Fact-checked by Grok 2 weeks ago

Expansion

Expansion is the process by which something increases in physical size, spatial extent, numerical quantity, or conceptual scope, often resulting from internal forces, external influences, or systematic growth.^[1] This concept permeates numerous fields of study, manifesting in phenomena ranging from the dilation of materials under heat to the enlargement of economies and empires.^[2] In mathematics, expansion commonly denotes the algebraic process of expressing a polynomial or series in a fully multiplied-out form, with the binomial theorem serving as a prime example for expanding expressions like (a + b)^n into sums of terms involving binomial coefficients.^[3] This method, dating back to contributions from mathematicians like Isaac Newton for non-integer exponents, enables approximations and exact computations essential in calculus, probability, and engineering applications.^[3] In physics, expansion frequently refers to thermal expansion, the tendency of most materials to increase in length, surface area, or volume when heated, due to heightened molecular vibrations that push particles farther apart.^[4] This property, quantified by coefficients of linear, areal, or volumetric expansion, influences engineering designs such as bridges and railways to accommodate temperature-induced changes.^[4] On a cosmic scale, the expansion of the universe describes the metric expansion whereby space itself stretches, causing distant galaxies to recede from one another, an observation first confirmed through Edwin Hubble's 1929 analysis of galactic redshifts.^[5] This expansion, accelerating since approximately 5 billion years ago due to dark energy, implies that the observable universe's scale factor continues to grow without bound.^[6] In economics, expansion characterizes a phase of the business cycle marked by rising real gross domestic product (GDP), increased production, employment, and consumer spending over two or more consecutive quarters.^[7] Such periods, often following recessions, drive innovation and investment but can lead to inflationary pressures if unchecked.^[7] Historically and politically, expansion pertains to territorial expansion, the extension of a nation's borders through mechanisms like military conquest, diplomatic annexation, or colonial settlement, as seen in 19th-century American westward movements or European imperialism.^[8] These processes have profoundly shaped global geopolitics, resource distribution, and cultural exchanges, though they frequently involved conflicts and displacements.^[8]

Science, Technology, and Mathematics

Thermal Expansion

Thermal expansion refers to the tendency of materials to increase in their dimensions—specifically length, area, or volume—when subjected to a rise in temperature, primarily due to enhanced atomic vibrations that lead to greater average interatomic spacing. This phenomenon arises from the anharmonic nature of interatomic potential energies, where increased thermal energy causes atoms to oscillate with larger amplitudes, effectively widening the mean separation between them in a solid lattice. In most materials, this results in positive expansion, though some exhibit contraction under heating.^[9] The linear thermal expansion describes the change in length along one dimension and is quantified by the formula \Delta L = \alpha L_0 \Delta T, where \Delta L is the change in length, \alpha is the material-specific coefficient of linear thermal expansion, L_0 is the original length, and \Delta T is the temperature change. This equation derives from the microscopic increase in average atomic spacing: as temperature rises, the anharmonic potential causes the equilibrium position of atoms to shift outward, with the relative expansion \Delta L / L_0 approximating the fractional increase in interatomic distance, averaged over the material's lattice. For steel, a typical value is \alpha \approx 12 \times 10^{-6} /^\circ\mathrm{C}.^[4]^[10]^[11] For three-dimensional changes, volumetric thermal expansion is given by \Delta V = \beta V_0 \Delta T, where \beta is the coefficient of volumetric expansion, V_0 is the original volume, and \beta \approx 3\alpha for isotropic materials that expand uniformly in all directions. This approximation holds because volume change is the product of three linear expansions, assuming no directional preferences in the material's structure. A practical application is the bimetallic strip in thermostats, where two metals with differing \alpha values—such as brass (\alpha \approx 19 \times 10^{-6} /^\circ\mathrm{C}) and steel—bend upon heating due to unequal expansion, actuating a switch to regulate temperature.^[4]^[12]^[11] The systematic study of thermal expansion emerged in the 18th century amid advancements in thermometry and calorimetry, with key experiments by Antoine Lavoisier and Pierre-Simon Laplace measuring the expansion of metals alongside specific heats to understand heat's effects on matter. Coefficients vary widely by material, reflecting differences in atomic bonding and structure; the table below lists values for select common substances at room temperature:

Material	\alpha ($10^{-6}/^\circ\mathrm{C})
Aluminum	23
Copper	17
Steel	12
Glass (soda-lime)	9
Concrete	12

These values enable predictions of dimensional changes in design.^[11]^[13] In engineering, thermal expansion necessitates accommodations to prevent structural failure, such as gaps in railroad tracks that allow elongation without buckling during heat waves, and similar provisions in bridges to avoid stress-induced cracks from seasonal temperature swings.^[14] Materials with negative thermal expansion, which contract upon heating, offer unique solutions; zirconium tungstate (ZrW_2O_8) exemplifies this, exhibiting isotropic contraction over 0.3 to 1050 K due to transverse vibrations in its framework structure, first reported in 1996. As of 2025, advances in nanomaterials, including nanocomposites incorporating negative thermal expansion phases, enable precise control of expansion in electronics, reducing thermal mismatch stresses in devices like semiconductors and improving reliability under varying operating temperatures.^[15]^[16]

Expansion of the Universe

The expansion of the universe refers to the ongoing increase in the distance between gravitationally unbound structures, such as galaxies, due to the stretching of space itself rather than motion through space.^[17] This uniform expansion is observed through the redshift of light from distant galaxies, where wavelengths are stretched to longer, redder values as space expands during the light's journey to Earth.^[18] The phenomenon implies that the universe is not expanding into preexisting space but that the metric of spacetime is dynamically changing on cosmological scales.^[19] Key historical milestones trace the concept's development. In 1917, Albert Einstein introduced a cosmological constant into his field equations of general relativity to permit a static universe, counteracting gravitational collapse.^[20] However, in 1929, Edwin Hubble published observations showing that galaxies recede from Earth at velocities proportional to their distances, providing empirical evidence for an expanding universe.^[21] This discovery prompted Einstein to later describe the cosmological constant as his "biggest blunder," though it would regain relevance decades later.^[20] Hubble's law quantifies this expansion empirically as v = H_0 d, where v is the recession velocity of a galaxy, d is its proper distance, and H_0 is the Hubble constant, currently measured at approximately 70 km/s/Mpc based on 2025 observations.^[22] The law derives theoretically from the Friedmann equations, which solve Einstein's field equations under the cosmological principle assuming homogeneity and isotropy; these equations describe how the scale factor a(t) of the universe evolves, with H = \dot{a}/a as the Hubble parameter, reducing to H_0 at present.^[23] Within the Big Bang model, this expansion traces back to an initial hot, dense state approximately 13.8 billion years ago, supported by evidence like the cosmic microwave background (CMB) radiation, discovered serendipitously in 1965 by Arno Penzias and Robert Wilson as a uniform 2.7 K glow permeating space.^[24]^[25] Observations in the late 1990s revealed that the expansion is accelerating, rather than decelerating as expected from gravity alone, an effect attributed to dark energy, which comprises about 68% of the universe's energy density.^[6] This discovery, based on Type Ia supernovae as standard candles showing unexpectedly dim distant explosions, earned the 2011 Nobel Prize in Physics for Saul Perlmutter, Brian Schmidt, and Adam Riess.^[26] Recent 2025 data from the James Webb Space Telescope (JWST) have refined measurements of the Hubble constant, helping to probe the so-called H_0 tension between local and early-universe estimates while supporting the accelerating model amid ongoing refinements.^[27] If acceleration persists, the universe's fate is likely "heat death," a cold, dilute state where entropy maximizes and no work can be extracted, as galaxies recede beyond interaction and stars exhaust fuel over trillions of years.^[28]

Series Expansion in Mathematics

In mathematics, a series expansion represents a function as an infinite sum of simpler terms, such as powers or trigonometric functions, to facilitate approximation, analysis, and computation within specific domains of convergence or asymptotic regimes.^[29] Power series expansions, in particular, express a function f(x) around a point c as \sum_{n=0}^{\infty} a_n (x - c)^n, where the coefficients a_n are determined by the function's behavior near c. This form enables local approximations of complex functions by polynomials of increasing degree, with the error controlled by the remainder term.^[30] The Taylor series provides a canonical power series expansion for sufficiently smooth functions, given by

f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!} (x - c)^n,

where f^{(n)}(c) denotes the nth derivative of f at c.^[31] This series is derived by assuming f(x) can be approximated by a polynomial p_n(x) that matches f and its first n derivatives at c, obtained through repeated differentiation: starting from f(x) = f(c) + (x - c) f'(c) + \cdots, integrating the (n+1)th derivative yields the next term, with the process continuing indefinitely for infinite differentiability.^[32] The Maclaurin series is the special case where c = 0, so f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(0)}{n!} x^n, as formalized by the Maclaurin theorem, which asserts that if such a power series converges to f(x) on an interval, it must be the unique Taylor series representation.^[31] Convergence is assessed using the ratio test on the coefficients: the radius of convergence R satisfies \frac{1}{R} = \lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right|, beyond which the series may diverge.^[31] Representative examples illustrate the utility of Taylor series. For the exponential function, the Maclaurin series is e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}, which converges for all real x since the ratio test yields \lim_{n \to \infty} \left| \frac{x}{n+1} \right| = 0 < 1.^[31] Similarly, \sin x = \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n+1}}{(2n+1)!}, also converging everywhere, derived by repeated differentiation of \sin x at 0, where even derivatives vanish and odd ones cycle through \pm 1, \pm \cos x, \mp \sin x.^[31] These expansions find applications in calculus for evaluating limits, such as \lim_{x \to 0} \frac{\sin x}{x} = 1 by truncating the series to first order, and for integrals, where term-by-term integration of e^x or \sin x series computes antiderivatives or definite integrals without closed forms.^[31] Fourier series extend expansions to periodic functions, representing f(x) with period $2L as

f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} \left[ a_n \cos\left(\frac{n \pi x}{L}\right) + b_n \sin\left(\frac{n \pi x}{L}\right) \right],

where coefficients are computed via orthogonality of sines and cosines over [-L, L]: a_0 = \frac{1}{L} \int_{-L}^{L} f(x') \, dx', a_n = \frac{1}{L} \int_{-L}^{L} f(x') \cos\left(\frac{n \pi x'}{L}\right) \, dx', and b_n = \frac{1}{L} \int_{-L}^{L} f(x') \sin\left(\frac{n \pi x'}{L}\right) \, dx'.^[33] This decomposition is essential in signal processing, where periodic signals are broken into harmonic components for filtering, compression, and analysis.^[33] Asymptotic expansions approximate functions for large arguments or parameters, where the series may diverge but partial sums improve accuracy successively, unlike convergent Taylor series. For instance, Stirling's series provides an asymptotic expansion for the factorial: n! \sim \sqrt{2 \pi n} \left( \frac{n}{[e](/page/E!)} \right)^n \left( 1 + \frac{1}{12n} + \frac{1}{288n^2} - \frac{139}{51840n^3} + \cdots \right), derived from the expansion of \ln \Gamma(z) as \ln \Gamma(z) = (z - 1/2) \ln z - z + \frac{1}{2} \ln (2\pi) + \sum_{k=1}^{\infty} \frac{B_{2k}}{2k(2k-1) z^{2k-1}}, with Bernoulli numbers B_{2k}.^[34] This yields high-precision approximations for large n, such as Stirling's approximation n! \approx \sqrt{2 \pi n} (n/[e](/page/E!))^n.^[34] The concept of series expansions originated with Brook Taylor, who introduced the Taylor series in his 1715 work Methodus incrementorum directa et inversa, formalizing expansions via finite differences and derivatives.^[35] Joseph Fourier advanced the field in 1822 with Théorie analytique de la chaleur, developing trigonometric series for heat conduction solutions, despite initial resistance from contemporaries like Lagrange.^[36] In modern computational contexts, such as AI optimization as of 2025, series expansions like Taylor approximations enhance machine learning by enabling polynomial surrogates for loss functions in gradient-based methods and neural network training on manifolds, achieving error rates like O(n^{-\gamma}) for smooth functions via Fourier or polynomial bases.^[37]

Expansion Joints in Engineering

Expansion joints in engineering are specialized gaps or mechanical devices incorporated into structures such as bridges, pipelines, and buildings to accommodate movements resulting from thermal expansion, contraction, seismic activity, or other stresses, thereby preventing damage to the overall system. These components provide flexibility by allowing controlled displacement while maintaining structural integrity and sealing against environmental elements like moisture and debris. For instance, in piping systems, they absorb dimensional changes due to temperature variations, reducing stress on connected equipment.^[38] Common types include sliding joints, which use lubricated plates to permit linear movement; bellows-type joints, often metallic and convoluted for axial, lateral, and angular flexibility; and rubber expansion joints, such as neoprene compression seals or strip seals, valued for their elasticity and vibration damping. Materials like neoprene offer superior flexibility and resistance to weathering, making them suitable for applications requiring corrosion protection and ease of installation. These types are selected based on the anticipated movement range and environmental conditions, with rubber variants excelling in low-pressure scenarios and metallic bellows in high-temperature or pressure environments.^[40]^[41]^[42] Design principles for expansion joints emphasize sizing to match expected thermal movements, calculated using the coefficient of thermal expansion (α, typically 6 × 10^{-6}/°F for steel and concrete) and temperature differential (ΔT), where the maximum movement is approximated as α × ΔT × L (L being the effective length). Joint width is then determined as a multiple of this movement (e.g., 1.4 to 2.0 times for buildings, adjusted for heating or air conditioning), ensuring sufficient gap without excessive deflection. Load-bearing capacity is evaluated through finite element analysis to simulate stresses under combined thermal, seismic, and operational loads, optimizing for durability and minimal leakage.^[43]^[44] In applications, expansion joints are integral to highways and bridges, where modular designs like strip seal joints handle up to 4 inches of movement to accommodate traffic-induced rotations and temperature swings. In buildings, they appear as floor gaps to prevent cracking in concrete slabs, while in pipelines, they mitigate thermal and seismic stresses in high-pressure fluid transport systems, such as oil and gas lines. These implementations ensure longevity in diverse infrastructures, from urban overpasses to industrial piping networks.^[45]^[46]^[38] Standards governing expansion joints include AASHTO LRFD Bridge Design Specifications Section 14.5, which outlines selection and performance criteria for bridge joints to ensure watertightness and movement capacity up to 4 inches. The National Cooperative Highway Research Program (NCHRP) provides maintenance guidelines for small-movement joints, covering types like compression seals and pourable fillers to address debris accumulation and deterioration. Historical failures, such as pipeline ruptures in the 1980s attributed to inadequate bellows design leading to squirming and joint instability, underscore the need for rigorous adherence to these standards to avoid catastrophic leaks or explosions.^[47]^[48]^[49] Recent advances as of 2025 include smart expansion joints embedded with IoT sensors for real-time monitoring of strain, temperature, and wear, enabling predictive maintenance through AI analytics in sustainable infrastructure projects. Climate change exacerbates these needs by increasing ΔT, with projections indicating up to a 2% rise in stress per 1°C temperature increase, potentially overwhelming clogged joints in northern U.S. bridges by 2100 and necessitating wider gaps or enhanced materials.^[50]^[51]

Economics

Business Expansion

Business expansion refers to the process by which companies scale their operations, increase market reach, or diversify product lines to achieve growth beyond their current scope, often involving entry into new geographic areas, acquisition of competitors, or development of new offerings.^[52] This growth can be pursued through various strategies, with organic expansion relying on internal resources such as research and development (R&D) or enhanced sales efforts to build capabilities gradually, as seen in companies investing in product innovation without external acquisitions.^[53] In contrast, inorganic expansion involves external mechanisms like mergers and acquisitions (M&A) to rapidly acquire market share or capabilities from other firms.^[54] A key framework for evaluating these strategies is the Ansoff Matrix, which categorizes growth options into four quadrants: market penetration (selling more existing products to current markets), market development (entering new markets with existing products), product development (introducing new products to current markets), and diversification (new products in new markets).^[55] This matrix helps businesses assess risk levels, with penetration being the least risky and diversification the most, guiding decisions on whether to prioritize organic or inorganic approaches.^[56] To measure the success of expansion efforts, companies track key metrics such as revenue growth rate, which indicates the percentage increase in sales over time and reflects overall scaling effectiveness; market share increase, showing competitive positioning gains; and return on investment (ROI), calculated as net profit divided by expansion costs to evaluate project profitability.^[57]^[58] These metrics provide essential context for assessing impact, though they must be benchmarked against industry standards to account for variables like economic conditions.^[59] Expansion initiatives often face significant challenges, including substantial capital requirements to fund infrastructure, hiring, or acquisitions, which can strain resources for smaller firms.^[60] Regulatory hurdles, such as compliance with international trade laws or environmental standards, further complicate efforts, particularly in cross-border ventures.^[61] For instance, Amazon's global expansion in the 2010s involved navigating diverse regulatory environments while investing heavily in logistics and localization, enabling entry into markets like India and Europe through acquisitions and partnerships.^[62] Historically, Henry Ford's introduction of the moving assembly line in 1913 revolutionized business expansion by enabling mass production of the Model T, reducing costs from $850 to $300 per vehicle and allowing Ford Motor Company to scale output dramatically while increasing worker wages to $5 per day.^[63] In 2025, trends emphasize sustainable expansion through green technology investments, with clean energy sectors like solar PV attracting over half of cleantech funding to support eco-friendly scaling amid regulatory pushes for decarbonization.^[64]^[65] However, risks such as overexpansion can lead to financial distress, as exemplified by WeWork's 2019 collapse, where rapid opening of nearly 100 new offices without matching demand resulted in doubled losses to $1.8 billion and a failed IPO, slashing its valuation from $47 billion to under $8 billion.^[66]^[67] This case underscores the dangers of aggressive inorganic growth without sustainable revenue models, often exacerbated by high debt loads.^[68]

Economic Expansion in Business Cycles

Economic expansion refers to the phase of a business cycle characterized by increasing economic activity, occurring between a trough (the end of a recession or recovery) and a peak, as part of the standard four-phase cycle that also includes peak, contraction, and trough.^[69] This period typically features sustained growth in output and employment, distinguishing it from the preceding recovery and the subsequent slowdown at the peak.^[69] Key indicators of economic expansion include rising real gross domestic product (GDP), declining unemployment rates, and increasing consumer spending, with the National Bureau of Economic Research (NBER) using a composite of metrics such as real GDP, economy-wide employment, real personal income excluding transfers, industrial production, and wholesale-retail sales to date these phases.^[69] In the United States, annual real GDP growth during expansions has averaged approximately 3 percent, while unemployment rates often fall below 5 percent, reflecting broader aggregate demand and supply alignment.^[70] These indicators signal a healthy economy where business investment and household consumption drive further activity, though the NBER emphasizes that no single metric defines the phase.^[71] Expansions are often triggered by fiscal and monetary stimuli, such as government spending increases or interest rate cuts, which boost aggregate demand and initiate the multiplier effect, whereby an initial injection of spending generates successive rounds of income and expenditure across the economy.^[72] Technological innovations also play a key role by enhancing productivity and supply-side capacity, allowing for higher output without proportional input increases.^[73] For instance, the multiplier effect can amplify a $1 billion fiscal stimulus into $1.5–2 billion in total economic output, depending on economic conditions like the marginal propensity to consume.^[74] The average duration of U.S. postwar expansions has been about 5–6 years (roughly 65 months), though lengths vary, with expansions ending when growth reaches unsustainable levels leading to a peak and potential recession.^[75] The expansion from June 2009 to February 2020 lasted a record 128 months, supported by accommodative monetary policy and recovery from the Great Recession, before concluding with the COVID-19 downturn.^[70] Globally, the post-World War II economic boom from 1948 to 1973 exemplified prolonged expansion, driven by pent-up consumer demand, industrial reconversion, and international trade growth, with U.S. real GDP rising over 4 percent annually on average during this era.^[76] In emerging markets, India's economy in the 2020s has seen robust expansion fueled by digital infrastructure investments, with GDP growth averaging 6–7 percent amid a burgeoning digital economy that expanded internet access to over 800 million users by 2023.^[77] More recently, as of 2025, artificial intelligence advancements have contributed to productivity gains in advanced economies, potentially supporting recovery phases through enhanced efficiency in sectors like manufacturing and services.^[78] Theoretical explanations for expansions differ notably between Keynesian and real business cycle (RBC) frameworks. Keynesian theory attributes growth to demand-side factors, where fiscal and monetary policies stimulate spending to overcome deficiencies, leading to higher output via the multiplier process during periods of underutilized resources.^[79] In contrast, RBC theory emphasizes supply-side shocks, such as positive technological innovations or resource discoveries, which shift the production frontier outward and drive expansions through efficient resource allocation without relying on demand management.^[80] Individual firms often experience correlated benefits during these economy-wide expansions, enabling scaled operations and investment.^[69]

Sport

Expansion Teams

Expansion teams refer to new franchises granted entry into an existing professional sports league, typically formed through an expansion draft where they select players from established teams to build their initial rosters.^[81] These additions often target untapped markets to expand the league's fanbase, increase viewership, and generate additional revenue streams for the organization.^[82] The process for establishing an expansion team involves rigorous league approval, competitive ownership bids, and sometimes debates over relocations from existing markets. Prospective owners must demonstrate financial stability, secure a suitable venue, and pay a substantial expansion fee, which is distributed among current teams; for instance, in the NFL, relocation fees for teams like the Rams and Chargers exceeded $645 million each in the late 2010s, reflecting the high costs associated with market entry in the 2020s.^[83] Once approved, the team participates in an expansion draft, selecting unprotected players under league rules to form a competitive roster.^[84] Historically, Major League Baseball (MLB) expanded in 1961 by adding the Los Angeles Angels and Washington Senators (the latter now the Texas Rangers) to the American League, marking the first significant growth beyond 16 teams since 1901 and aiming to capitalize on West Coast and capital markets.^[85] In the National Basketball Association (NBA), the 1980s saw key expansions, including the Dallas Mavericks in 1980, bringing the league to 23 teams, followed by the Charlotte Hornets and Miami Heat in 1988, and the Orlando Magic and Minnesota Timberwolves in 1989, which helped broaden the league's national footprint amid rising popularity.^[86]^[87] The introduction of expansion teams can initially dilute the talent pool across the league, leading to shorter-term competitive imbalances as new rosters build experience, though it ultimately fosters greater overall competition and rivalries. Economically, these teams provide significant boosts to host cities; the Vegas Golden Knights, added to the NHL in 2017, generated over $90 million in sponsorship revenue in their debut season and contributed to billions in local economic activity through tourism and job creation.^[88]^[89] Challenges for expansion teams include meeting stringent stadium requirements, often necessitating public-private partnerships for construction or upgrades, and gaining draft advantages, such as priority selections or protected status in expansion drafts to accelerate competitiveness. As of 2025, Major League Soccer (MLS) is expanding with San Diego FC debuting as the 30th team, influenced by growing European-style soccer interest in North America, though further growth to 32 teams remains under discussion. In women's leagues like the WNBA, expansions to 18 teams by 2030—with recent additions including the Golden State Valkyries in 2025 and further teams planned for 2026 (Toronto and Portland), 2028 (Cleveland), 2029 (Detroit), and 2030 (Philadelphia)—have raised concerns about player salaries and parity, as the league's low revenue share (around 9-10%) limits wage growth despite potential influxes from expansion fees, which could indirectly support higher payrolls if negotiated into collective bargaining agreements.^[90]^[91]^[92]^[93]^[94]^[95]

League Expansion

League expansion refers to the process by which professional sports leagues increase their number of teams, add divisions, or extend their geographical footprint to tap into new markets, thereby boosting profitability through expanded revenue streams and enhancing overall competitiveness.^[82] This growth strategy allows leagues to access untapped fan bases and sponsorship opportunities, often involving the sale of franchise rights to new owners in underserved regions.^[82] Unlike simple team relocations, expansion fundamentally alters league structure to accommodate broader participation and market penetration.^[96] The mechanisms for league expansion typically require approval through voting by existing team owners, who must agree on criteria such as market viability and financial commitments from prospective franchisees.^[97] Territorial rights are often sold as part of the process, granting exclusive operating areas to new entrants and preventing intra-league competition in overlapping markets.^[97] International expansions frequently begin with exploratory games or series to gauge demand, as seen in the National Football League's (NFL) series of matches in London during the 2020s, which have paved the way for discussions on establishing a permanent franchise there.^[98] These steps culminate in the formation of expansion teams, representing the tangible outcome of such league-wide decisions. Notable examples illustrate the impact of these mechanisms. In 1967, the National Hockey League (NHL) doubled its size from six to twelve teams in the largest single expansion in professional sports history, adding franchises in Los Angeles, Minnesota, Oakland, Philadelphia, Pittsburgh, and St. Louis to broaden its national appeal.^[99] Similarly, the English Premier League has achieved indirect expansion through lucrative global television deals, which increased overseas broadcast revenue by 23% for the 2025-2028 cycle, enabling the league to extend its reach without adding domestic teams.^[100]^[101] Expansion yields significant benefits, including elevated media rights revenue from larger audiences and the influx of diverse talent from expanded recruiting pools, which can elevate league quality and global appeal.^[82] However, it also introduces drawbacks such as increased travel costs for teams operating across wider geographies and added scheduling complexities that can strain player health and game balance.^[102] Regulatory frameworks facilitate these changes, particularly in the United States, where the Sports Broadcasting Act of 1961 provides antitrust exemptions allowing leagues to collectively negotiate television contracts without violating competition laws, thereby supporting revenue growth essential for funding expansions.^[103] In 2025, e-sports leagues are trending toward rapid expansions integrated with metaverse technologies, incorporating virtual reality and augmented reality for immersive global tournaments that attract new demographics without physical travel.^[104] Historically, league expansion evolved from regional configurations in the early 20th century—such as Major League Baseball's initial focus on East Coast cities—to national scales by mid-century, driven by population shifts and transportation improvements that made cross-country play feasible.^[105] This progression has raised incomplete concerns about sustainability, including the carbon footprint of global travel, with professional football alone contributing an estimated 64-66 million tonnes of CO2 equivalent annually, much of it from international fixtures.^[106]

Arts, Entertainment, and Media

Expansion in Music

In music, "expansion" often refers to works titled with the term or exploring motifs of growth, broadening sonic landscapes, and artistic evolution. These pieces frequently employ extended compositions, layered instrumentation, and improvisational elements to evoke a sense of unfolding or enlargement, drawing from genres like jazz-funk, hip hop, and experimental rock. Notable examples highlight how musicians have used the concept to push boundaries, reflecting personal, cosmic, or collective development. One prominent album is Expansions by Lonnie Liston Smith & the Cosmic Echoes, released in 1975 on Flying Dutchman Records. This jazz-funk record features ethereal keyboards, flute, and rhythmic grooves, with themes centered on spiritual and cosmic expansion, as heard in the title track's mantra-like chant: "Expand your mind to understand / We all must live in peace and harmony."^[107] The album's production, blending Miles Davis-inspired fusion with Afrocentric spirituality, marked Smith's shift from free jazz toward accessible, groove-oriented sounds. Another key work is McCoy Tyner's Expansions, a 1973 Blue Note release that broadened post-Coltrane jazz horizons through modal explorations and ensemble interplay, featuring Woody Shaw on trumpet and expansive tracks like the 12-minute "Vision." In hip hop, Dilated Peoples' Expansion Team (2001, Capitol Records) uses the title metaphorically for crew growth and lyrical reach, with tracks like "Worst Comes to Worst" showcasing intricate rhymes and beats that expand underground West Coast rap's scope. Complementing these albums are standalone tracks and experimental releases. The title track "Expansion" from Lonnie Liston Smith's album, recorded in 1974, serves as an instrumental jazz-funk opener that builds through repetitive motifs and swelling orchestration, symbolizing meditative growth. In avant-garde circles, the Gravity Adjusters Expansion Band's debut One (1973, Nocturne Records) delivers spacey, improvisational soundscapes using invented instruments like the waterphone, evoking cosmic expansion in a progressive, free-form style rooted in San Francisco's psychedelic scene. These works often symbolize sonic or artistic broadening, with production techniques such as multi-tracked synthesizers, reverb-heavy layers, and gradual builds mimicking physical or metaphorical expansion—evident in Smith's cosmic echoes or Tyner's modal extensions. The cultural impact of these "expansion"-themed works lies in their role in genre evolution. Lonnie Liston Smith's Expansions influenced 1980s acid jazz and 1990s hip hop sampling, with its title track looped in productions by artists like A Tribe Called Quest, bridging jazz-funk to modern electronic hybrids.^[108] Tyner's album helped solidify modal jazz's legacy, impacting fusion acts like Weather Report. By 2025, revivals via streaming playlists on platforms like Spotify have resurged interest, with Expansions appearing in "Cosmic Jazz" and "Funk Essentials" curated lists, inspiring neo-soul remixes.^[109] Historically, the 1970s saw a trend in progressive rock toward expansive suites, as bands like Yes and Genesis crafted multi-part epics that mirrored thematic growth, though few directly titled works after "expansion." Coverage of non-Western traditions remains incomplete; in Indian classical music, the alap section of a raga performance denotes melodic expansion, where performers gradually unfold the scale's notes without rhythm, building emotional depth through microtonal elaboration—a core motif of growth in Hindustani and Carnatic systems.^[110]

Expansion in Video Games

In video games, expansions refer to additional content released after the base game's launch, typically in the form of downloadable content (DLC) or expansion packs that extend the original game's world, storyline, or mechanics. These additions often include new levels, characters, quests, or features that require the base game to function, building directly upon its foundation to provide a more comprehensive experience. A prominent example is The Witcher 3: Wild Hunt – Blood and Wine (2016), developed by CD Projekt Red, which introduces the picturesque region of Toussaint, complete with over 20 hours of new adventures, a branching narrative involving vampire mysteries, and gameplay enhancements like armor dyeing and mutations.^[111]^[112] This expansion exemplifies how such content can rival the scale of the original game while maintaining narrative continuity. Expansions come in various types, broadly categorized as story-driven or mechanical. Story expansions focus on narrative continuations, adding substantial plotlines, characters, and environments to advance the game's lore, as seen in Blood and Wine's self-contained tale that serves as an epilogue to the base game. Mechanical expansions, by contrast, introduce new gameplay modes, such as multiplayer features, revamped systems, or additional tools, often enhancing replayability without heavy emphasis on story. Pricing models vary, with some expansions offered for free to retain player engagement—particularly in live-service titles—while paid options dominate, ranging from modest cosmetic packs to full-scale releases costing $20–$50, reflecting the content's depth and development investment.^[113]^[114] The industry evolution of expansions traces back to the 1990s, when physical cartridge or disk-based add-ons were common for PC and console games, such as mission packs for titles like Wing Commander that required manual installation and expanded campaigns. By the early 2000s, digital distribution facilitated the shift to DLC, enabling smaller updates and eventually microtransactions for incremental content. Massive multiplayer online games like World of Warcraft (Blizzard Entertainment) pioneered annual expansion cycles, with Dragonflight (2022) introducing the Dragon Isles, a new playable race (Dracthyr Evoker), dragonriding mechanics, and overhauled professions, marking the ninth major expansion and sustaining the game's 20-year lifespan through iterative world-building. This progression has integrated expansions into core monetization strategies, blending them with in-game purchases for ongoing revenue.^[115]^[116]^[117] Expansions significantly impact the industry by extending game lifespans—often doubling playtime through fresh content—and generating substantial revenue; for instance, successful DLC can contribute 15–20% of a title's total earnings while boosting base game sales via bundled editions. However, they have sparked controversies, particularly around paywalls that fragment player experiences, such as locking essential story missions or base activities behind purchases, as criticized in cases like Destiny 2: Curse of Osiris (2017) where core content access was restricted, leading to developer acknowledgments of design missteps. These practices have drawn scrutiny for prioritizing profits over accessibility, though they remain a staple for post-launch support.^[118]^[119]^[120] As of 2025, trends in expansions emphasize immersive technologies, with VR and AR integrations expanding metaverse-style games to create persistent, shared worlds where players can access modular content updates, such as social VR hubs or AR-overlaid real-world quests, driven by hardware advancements from companies like Meta and Sony. Indie developers are increasingly leveraging platforms like Steam Workshop for community-driven expansions, enabling free or low-cost mods that function as official add-ons—exemplified by Downfall: A Slay the Spire Fan Expansion (2022), which adds a new character and game mode through user-created assets, fostering creativity without large budgets.^[121]^[122]^[123] Developing expansions involves a structured process akin to base game production but tailored for integration: pre-production prototypes test new assets like models, textures, and levels to ensure compatibility; production phases focus on scripting narratives or balancing mechanics to prevent disruptions to the core game, such as adjusting difficulty curves or UI elements; and post-production includes rigorous testing for bugs across platforms. This requires close coordination to reuse base engine code while creating seamless extensions, often taking 6–18 months depending on scope.^[124]^[125]

Expansion in Television and Film

In television and film, "expansion" often manifests as a thematic motif exploring the broadening of human frontiers, whether through interstellar colonization, technological augmentation, or narrative universe-building in franchises. This concept underscores stories of growth, both literal and metaphorical, where characters confront the consequences of overreach or discovery. For instance, the Syfy series The Expanse (2015–2022), adapted from James S.A. Corey's novels, depicts humanity's tense expansion across the solar system amid political rivalries between Earth, Mars, and the Belt, highlighting resource scarcity and cultural clashes as core drivers of conflict.^[126] The series' intricate world-building, praised for its realistic physics and geopolitical depth, exemplifies how expansion narratives propel serialized storytelling in modern sci-fi. A seminal example from early anthology television is the episode "Expanding Human" from The Outer Limits (Season 2, Episode 4, 1964), where a psychiatrist experiments with an alien device that accelerates intellectual growth, leading to uncontrollable evolution and ethical dilemmas about human limits. This self-contained story, typical of the show's format, uses expansion as a cautionary theme, blending psychological horror with speculative science to warn of unchecked ambition. Similarly, short films like the French sci-fi entry Expansion, directed by Jean-Clément Gunter, portray mysterious sky phenomena disrupting a monastic community, symbolizing disruptive growth and societal upheaval in a minimalist narrative.^[127] Thematically, expansion in television and film frequently involves world-building through franchise extensions, where prequels, sequels, and spin-offs deepen lore to sustain audience investment. The Star Wars saga illustrates this, with spin-offs like The Mandalorian (2019–present) and Andor (2022–present) extending the original trilogy's universe by exploring peripheral eras and characters, such as the post-Empire reconstruction, thereby enriching the canon without altering core events. In the Marvel Cinematic Universe, expansions like the WandaVision (2021) series branch into multiversal explorations, allowing narrative growth that ties into films like Doctor Strange in the Multiverse of Madness (2022) and fosters interconnected storytelling across media. These extensions prioritize conceptual depth, such as moral ambiguities in imperial expansion, over exhaustive timelines. Production aspects of expansion-focused works emphasize resource allocation for immersive environments, particularly through computer-generated imagery (CGI) to render vast, alien landscapes. The Star Wars prequel trilogy (1999–2005), directed by George Lucas, allocated significant budgets—over $100 million per film—to pioneering CGI for expansive worlds like Coruscant, revolutionizing visual effects by integrating digital crowds and planetary vistas that grounded the saga's galactic scale. Sequels and prequels in franchises like The Lord of the Rings trilogy (2001–2003) similarly invested in CGI for lore expansion, with Peter Jackson's team spending millions on motion-capture and set extensions to depict Middle-earth's sprawling history, setting benchmarks for epic-scale productions. Culturally, expansion narratives thrive in the binge-watching era of streaming, where platforms like Netflix cultivate extended universes to encourage prolonged viewer immersion. In 2025, Netflix's Stranger Things Season 5 is set to conclude its Upside Down saga by expanding the 1980s-inspired world with deeper lore on interdimensional threats, capitalizing on fan-driven anticipation for narrative closure amid binge habits. Similarly, the second season of 3 Body Problem (expected to premiere in 2026), adapted from Liu Cixin's novel, broadens its alien contact premise into global-scale expansions, resonating with audiences through serialized reveals that mirror real-world anxieties about extraterrestrial outreach.^[128] This format has elevated sci-fi's role in viewer retention, with expanded arcs fostering communal discussions on platforms like Reddit and Twitter. Historically, early television anthologies laid the groundwork for expansion motifs, often using standalone episodes to probe sci-fi ideas of growth and exploration. The Twilight Zone (1959–1964), created by Rod Serling, featured tales like "The Monsters Are Due on Maple Street" (1960), where paranoia simulates societal expansion's breakdown, blending allegory with speculative fiction to critique conformity. The Outer Limits (1963–1965) complemented this with episodes emphasizing technological or biological expansion, such as "The Sixth Finger" (1963), where a miner's evolution via a machine explores human potential's perils, influencing later series' thematic boldness. Internationally, Japanese anime frequently employs expansion through sequels and spin-offs, transforming limited manga adaptations into sprawling multimedia universes. Franchises like Dragon Ball (1986–present) have expanded via sequels such as Dragon Ball Super (2015–2018), introducing multiversal tournaments and divine lore that extend the original's martial arts premise into cosmic scales, boosting global viewership. One Piece (1999–present) similarly grows its pirate adventure through spin-offs like One Piece Film: Red (2022), adding musical and familial backstories to Eiichiro Oda's world, with Toei Animation's 2025 global push aiming to amplify these extensions via new IPs. The impact of these expansions lies in heightened fan engagement, as extended canons invite deeper investment and community interaction. In Star Wars, the shift from Expanded Universe novels to a streamlined canon post-2014 has sustained discourse, with fans debating lore additions in shows like Ahsoka (2023), driving merchandise sales and conventions. Studies on fan cultures note that such extensions, by validating viewer interpretations through official content, enhance loyalty and social media buzz, as seen in Marvel's universe where post-credit scenes spark theories and boost theatrical returns.^[129] This dynamic transforms passive viewing into participatory storytelling, solidifying expansion's enduring appeal in television and film.

Other Uses

Territorial Expansion

Territorial expansion refers to the process by which states or empires extend their sovereign control over new lands, typically through annexation, colonization, or settlement, often facilitated by military conquest, diplomatic treaties, or legal claims.^[130] This geopolitical phenomenon has historically aimed to enhance political influence, secure resources, and establish dominance over unoccupied or contested regions deemed as frontiers.^[131] A prominent example is the United States' Manifest Destiny in the 19th century, which justified westward expansion across North America. In 1803, the U.S. acquired the Louisiana Territory from France through the Louisiana Purchase, doubling the nation's size for approximately $15 million and opening vast lands for settlement.^[132] This was followed by the 1848 Mexican Cession, where, after the Mexican-American War, Mexico surrendered over 500,000 square miles of territory—including present-day California, Nevada, Utah, and parts of other southwestern states—via the Treaty of Guadalupe Hidalgo.^[133] Similarly, the Roman Empire in the 1st century BCE to 1st century CE aggressively expanded its borders through military campaigns, conquering Gaul under Julius Caesar (58–50 BCE) and incorporating Britain under Claudius in 43 CE, thereby controlling much of the Mediterranean littoral and beyond by 100 CE.^[134]^[135]^[136] Mechanisms of territorial expansion have varied, including diplomatic negotiations and military force. The 19th-century Scramble for Africa exemplified diplomatic partitioning, where European powers like Britain, France, and Germany divided the continent into over 50 colonies between 1880 and 1914 through conferences such as the Berlin Conference (1884–1885), often without African input, to preempt conflicts among themselves.^[137] Military conquest was central to Roman expansions, with legions subduing resistant populations to impose direct rule. Legal doctrines like terra nullius—Latin for "land belonging to no one"—further enabled claims by portraying territories as unoccupied, even when inhabited by indigenous groups, as applied by European colonizers in Australia and the Americas to justify sovereignty without treaties.^[138]^[139] Such expansions often led to profound consequences, including cultural assimilation, where dominant powers imposed languages, religions, and governance on subjugated peoples, eroding local identities.^[140] They also sparked conflicts, such as ethnic rivalries and resistance movements, exacerbating instability and human rights violations. Post-World War II decolonization marked a reversal, with over three dozen Asian and African states gaining independence between 1945 and 1960 through negotiations, armed struggles, or UN oversight, dismantling European empires and redrawing global maps.^[141] Economic motives, akin to those in business cycles, sometimes underpinned these drives by seeking resources to fuel growth.^[142] In 2025, debates on territorial expansion extend to extraterrestrial realms, with the Artemis Accords—signed by 60 nations including the U.S. as of November 2025—promoting principles for lunar exploration while adhering to the 1967 Outer Space Treaty that prohibits national sovereignty claims, aiming to regulate resource use and prevent disguised territorial grabs on the Moon.^[143] Recent additions include nations like Austria and Panama in late 2024, reflecting growing international cooperation. Discussions on cyber-territory remain nascent, focusing on digital sovereignty where states fortify data borders and enact localization laws to assert control over virtual domains amid geopolitical tensions, such as the European Union's General Data Protection Regulation (GDPR) and China's Cybersecurity Law requiring data storage within national borders.^[144]^[145]^[146] Theoretical frameworks, such as Vladimir Lenin's 1917 Imperialism, the Highest Stage of Capitalism, describe imperialism as monopoly capitalism's final phase, characterized by finance capital's export, colonial division of the world, and inevitable territorial rivalries leading to war.^[147]

Narrative Expansion

Narrative expansion refers to the process of extending a story's universe through sequels, prequels, spin-offs, or supplementary materials such as detailed backstories, thereby deepening reader immersion and enriching the fictional world.^[148] This technique allows creators to explore additional facets of characters, settings, and lore beyond the original narrative, fostering a broader engagement with the audience.^[149] Key techniques in narrative expansion include foreshadowing elements that hint at future developments and meticulous world-building through lore, as exemplified by J.R.R. Tolkien's appendices in The Lord of the Rings, which provide extensive historical, linguistic, and genealogical details for Middle-earth.^[150] These appendices not only contextualize the primary plot but also invite readers to inhabit a fully realized secondary world, influencing subsequent fantasy expansions.^[151] Prominent examples include J.K. Rowling's Harry Potter series, expanded via the *Fantastic Beasts* film series, which delves into the wizarding world's prequel era and introduces new characters like Newt Scamander to explore global magical history.^[152] Unofficial expansions, such as fanfiction, further proliferate these universes by allowing fans to create derivative stories that fill gaps or extend arcs, often gaining cultural significance within literary communities.^[153] In literary theory, narrative expansion aligns with extensions of Joseph Campbell's monomyth, or hero's journey, where protagonists' arcs cycle across multiple installments, as seen in serialized novels by Charles Dickens, whose works like The Pickwick Papers unfolded in monthly parts, building ongoing narratives responsive to reader feedback.^[154] This serialization pioneered expansive storytelling, layering social commentary and character development over time.^[155] Modern applications encompass transmedia storytelling, where narratives migrate from books to games, as theorized by Henry Jenkins, enabling dispersed yet interconnected experiences that reward multi-platform engagement.^[156] By 2025, AI-assisted tools like those in AI Dungeon facilitate interactive fiction expansions, generating dynamic plot branches and character dialogues in real-time to personalize narrative growth.^[157] Challenges in narrative expansion include maintaining consistency across extensions to avoid plot holes, where logical discrepancies undermine immersion, requiring rigorous outlining and revision.^[158] Scholarly coverage of such techniques remains incomplete for non-Western traditions, such as epic sagas in African oral literature, where performers dynamically expand tales like the Ozidi Saga through improvisation, yet documentation often overlooks regional variations due to the ephemeral nature of oral transmission.^[159]^[160]

References

[1]
EXPANSION | definition in the Cambridge English Dictionary
an increase in the size, number, or importance of something: a rapid/major/massive expansion, the rapid expansion of the software industry.
[2]
EXPANSION Definition & Meaning - Dictionary.com
An increase in the volume of a substance while its mass remains the same. Expansion is usually due to heating. · A number or other mathematical expression ...<|control11|><|separator|>
[3]
8.8: The Binomial Expansion - Mathematics LibreTexts
May 23, 2024 · The binomial expansion is a special series expansion used to approximate expressions of the form ( a + b ) p for b ≪ a , or ( 1 + x ) p for | x ...General Binomial Expansion · Example 8 . 8 . 1 · Example 8 . 8 . 2 : Time...
[4]
Thermal Expansion of Solids and Liquids | Physics - Lumen Learning
Thermal expansion is the change in size or volume of a mass with temperature. It occurs in solids, liquids, and gases, and is related to temperature change.
[5]
13.3: The Universe is Expanding - Physics LibreTexts
Apr 13, 2023 · In the Universe, the internal forces in galaxies, stars, people, and other objects overwhelm the expansion locally, so they remain the same size ...
[6]
What is Dark Energy? Inside Our Accelerating, Expanding Universe
Nine billion years after the universe began, its expansion started to speed up, driven by an unknown force that scientists have named dark energy.
[7]
Expansion: Definition in Economics, Length, and Indicators
Expansion is the phase of the business cycle where real gross domestic product (real GDP) grows for two or more consecutive quarters, moving from a trough to a ...
[8]
Annexation and Expansion | Encyclopedia.com
Historians often categorize American expansionism during the period between 1870 and 1920 into two sections: westward acquisition before 1898 and overseas ...
[9]
Fundamentals of Thermal Expansion and Thermal Contraction - PMC
When the temperature is increased, the kinetic energy of atoms increases, and the atoms vibrate and move, resulting in a greater average separation of atoms and ...
[10]
Thermal Expansion
The coefficient of linear thermal expansion of a solid is defined where $\langle x\rangle$ is the mean distance between nearest neighbor atoms.Missing: formula spacing<|separator|>
[11]
Linear Thermal Expansion Coefficients of Materials
Linear thermal expansion coefficients of common materials, including metals, plastics, and composites. When an object is heated or cooled, its length change.
[12]
Bimetallic Strips - The Engineering ToolBox
Bi-metallic strips are subject to bending due to heat - and can be used to convert change in temperature to mechanical displacement.
[13]
[PDF] mechanical properties of metals and alloys
... thermal expansion by P. Hidnert, and the portionon ... engineering materials but contains data on the properties of many materials not usually classed as.<|separator|>
[14]
Why Railroads Don't Need Expansion Joints - Practical Engineering
Dec 5, 2023 · Structures like bridges with expansion joints and jointed rail are designed to allow unrestricted thermal expansion. When the hot day comes ...
[15]
(PDF) Negative thermal expansion from 0.3 to 1050 K in zirconium ...
Aug 6, 2025 · PDF | On Aug 1, 1996, J. S. O. Evans and others published Negative thermal expansion from 0.3 to 1050 K in zirconium tungstate, ...
[16]
Expansion of the Universe | CK-12 Foundation
The universe expands as space stretches, causing galaxies to move away from us, with the farther away galaxies moving faster, as shown by redshift.
[17]
Cosmological Redshift | COSMOS
Cosmological redshift is the shift of spectral lines to longer wavelengths due to the expansion of the Universe, lengthening the emitted radiation's wavelength.<|separator|>
[18]
ESA - What is 'red shift'? - European Space Agency
Red shift is when light's wavelength stretches, shifting it towards red. This occurs when light from moving sources, like galaxies, is shifted to longer ...
[19]
Hubble's diagram and cosmic expansion - PNAS
In 1917, Einstein had shown how to construct a universe that was static by introducing a “cosmological constant” into his equations. This matched well with the ...Missing: milestones | Show results with:milestones
[20]
This Month in Physics History | American Physical Society
With two discoveries, announced in January 1925 and January 1929, astronomer Edwin Hubble radically changed our idea of the cosmos.
[21]
Webb telescope's largest study of universe expansion confirms ...
Dec 9, 2024 · All galaxies observed by Webb together with their supernovae yielded a Hubble constant of 72.6 km/s/Mpc, nearly identical to the value of 72.8 ...
[22]
[PDF] Cosmological Principle and Dynamics - MIT OpenCourseWare
Dynamics of cosmological expansion: Hubble's law implies cosmological expansion. General relativity allows a detailed derivation.
[23]
Clearest images yet of 380,000-year-old baby universe released
Mar 19, 2025 · The new data confirm that the age of the universe is 13.8 billion years, with an uncertainty of only 0.1%. “The results set the stage for our ...
[24]
The CMB: how an accidental discovery became the key to ...
Jul 24, 2015 · In July 1965, Arno Penzias and Robert Wilson made a discovery that would cement our understanding of how the universe came into being.
[25]
The 2011 Nobel Prize in Physics - Press release - NobelPrize.org
Oct 4, 2011 · They have studied several dozen exploding stars, called supernovae, and discovered that the Universe is expanding at an ever-accelerating rate.
[26]
Webb telescope helps refine Hubble constant, suggesting resolution ...
May 27, 2025 · Scientists have made a new calculation of the speed at which the universe is expanding, using the data taken by the powerful new James Webb Space Telescope on ...
[27]
The Big Freeze: How the universe will die - Astronomy Magazine
Sep 5, 2023 · The universe's expansion is accelerating due to dark energy. · Star formation will eventually cease. · Black holes will be the last remaining ...
[28]
Series Expansion -- from Wolfram MathWorld
A series expansion is a representation of a particular function as a sum of powers in one of its variables, or by a sum of powers of another (usually ...
[29]
Taylor Series -- from Wolfram MathWorld
A Taylor series is a series expansion of a function about a point. A one-dimensional Taylor series is an expansion of a real function f(x) about a point x=a.
[30]
https://mathworld.wolfram.com/TaylorSeries.html
[31]
Taylor's Theorem -- from Wolfram MathWorld
Taylor's theorem states that any function satisfying certain conditions may be represented by a Taylor series.
[32]
Fourier Series -- from Wolfram MathWorld
A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality ...Missing: signal | Show results with:signal
[33]
Stirling's Series -- from Wolfram MathWorld
The expansion of lnGamma(z) is what is usually called Stirling's series. It is given by the simple analytic expression (OEIS A046968 and A046969), where B_n is ...
[34]
Brook Taylor (1685 - 1731) - Biography - University of St Andrews
Brook Taylor was an English mathematician who added to mathematics a new branch now called the 'calculus of finite differences', invented integration by parts, ...Missing: Joseph Fourier 1822<|separator|>
[35]
Joseph Fourier (1768 - 1830) - Biography - MacTutor Index
Joseph Fourier studied the mathematical theory of heat conduction. He established the partial differential equation governing heat diffusion and solved it by ...
[36]
[PDF] An Approximation Theory Perspective on Machine Learning - arXiv
Jun 6, 2025 · We will discuss emerg- ing trends in machine learning including the role of shallow/deep networks, approximation on manifolds, physics-informed ...
[37]
About Expansion Joints - EJMA
Expansion joints provide an excellent solution for isolation of settlement, seismic deflection, mechanical vibration and sound attenuation transmission.
[38]
Expansion Joints | Ohio Department of Transportation
Jul 16, 2021 · Expansion joints allow the bridge to expand and contract with temperature changes and to allow for rotation of the beam ends as the beams deflect under traffic ...
[39]
What are the different types of expansion joints? - US Bellows
The primary categories are metallic, fabric, and rubber, each offering unique benefits and being suited for different operating conditions. These components ...
[40]
What are the Different Types of Expansion Joints? - ADSCO
Slip-Type Expansion Joints · Bellows-Type Expansion Joints · Gimbal Expansion Joints · Rubber Expansion Joints · ADSCO: Designing Expansion Joints for Industries ...Slip-Type Expansion Joints · Bellows-Type Expansion... · Rubber Expansion Joints
[41]
[PDF] Expansion Joints in Buildings: Technical Report No. 65 - Vulcraft
THE DESIGN OF EXPANSION JOINTS. The following principles are considered basic to sound expansion joint design. 1. The width of the expansion joint should ...Missing: finite | Show results with:finite
[42]
Design verification of expansion joints using finite element
Jul 18, 2002 · The objective of this project is to implement finite element as a design tool to aid the design and analysis of the expansion joints. An ...Missing: principles ΔT α
[43]
The Ultimate Guide to Understand Expansion Joints Types
Apr 8, 2019 · Expansion joints can be used in parking garages, overpasses, roadways, sidewalks, piping structures and railway tracks. There are many types ...
[44]
Withstand the Pressure with Expansion Joints - Badger Industries
Nov 5, 2015 · High-pressure expansion joints are often used in applications such as pipelines, which are under high pressure to maintain desired fluid flow ...
[45]
AASHTO Publishes New Small Bridge Expansion Joints Guide
May 21, 2021 · This new publication provides bridge maintenance practitioners with detailed procedures for replacing, repairing, and maintaining Small Movement Expansion ...
[46]
https://www.badgerind.com/Blog-Item-Withstand-the-Pressure-with-Expansion-Joints
[47]
Analysis and design guidance for the lateral stiffness of bellows ...
The cause of the explosion was traced back to failure of a bellows expansion joint that suffered from a combination of squirming and jack-knifing of pipe joints ...
[48]
Bridge Expansion Joints Market Size & Forecast 2025 to 2035
Apr 2, 2025 · Their latest innovations include smart monitoring systems integrated into expansion joints to track real-time stress and movement data.
[49]
Impact of climate change on the integrity of the superstructure ... - NIH
Oct 23, 2019 · In this study, we attempt to quantify the effect of clogged joints and climate change on failure of the superstructure of a class of steel bridges around the ...
[50]
8 Growth Strategies for the Modern Business Landscape - Terakeet
Nov 3, 2023 · Organic growth means expanding naturally through internal efforts, like increasing sales, launching new products, or entering new markets, ...
[51]
https://pmc.ncbi.nlm.nih.gov/articles/PMC6808546/
[52]
Internal and External Growth Strategies - Business-to-you.com
Jan 19, 2017 · The Ansoff Matrix (also known as the Product/Market Expansion Grid) allows managers to quickly summarize these potential growth strategies and ...External Growth · Mergers And Acquisitions · Strategic Alliances<|separator|>
[53]
Ansoff Matrix - Overview, Strategies and Practical Examples
The Ansoff Matrix, also called the Product/Market Expansion Grid, is a tool used by firms to analyze and plan their strategies for growth. The matrix shows.Market Penetration · Market Development · DiversificationMissing: organic inorganic
[54]
The Ansoff Matrix: A Powerful Tool for Business Strategy and Growth
May 10, 2024 · The Ansoff Matrix is a powerful strategy framework used by business leaders to evaluate risks and opportunities for driving business growth.Missing: organic inorganic
[55]
15 examples of Revenue Growth metrics and KPIs - Tability
1. Revenue Growth Rate. The percentage increase in revenue over a specific period, indicating business expansion. · 2. Customer Acquisition Cost (CAC) · 3.
[56]
Key Performance Indicators (KPIs) That Drive Business Transformation
Feb 24, 2025 · It measures the increase in sales or turnover over a specific period and provides insight into the company's ability to grow its market share, ...<|separator|>
[57]
30 Financial Metrics and KPIs to Measure Success in 2025 - NetSuite
May 5, 2025 · These 30 financial KPIs provide actionable information you can use to boost performance by measuring profitability, liquidity, risk and ...Missing: expansion | Show results with:expansion
[58]
Removing Barriers to Small Business Capital Formation and ...
Feb 4, 2025 · Congress can take action to support small business growth and individual investor opportunity by creating an exemption for micro offers of equity securities.
[59]
Regulatory Issues & Challenges Facing Businesses in 2025 - Paychex
Dec 10, 2024 · The new year's most notable regulatory and legislative challenges are tax policy and taxes, retirement, artificial intelligence and privacy, paid leave, and ...Missing: expansion capital
[60]
Amazon marketing strategy business case study | Smart Insights
Feb 27, 2023 · Our business case study explores Amazon's revenue model and culture of customer metrics, history of Amazon.com and marketing objectives.
[61]
Assembly Line Revolution | Articles - Ford Motor Company
Sep 3, 2020 · Discover the 1913 breakthrough: Ford's assembly line reduces costs, increases wages and puts cars in reach of the masses.
[62]
[PDF] Top Cleantech Trends for 2025 - S&P Global
In 2025, clean energy technology is set to surpass investments in upstream oil and gas for the first time. Solar PV will account for half of all cleantech ...
[63]
Q1 2025 Carbon Transition & Sustainability Trends - J.P. Morgan
What's on deck for 2025? Our experts share the trends in renewable energy, sustainable finance and climate tech they'll be tracking this year.Where is sustainability headed... · Employee spotlight · Client highlights · Insights
[64]
WeWork losses doubled as it opened offices ahead of failed IPO
Nov 13, 2019 · WeWork losses doubled as it rushed to open new offices ahead of its failed IPO ... WeWork opened almost 100 offices between the end of June and ...Missing: overexpansion | Show results with:overexpansion
[65]
WeWork's Rise To $47 Billion—And Fall To Bankruptcy: A Timeline
Nov 7, 2023 · $47 billion. That was WeWork's peak private valuation in January 2019 before its failed IPO. Forbes Valuation. We estimate Neumann to be worth ...
[66]
The Rise and Fall of WeWork: From $47 Billion to Zero
May 31, 2025 · WeWork's collapse sent ripples across the startup industry. For ... Overexpansion - WeWork opened hundreds of locations without proven demand.
[67]
Business Cycle Dating | NBER
The chronology identifies the months of peaks and troughs of economic activity. Expansions are the periods between a trough and a peak; recessions are the ...Contractions in economic activity · Frequently Asked Questions · Announcements
[68]
Introduction to U.S. Economy: The Business Cycle and Growth
Oct 3, 2024 · Business cycles are dated according to the peaks and troughs of economic activity. A single business cycle is dated from peak to peak or trough ...
[69]
Business Cycle Dating Procedure: Frequently Asked Questions
The NBER business-cycle chronology considers economic activity, which grows along an upward trend. As a result, the unemployment rate sometimes rises before the ...
[70]
Fiscal Policy: Economic Effects | Congress.gov
Jan 21, 2021 · To engage in fiscal stimulus by either increasing spending or decreasing tax revenue, the government must increase the size of its deficit and ...
[71]
Effects of Innovation on Fiscal Policies and Economic Growth
Nov 28, 2022 · There is a positive relationship between economic growth and innovation according to an IMF study. So driving innovation offers a way forward in some countries.
[72]
How does the multiplier effect influence fiscal policy?
Apr 24, 2018 · The fiscal multiplier effect occurs when an initial injection into the economy causes a bigger final increase in national income.
[73]
US Business Cycle Expansions and Contractions | NBER
contractions in economic activity — start in the month after a peak in the business cycle, and end in the month of the trough.
[74]
The Post World War II Boom: How America Got Into Gear - History.com
May 14, 2020 · After years of wartime rationing, American consumers were ready to spend money—and factories made the switch from war to peacetime production.
[75]
[PDF] Becoming a High-Income Economy in a Generation - The World Bank
Trade Policy, 2023 aims to increase India's exports to USD 2 trillion by 2030 ... “One polity, many countries: economic growth in India, 1873-2000. Search of ...
[76]
Speech by Governor Cook on productivity dynamics - Federal ...
May 9, 2025 · The second ongoing economic development I see altering productivity is the rapidly expanding use of AI. I view this emerging technology as ...
[77]
Keynesian Economics - Econlib
Keynesian economics is a theory of total spending in the economy (called aggregate demand) and its effects on output and inflation. Although the term has ...<|control11|><|separator|>
[78]
[PDF] Real Business Cycles: A New Keynesian Perspective
Keynesian theory explains the reduction in welfare by a failure in economic coordination: because wages and prices do not adjust instantaneously to equate ...Missing: expansion | Show results with:expansion
[79]
EXPANSION TEAM Definition & Meaning - Dictionary.com
a new team in a league, composed largely of players from established league teams and formed when the league expands its membership.
[80]
How league expansion is unlocking growth opportunities in sports
League expansion in sports can offer a unique opportunity for growth and monetization. By tapping into new markets, both domestically and internationally, ...
[81]
Relocation fees to cost Rams, Chargers $645M, Raiders $378M
Jul 12, 2017 · The Rams and the Chargers will each pay $645 million beginning in December 2019 and ending in December 2028.Missing: expansion 2020s
[82]
Everything you need to know about expansion drafts - The GIST
Dec 8, 2024 · An expansion draft involves a team's front office hand-selecting players to join their roster. Here are some expansion draft basics.
[83]
A look back at MLB Expansion Draft history
Dec 13, 2023 · The first one was held on Dec. 14, 1960, when the Los Angeles Angels and the Washington Senators (now the Texas Rangers) made their picks before ...
[84]
How Many NBA Teams Are There? A Brief History of Expansion and ...
Jul 16, 2025 · The 1980s and '90s saw the addition of seven new teams. The '80s saw the rise of Magic Johnson in Los Angeles and Larry Bird in Boston, which ...
[85]
This Week in History: NBA adds four teams - Sports Business Journal
Nov 4, 2024 · November 4, 1987 -- The NBA announces four new franchises: Charlotte and Miami for the 1988 season and Minneapolis and Orlando for the 1989 ...
[86]
NBA expansion hasn't happened for 20 years, so what does the ...
Nov 4, 2024 · Expansion teams start as blank slates. The majority of their rosters come through a process called the expansion draft. In this exercise, teams ...
[87]
Las Vegas: From Sin City to Sports City - TicketManager
Nov 28, 2023 · In just their first season, the Golden Knights ranked in the league's top 10 in total revenue and raked in over $90 million in sponsorship ...
[88]
The Benefits and Challenges of Developing Sports and ... - NAIOP
This involves monitoring city council agendas, sports franchise relocation rumors and economic development incentives.
[89]
The Pros and Cons of MLS Expansion - The Georgetown Voice
Sep 27, 2017 · However, expansion also has its downsides. The first of these is the dreaded Expansion Draft, in which expansion teams are allowed to select ...Missing: advantages | Show results with:advantages
[90]
Expansion News | MLSSoccer.com
Right to Dream finds "natural spot" with MLS expansion to San Diego ... MLS San Diego aims to "build something special" before 2025 launch. Columnist ...
[91]
https://georgetownvoice.com/2017/09/27/the-pros-and-cons-of-mls-expansion/
[92]
WNBA Players Getting Share of Expansion Fees Would Be Unique
Jul 18, 2025 · The NBA, NFL and NHL all exclude expansion fees in their CBAs when calculating revenue that shape their payroll ranges.
[93]
Structuring Considerations for Start-Up Sports Leagues - Akin Gump
Dec 11, 2024 · Strategic Expansion and Team Placement: Teams can be placed in markets that best support the league's growth objectives, rather than where ...
[94]
Valuations of Sports Teams on the Rise: A Tale of Two Continents
Oct 9, 2023 · Each team has exclusive rights in a territory, and new teams are added to new territories as part of the “expansion” of the league. The ...
[95]
NFL International Games
The official source for NFL news, video highlights, fantasy football, game-day coverage, schedules, stats, scores and more.NFL announces schedule for... · Miami Dolphins announced as...Missing: expansion | Show results with:expansion
[96]
From six teams to 31: History of NHL expansion
Jun 22, 2016 · 1967: The NHL adds six teams, the largest expansion in professional sports history. The addition of the California Seals (later renamed the ...
[97]
Premier League TV and commercial revenue up 17% to UK£12.25 ...
Nov 22, 2024 · The Premier League's global and domestic commercial and broadcast revenue has gone up by 17 per cent to UK£12.25 billion (US$15.3 billion) for the 2025 to 2028 ...
[98]
Structure of Sports Leagues Flashcards | Quizlet
Travel costs increase with size of team -Venue Venue ... •American professional leagues set extremely high expansion fees for teams looking to enter • ...
[99]
15 U.S. Code § 1291 - Exemption from antitrust laws of agreements ...
15 U.S. Code § 1291 exempts agreements for telecasting rights of sports leagues and combining football leagues if it increases the number of clubs.
[100]
Top esports trends for 2025 | GWI
Key esports trends driving the 2025 landscape · Mainstream integration with traditional sports · Mobile-first viewership is now the norm · Women are claiming their ...Missing: expansions metaverse
[101]
A Brief History of MLB's Expansion and How It Got to 30 Teams
Apr 6, 2025 · Things started rather quickly with two teams, the Los Angeles Angels and the Washington Senators, joining in 1961. A year later, the Houston ...
[102]
How big is the carbon footprint of football? | SGR
Feb 3, 2025 · The carbon footprint of football is estimated at 64-66 million tonnes of CO2e, with 75% from sponsorship deals. A World Cup match can emit 44, ...
[103]
Expansions - Lonnie Liston Smith, Lonnie Listo... - AllMusic
Rating 8.6/10 (170) Expansions by Lonnie Liston Smith, Lonnie Liston Smith & the Cosmic Echoes released in 1974. Find album reviews, track lists, credits, awards and m...
[104]
Listening session deep dive: Lonnie Liston Smith's 'Expansions'
Oct 2, 2023 · Dismissed for its over reliance on chops and musicianship at the expense of emotiveness and nuance, mid-1970s fusion mixed funk, jazz, rock, ...
[105]
'I'm cosmic': Lonnie Liston Smith experiences a revival of interest in ...
Jul 5, 2023 · It's called Jazz is Dead 17 and it's the brainchild of Ali Shaheed Muhammad and Adrian Younge, who convinced Lonnie to create some new music.
[106]
A Beginner's Guide to Developing Raga Alaap | Artium Academy
Sep 8, 2025 · How to Make Raga Phrases? Raga phrases are short melodic motifs or patterns that define the character of a raga in Indian classical music.Table Of Contents · 1) Raga Knowledge · 5) PakadMissing: growth | Show results with:growth
[107]
The Witcher 3: Wild Hunt - Blood and Wine Review - IGN
Rating 9/10 · Review by Leif JohnsonMay 25, 2016 · The expansion also brings some welcome gameplay enhancements, including mutations, the ability to dye armor, and a vineyard for growing herbs.
[108]
The Witcher 3: Wild Hunt – Blood and Wine - Xbox
In stock 6–7 day deliveryBlood and Wine offers over 20 hours of adventure, where beauty clashes with horror, and love dances with deceit. IMPORTANT NOTICE The Blood and Wine Expansion ...
[109]
DLCs, Expansions and Sequels: How developers decide to build on ...
Mar 6, 2024 · DLC is essentially any additional content that gets added to the game. This can be new maps, outfits, weapons... Expansions are larger, usually in scope.
[110]
What is DLC? Its History and Implementation Considerations
DLC, or downloadable content, is digital content that game developers release on top of their base games, including levels, skins, and items.
[111]
From Expansion Packs to DLC: The Evolution of Additional Video ...
Oct 2, 2016 · Downloadable content – or DLC – has become a mainstay in the video game industry. Now, every high profile game is expected to have additional content roll out.<|separator|>
[112]
World of Warcraft: Dragonflight Now Live! - Blizzard Entertainment
Nov 28, 2022 · Dragonflight introduces the Dracthyr Evoker, new talents, updated professions, and a new UI. The Dragon Isles are awakening, and the pre-season ...
[113]
World of Warcraft: Dragonflight Expansion Overview - Wowhead
Mar 19, 2025 · WoW's ninth expansion features Dracthyr Evokers - a new flying-based movement system in Dragonriding, a HUD, professions, and talents revamp, and 5 new zones.Dragonflight Pre-Orders · Dragonflight Lore · Dragonflight Zones
[114]
From extra content to extra revenue: DLC works best for strategy ...
Jun 12, 2023 · Successful DLC prolongs a game's lifespan and generates additional revenue beyond the initial release. Newzoo analyzed over 1,600 DLC ...
[115]
Destiny 2 dev admits it 'made mistakes' with Curse of Osiris paywall
Dec 12, 2017 · Destiny 2 developer Bungie caused some controversy when it locked base game activities behind DLC. It's now aiming to fix these problems in ...
[116]
Rise of DLCs: How In-Game Purchases Revolutionized Gaming
Sep 10, 2023 · DLCs and in-game purchases shifted the industry to a more sustainable model, extended game lifespans, and provided ongoing revenue streams.
[117]
Video Game Trends of 2025 - License Global
Gaming as a Fully Immersive Experience By 2025, AR and VR technologies will be further integrated into gaming, blurring the lines between digital and physical ...Video Game Trends Of 2025 · At A Glance · Gaming As A Fully Immersive...
[118]
https://premortem.games/2023/06/12/from-extra-content-to-extra-revenue-dlc-works-best-for-strategy-games/
[119]
Downfall - A Slay the Spire Fan Expansion on Steam
Rating 10/10 (2,041) A FREE complete expansion for Slay the Spire, made by the modding community. Features one brand new normal character, plus a new game mode with SEVEN fully ...
[120]
Game Designer Explains: How DLC gets Made - YouTube
Oct 15, 2025 · 0:00 - Introduction ; 1:22 - Prototypes, Pre-Production & Publishers ; 5:02 - The Production Process ; 8:02 - Public vs Internal Release Dates ; 10: ...Missing: expansions | Show results with:expansions
[121]
The DLC Transition and Expanding the Expansion Pack
The lines between expansion packs and DLC have blurred in the digital era and today's post examines how DLC has overtaken expansion packs and what this means ...
[122]
The Expanse (TV Series 2015–2022) - IMDb
Rating 8.5/10 (187,264) Reviewers say 'The Expanse' is acclaimed for its intricate world-building, realistic space travel, and complex political intrigue. The series is celebrated for ...Full cast & crew · Episode list · Parents guide · Season 6 Official Trailer
[123]
Expansion - IMDb
Expansion. FrenchSci-Fi. What are these huge forms suddenly appearing in the sky? Why did the children-monks of the community begin to be moved? Rumors of ...
[124]
Upcoming sci-fi TV shows for 2025/2026: Fallout S2, Star Trek - Space
Oct 27, 2025 · Pluribus; Stranger Things (Season 5); Fallout (Season 2); Star Trek: Starfleet Academy; Wonder Man; Daredevil: Born Again (Season 2); 3 Body ...
[125]
[PDF] Fan Films and Fanworks in the Age of Social Media
As illustrated by this fan's comments, fans are important in extending the life of television shows and movies because they allow the works to flourish even ...
[126]
[PDF] Revisiting Insularity and Expansion: A Theory Note - cissm | umd
3 We define expansion, in turn, as the extension of a state's territorial control or political influence (Gilpin 1981, 106). 2 Perspectives on Politics.
[127]
Definitions | GEOG 128: Geography of International Affairs
Frontiers: the process of territorial expansion in what is deemed (usually falsely) as “empty” areas, e.g., the American Frontier. Watch. Watch Boundaries ...
[128]
Louisiana Purchase, 1803 - Office of the Historian
The Louisiana Purchase encompassed 530,000,000 acres of territory in North America that the United States purchased from France in 1803 for $15 million.
[129]
Era of U.S. Continental Expansion | US House of Representatives
President Thomas Jefferson spearheaded westward expansion when the United States acquired the Louisiana territory from France in 1803.
[130]
The Roman Republic (article) | Rise of Rome - Khan Academy
Rome became the most powerful state in the world by the first century BCE through a combination of military power, political flexibility, economic expansion, ...
[131]
Territorial Expansion and the Roman Empire - jstor
Rome was the first and only polity to control the Mediterranean and its littoral. That unified control lasted for some 500 years.Missing: 1st primary
[132]
[PDF] The Partitioning of Africa - African Economic History Network
During the first phase of the colonial period, between roughly 1880 and 1914, the African continent was partitioned into more than 50 colonies.
[133]
Terra Nullius | Rule of Law Education Centre
' In legal jargon, terra nullius means 'land over which no previous sovereignty has been exercised.' It wasn't until the late 20th century that the term terra ...
[134]
The Doctrine of Occupation through “Terra Nullius” as a Right of Self ...
Under international law, the doctrine of terra nullius has two components. First, it facilitates the occupation of an empty territory; second, it asserts ...
[135]
Colonialism facts and information | National Geographic
Feb 2, 2019 · Colonialism's impacts include environmental degradation, the spread of disease, economic instability, ethnic rivalries, and human rights ...When Did Colonialism Start? · Subjugation And Revolutions · Colonial Rationale And...<|separator|>
[136]
Decolonization of Asia and Africa, 1945–1960 - Office of the Historian
Between 1945 and 1960, three dozen new states in Asia and Africa achieved autonomy or outright independence from their European colonial rulers.
[137]
[PDF] Political Changes That Led To Territorial Changes
Economic Interests: Control over resources and strategic trade routes can motivate political actors to pursue territorial expansion or realignment. Geopolitical ...
[138]
Artemis Accords - United States Department of State
Artemis Accords signatories as of May 2025: Angola, Argentina, Armenia, Australia, Austria, Bahrain, Bangladesh, Belgium, Brazil, Bulgaria, Canada, Chile ...Missing: territorial | Show results with:territorial
[139]
https://www.scirp.org/journal/paperinformation?paperid=115887
[140]
[PDF] Imperialism, the Highest Stage of Capitalism A Popular Outline
We see the rapid expansion of a close network of channels which cover the whole country, centralising all capital and all revenues, transforming thousands and ...
[141]
Expanded Universe: Definition and How to Create One
May 16, 2023 · An expanded universe refers to a vast collection of narratives set within the same fictional universe. These narratives are often interconnected.
[142]
Fictional universe - (Intro to Creative Writing) - Fiveable
Many successful franchises expand their fictional universes through sequels, spin-offs, or adaptations across different media, enhancing the depth and richness ...
[143]
[PDF] Building Middle-earth: an Exploration into the uses of Architecture in ...
The Hobbit and The Lord of the Rings (abbreviated to TH and LotR) are the primary texts used to locate this exploration of architecture in Tolkien's fantasy.
[144]
World-building in J. R. R. Tolkien's Works (edited by Dimitra Fimi ...
The collection aims to deepen discussions around Tolkien's legacy and contributions to the genre, although it leans heavily towards author-centric analysis and ...
[145]
Harry Potter and Fantastic Beasts Books - Wizarding World
Looking for Wizarding World? HarryPotter.com is the official home of Harry Potter, Fantastic Beasts, and the Wizarding World, formerly known as Pottermore.
[146]
[PDF] Fanfiction As: Searching for Significance in the Academic Realm
To give a broad definition, fanfiction is a work of fiction written by a fan that uses the characters, storyworld, or plot of an already existing form of media ...
[147]
Joseph Campbell and the Hero's Journey
One of Joseph Campbell's most well-known ideas is the hero's journey. Discover the origins of this powerful motif and how it still applies today.
[148]
[PDF] Dickens's Serial Novels and Victorian Literary Fandom
Nov 29, 2012 · In this thesis, I demonstrate that publishing novels in serial, over the course of many months, resulted in a mutually beneficial relationship ...
[149]
Transmedia Storytelling 101 — Pop Junctions
Mar 21, 2007 · Transmedia storytelling expands what can be known about a particular fictional world while dispersing that information, insuring that no one consumer knows ...Missing: themes | Show results with:themes
[150]
The Best AI Story Generators in 2025 - Storial
Aug 25, 2025 · AI Dungeon transforms storytelling into an interactive gaming experience, offering unlimited narrative possibilities through real-time AI ...
[151]
How to Fix Plot Holes in Your Story - 2025 - MasterClass
Dec 7, 2021 · Plot holes are inconsistencies or gaps in the storyline or character development. They are formed when a narrative stops following its own logic ...
[152]
African Oral Literature and the Humanities: Challenges and Prospects
This paper examines the origin, evolution and emergence of folklore (oral literature) as an academic discipline in Africa and its place in the humanities.Missing: expansion | Show results with:expansion
[153]
[PDF] Performance and Plot in The Ozidi Saga - Oral Tradition Journal
The Ozidi Saga1 tells the story of a culture hero (Ozidi) of the Ijo of the Niger Delta in southern Nigeria. In the traditional context in which the.