membership Definitions. Regular membership. A Regular Member is any individual employed in a bargaining unit for which the Union is the recognized ...Missing: trade | Show results with:trade
[113]
About the Independent Order of Odd Fellows
Through our lodges, members come together to promote goodwill, build connections, and engage in meaningful acts of service. Our Principles. The Odd Fellows ...Rebekahs · About us · Youth ProgramsMissing: definition | Show results with:definition
[114]
Elks Membership
Your application will be presented at a regular Lodge meeting. ... We look forward to welcoming you to the Benevolent and Protective Order of Elks!
[115]
Our Constitution - Ohio State Bar Association | OSBA
§3.1 Any person duly admitted to the practice of law, and not prohibited from being admitted to the practice of law in Ohio, may become a regular member of the ...
[116]
Membership Information | Southwest Louisiana Bar Association
The term “regular member in good standing” or “active member” means a lawyer who meets the eligibility requirements of an Active Member, who has been duly ...Missing: definition | Show results with:definition
[117]
The British Soldier of 1775 - Minute Man National Historical Park ...
The British Army in 1775 was composed of seventy regiments, all denoted by numerical order in status, seniority and privileges granted to them. The most senior ...
[118]
Lexington and Concord: 22 Hours and a Shot Heard Around the World
Apr 18, 2025 · The arrival of British warships and “Regulars” into Boston further escalated tensions in the colony. General Thomas Gage, the Royal Governor of ...
[119]
Biden's regular Joe side - Los Angeles Times
The personification of the white-haired Washington insider, Senate Foreign Relations Committee Chairman ...<|separator|>
[120]
'Joe the Plumber': Famous figure from Obama-McCain race dies at 49
Aug 28, 2023 · Samuel Wurzelbacher landed in the national spotlight after confronting Barack Obama on the 2008 campaign.
[121]
'Joe the Plumber', who challenged Obama on taxes in 2008, dies ...
Aug 28, 2023 · Samuel Joseph Wurzelbacher, famous for arguing with Barack Obama on the campaign trail, died of pancreatic cancer.Missing: guy | Show results with:guy
[122]
In Pleasanton, John Madden was 'a regular guy' for much of his life
Feb 14, 2022 · In Pleasanton, John Madden was 'a regular guy' for much of his life ... sports editor for 26 years.
[123]
Watch Regular Show Streaming Online - Hulu
Regular Show. Mordecai – a sarcastic blue jay, and Rigby – a somewhat responsible raccoon, are best friends. They even work together at a park ...
[124]
Inside 'Regular Show,' Where Every Clip Is A Big Production - NHPR
Mar 29, 2014 · Cartoon Network's Regular Show follows the misadventures of a blue jay named Mordecai and a raccoon named Rigby.
[125]
Regular Show Summary, Trailer, Season List, Cast ... - Screen Rant
Rating 9.8/10 (16) Regular Show is an animated television series that follows the surreal adventures of Mordecai, a blue jay, and Rigby, a raccoon, who work as groundskeepers ...
[126]
10 Hero Archetypes with Examples - Literary Devices
Everyman Hero Archetype. Such archetypes are just ordinary persons without ... Holden in The Catcher in the Rye by J. D. Salinger; Stephen Dedalus in A ...
[127]
Archetype Examples: Write Great Characters from Universals
Mar 29, 2018 · Salinger's wry novella, Catcher in the Rye (1951). Although authors ... Find out why and how to use the everyman archetype in your writing.
[128]
Archie Andrews
Pep Comics #22, 1941. Originally known as “America's Typical Teenager,” Archie Andrews has become the most lovable kid in town and is anything but typical!
[129]
Twelve-Cent Archie on JSTOR
Archie Andrews is an atypical comic-book protagonist. He is a young man to ... A high school junior, Archie is the quintessential everyman—the typical American ...
[130]
Call of the mild: Comic book icon Archie Andrews leaps into the 21st ...
Jul 27, 2015 · For much of the 20th century the blandly average, ginger-haired, freckle-faced perpetual teenager Archie Andrews became a mascot for white, ...
[131]
The 4 Stages of Tom Hanks's Everyman Hero Persona - Inverse
Sep 8, 2016 · Philadelphia / Forrest Gump. While Hanks continued to cultivate the image of the charming regular guy with a touch of absurdity in movies ...
[132]
Inquiry-Based Music Theory | Overview 4a - Simple Meters
A regular meter is one in which every beat is the same length. Finally, do remember that meter is somewhat subjective and can be greatly altered by many ...
[133]
Simple and Compound Meter - musictheory.net
While beats in simple meter are divided into two notes, beats in compound meter are divided into three. · To demonstrate this, we will examine 6/8 time.
[134]
Discussion 4a - Simple Meters - Integrated Music Theory
Meters that divide the beat into two equal parts are simple meters. There are three types of standard simple meters in Western music: simple duple (beats group ...<|control11|><|separator|>
[135]
What makes a song sound "folk-y"? - Music Stack Exchange
Jul 22, 2014 · It is generally harmonically and rhythmically simple, revolving around 3 or 4 chords in a key, with the tendency to change keys between sections ...<|control11|><|separator|>
[136]
Canons and Counterpoints | Bach - Oxford Academic
Canon—the derivation of polyphony from a single melodic line through imitation of itself at a fixed interval of pitch and duration—is the strictest of all ...
[137]
Regular Show (TV Series 2010–2017) - IMDb
Rating 8.6/10 (70,091) Regular Show: Created by J.G. Quintel. With J.G. Quintel, William Salyers, Sam Marin, Mark Hamill. The surreal misadventures of two best friends--a blue jay ...Full cast & crew · Regular Show · Un show más · Apenas um Show
[138]
Inside 'Regular Show,' Where Every Clip Is A Big Production - NPR
Mar 29, 2014 · On the Regular Show's floor, J.G. Quintel is playing a game of table hockey in the hall. He's the creator of the cartoon, which is based around ...
[139]
The Regulars: witty, empowering women's fiction - Georgia Clark
Georgia Clark's The Regulars is a smart, funny novel about three best friends in New York City who discover a magical elixir that turns them into drop-dead ...<|control11|><|separator|>
[140]
15 Movies Like The Hangover That Are Absolutely Hilarious
May 27, 2025 · Animal House (1978) · Universal Pictures ; After Hours (1985) · Warner Bros. Pictures ; Mallrats (1995) · Gramercy Pictures ; Swingers (1996) · Miramax ...
[141]
Normal vs Classic Mode - Final Fantasy 7 Remake Guide - IGN
Normal Mode is great for players who are excited about the challenge and satisfaction of mastering several systems at once and Classic Mode is great for players ...