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Beta

Beta (uppercase Β, lowercase β; Ancient Greek: Βῆτα, romanized: Bêta) is the second letter of the Greek alphabet.^[1] In the system of Greek numerals, it has a numerical value of 2.^[1] Derived from the Phoenician letter Beth (𐤁), which depicted a house and represented the consonant /b/, beta adopted the name from its Phoenician predecessor around the 8th century BCE during the adaptation of the Phoenician script into the Greek alphabet.^[2]^[3] In Ancient Greek, beta denoted the voiced bilabial plosive /b/, but by the Byzantine era, its pronunciation shifted to the voiced labiodental fricative /v/, a change reflected in Modern Greek where it is called víta and pronounced accordingly.^[4]^[5] The letter's forms have remained stable, with the uppercase Β resembling a rightward-facing rounded rectangle and the lowercase β featuring a distinctive loop, influencing its widespread use in mathematics (e.g., beta function, beta distribution), physics (e.g., beta decay), and other sciences.^[1]^[6]

Etymology and Historical Development

Phoenician Origins and Early Forms

The Phoenician letter bet (𐤁), the direct precursor to the Greek beta, derives its name from the Semitic term bēt or bayt, signifying "house," with its glyph originally depicting a rudimentary floor plan or tent outline representing this concept.^[7] This acrophonic principle linked the letter's sound to the initial phoneme of the word, assigning bet the value of the voiced bilabial plosive /b/.^[7] In proto-Canaanite scripts, dated to approximately the 15th to 11th centuries BCE, bet appeared in more pictographic iterations, often resembling a squared or angular house shape derived from Egyptian hieroglyphic influences but adapted for Semitic phonology.^[8] By the standardization of the Phoenician alphabet around 1050 BCE, the form had simplified into a linear, two-lobed structure—typically an open square with a horizontal bar—facilitating chisel inscription on durable surfaces like stone and facilitating trade across the Mediterranean.^[9] Archaeological attestation of Phoenician bet emerges in inscriptions from Byblos, Lebanon, with the Ahiram sarcophagus providing one of the earliest examples around 1000 BCE, where the letter exhibits its canonical early form amid royal epitaphs.^[10] These artifacts confirm the script's role in administrative and funerary contexts, underscoring bet's consistency as the second consonant in the 22-letter abjad.^[11]

Adoption and Evolution in the Greek Alphabet

The Greek alphabet, including the letter beta (Β), emerged through adaptation of Phoenician script forms in the 8th century BCE, with beta assigned to represent the voiced bilabial plosive /b/, a sound absent in Phoenician but needed for Greek phonology.^[12] Early adoption is attested in inscriptions from sites like Pithekoussai and Athens, where beta appears in rudimentary alphabetic sequences. The Dipylon oinochoe from the Athenian Dipylon cemetery, dated to circa 740 BCE, provides one of the earliest substantial examples of Greek writing, incorporating beta amid hexametric verse praising a cup-bearer.^[13] In Archaic Greek epichoric alphabets (c. 8th–6th centuries BCE), beta's graphical form exhibited regional variation, ranging from angular, three-barred structures in Euboean and Attic scripts to more closed, looped variants in Corinthian and other dialects, reflecting local scribal preferences and inscription media like pottery and stone.^[14] Standardization occurred with the adoption of the Ionic alphabet in Athens by official decree in 403 BCE, yielding a more consistent, often squared or semicircular majuscule Β suited to monumental epigraphy.^[15] During the Hellenistic and Roman eras, beta's form evolved in response to writing materials and scripts; uncial hands on papyrus (c. 4th–9th centuries CE) introduced rounded, cursive contours for efficiency, while Byzantine minuscule scripts (post-9th century CE) developed compact variants with a vertical stem and descending rightward curve or loop, precursors to modern lowercase β. This graphical progression paralleled broader script transitions from lapidary rigidity to fluid bookhand.^[16] Phonetically, beta retained /b/ through Classical Greek but underwent fricativization amid Koine sound changes, shifting to a labiodental approximant or fricative /v/ or /β/ by late antiquity, with linguistic evidence pinpointing the transition between the 2nd and 5th centuries CE, fully entrenched in Medieval Greek.^[17] This evolution, distinct from vowel mergers like itacism, stemmed from intervocalic weakening of stops, influencing beta's role without altering its positional stability in the alphabet.^[18]

Linguistic and Phonetic Applications

Role and Pronunciation in Greek

Beta (uppercase Β, lowercase β) is the second letter of the Greek alphabet, following alpha and preceding gamma. In the ancient Greek system of isopsephy, a form of gematria assigning numerical values to letters, beta corresponds to the value 2, used for calculations involving words or names by summing their letter values.^[19] In ancient Greek, including the dialect of the Homeric epics composed circa 750–650 BCE, beta denoted a voiced bilabial stop, akin to the "b" in "boy." This pronunciation appears in textual representations of sounds, such as the onomatopoeic βῆ βῆ for a lamb's bleat in classical comedic texts reflecting earlier oral traditions.^[20]^[21] By the medieval Byzantine era, the sound underwent a shift known as betacism, evolving into a voiced labiodental fricative similar to the "v" in "vine" in modern Greek, a change completed by around the 10th century CE. In contemporary demotic Greek, beta thus produces this v-like sound in native words, as in βιβλίο (vivlio, "book"), diverging from its ancient articulation.^[22] Modern Greek lacks a distinct bilabial stop phoneme for beta, instead employing the digraph μπ to convey the "b" sound—pronounced as a true bilabial stop word-initially (e.g., μπύρα, bira, "beer" from loanwords) and as a nasalized variant medially (e.g., αμπέλι, ambeli, "vineyard"). This convention accommodates borrowings from languages retaining the b-sound, preserving orthographic distinction from native fricative uses of beta.^[22]^[23]

Representation in the International Phonetic Alphabet

In the International Phonetic Alphabet (IPA), the lowercase Greek letter β represents the voiced bilabial fricative sound /β/, a consonant produced by narrowing the lips to create fricative turbulence without complete closure, as opposed to the voiced bilabial plosive /b/, which involves a full momentary blockage of airflow.^[24]^[25] This distinction reflects empirical phonetic classification based on articulatory and acoustic properties, prioritizing precise transcription of airflow dynamics over orthographic conventions.^[26] The symbol β was incorporated into the IPA's repertoire during its formative revisions in 1888, drawing from Greek letter forms to denote fricatives absent in Latin scripts, and has remained standard for cross-linguistic documentation despite the sound's relative rarity in phoneme inventories.^[27] It finds application in transcribing languages with native or allophonic /β/, such as Spanish intervocalic realizations of underlying /b/ (e.g., cerveza [seɾˈβesa] 'beer'), and certain African languages including Ewe, where it serves as a distinct phoneme.^[25]^[24] Outside Greek contexts, its utility underscores the IPA's emphasis on universal phonetic categories rather than language-specific orthography, though the sound occurs infrequently compared to labiodental counterparts like /v/.^[26]

Typography, Variants, and Graphical Evolution

The uppercase beta (Β) in standard typographic forms consists of two vertical strokes joined by parallel horizontal bars, visually akin to the Latin B but adapted for proportional harmony within Greek alphabets, as seen in early printed editions from the late 15th century.^[28] The lowercase beta (β) features an upright ascender curving into a descender with a single loop, a design that emerged in printed typefaces influenced by cursive manuscript traditions post-1453.^[28] Variants include uncial forms, which present beta as a rounded majuscule without descenders, emulated in early printing to replicate manuscript aesthetics before the 15th century.^[28] Italic variants introduce slant to both cases, with the lowercase descender often extended for emphasis, as developed in 18th-century inclined types by German printers and later in Monotype Series 91 during the 20th century.^[28] A cursive variant known as curled beta (ϐ) appears in some typefaces, featuring a more looped descender for stylistic distinction.^[29] In serif typefaces, such as Baskerville from the 18th century, beta incorporates subtle terminal strokes on horizontals and curves for enhanced readability in book printing.^[28] Sans-serif renderings, exemplified by Helvetica adapted for Greek in the 1970s, employ geometric straight lines devoid of serifs, facilitating clean digital and phototypesetting applications.^[28]^[30] Graphical evolution in printing involved simplification from ligature-heavy designs in Aldus Manutius's 1495 types to standardized forms by the 1806 Porson typeface, which regularized beta's strokes for mechanical composition.^[28] Historical typesetting challenges for beta arose from its complex shape alongside letters like zeta and theta, complicating punch-cutting for early printers unfamiliar with Greek forms.^[28] In polytonic editions, diacritic placement over beta's ascender demanded precise kerning, addressed through innovations like extensive ligatures until phototypesetting in the 20th century alleviated alignment issues.^[28]^[31]

Mathematical, Scientific, and Statistical Uses

Numerical Value in Ancient Systems

In the ancient Greek alphabetic numeral system, also known as the Milesian or Ionic system, beta (β) denoted the numerical value of 2.^[1]^[32] This system, which supplanted earlier acrophonic numerals around the 5th to 4th century BCE in Ionia and spread throughout the Hellenistic world, assigned values sequentially to the letters of the alphabet: the first nine letters (alpha to theta) for units 1 through 9, the next nine (iota to sampi) for tens 10 through 90, and the following nine for hundreds 100 through 900.^[32] To distinguish numerals from ordinary text, letters were overlined, so β̅ specifically represented 2; this notation appeared in papyri, inscriptions, and manuscripts from the Hellenistic period onward, facilitating calculations in trade, astronomy (as in Ptolemy's Almagest, circa 150 CE), and administrative records.^[32] Isopsephy, a practice akin to gematria, computed the total numerical value of words or phrases by summing their letters' assigned figures, with beta contributing 2 to such aggregates; it was employed in antiquity for interpretive, mystical, or cryptographic purposes, such as equating words with identical sums in philosophical or religious texts (e.g., analyzing proper names in Hellenistic Jewish and early Christian writings).^[19]^[33] Evidence of isopsephy dates to at least the 2nd century BCE, with applications in literary analysis where numerical equivalences revealed hidden meanings, though its interpretive claims often relied on subjective correlations rather than empirical verification.^[19] Unlike the Roman numeral II, which evolved from an acrophonic system deriving symbols from the initial letters or sounds of number words (e.g., duo influencing early forms), the Greek alphabetic approach reflected a shift from acrophonic precursors—used in Archaic Greece for monumental inscriptions—to a position-based valuation independent of word etymologies, enabling more efficient arithmetic without additive or subtractive complexities.^[32] This evolution prioritized alphabetic sequence over mnemonic initials, contrasting with Rome's retention of acrophonic traits into the Imperial era.^[32]

Applications in Mathematics and Physics

In mathematics, the Greek letter β commonly denotes an angle in trigonometric contexts, such as in right triangles where β represents one of the acute angles opposite a side of length proportional to its sine, cosine, or tangent values.^[34] Addition formulas express functions of sums like α ± β in terms of individual trigonometric ratios, facilitating derivations in geometry and calculus.^[34] The beta function, denoted B(p, q), is defined as the integral ∫ from 0 to 1 of t^{p-1}(1-t)^{q-1} dt for Re(p) > 0 and Re(q) > 0, serving as a fundamental special function that extends factorial generalizations via its relation to the gamma function: B(p, q) = Γ(p)Γ(q)/Γ(p+q).^[35] In physics, β signifies the normalized velocity β = v/c in special relativity, where v is the relative speed and c is the speed of light, forming the basis for the Lorentz factor γ = 1/√(1 - β²), which accounts for time dilation and length contraction observed in particle accelerators reaching β ≈ 0.999999 at energies like 7 TeV in the LHC.^[36] This usage derives from empirical validations of relativistic effects, such as muon lifetime extensions measured in cosmic ray experiments. In nuclear physics, beta decay involves the emission of beta particles—high-energy electrons or positrons—from unstable nuclei, a process first distinguished and named in 1899 by Ernest Rutherford based on deflection experiments showing their negative charge and lower penetration than alpha particles.^[37] Beta decay drives radioactive chains, with decay rates quantifiable via Geiger-Müller counters detecting particle fluxes, as in uranium-238 series where thorium-234 undergoes beta emission with a half-life of 24.1 days.^[37]

Uses in Biology and Chemistry

In protein secondary structure, beta sheets form when multiple beta strands align either parallel or antiparallel, stabilized by hydrogen bonds between carbonyl oxygen and amide hydrogen atoms of adjacent strands, creating a pleated conformation that contributes to the folding and stability of globular proteins. This motif, comprising up to 30% of residues in many proteins, was theoretically predicted by Linus Pauling and Robert Corey in April 1951 through stereochemical modeling of polypeptide chains, prior to empirical confirmation via X-ray crystallography in structures like silk fibroin.^[38] Beta sheets enable diverse functions, including enzymatic catalysis in enzymes like chymotrypsin, where they form rigid scaffolds resistant to thermal denaturation due to the cooperative hydrogen bonding network.^[39] Pancreatic beta cells, comprising 50-70% of cells in the islets of Langerhans, synthesize and secrete insulin in response to glucose-stimulated depolarization, maintaining euglycemia by facilitating glucose uptake in peripheral tissues; dysfunction or loss of these cells underlies type 1 and progressive type 2 diabetes, with autopsy studies showing beta cell mass reduced by 60-90% in advanced type 2 cases.^[40] In pharmacology, beta-blockers competitively inhibit beta-adrenergic receptors (primarily β1 in cardiac tissue), reducing cyclic AMP-mediated calcium influx and contractility, which lowers heart rate by 10-20 beats per minute and systolic blood pressure by 10-15 mmHg in hypertensive patients, as demonstrated in randomized trials like the MRC trial from 1985 involving over 17,000 participants.^[41] In organic chemistry, the beta carbon denotes the atom adjacent to the alpha carbon attached to a leaving group, serving as the site for proton abstraction in beta-elimination reactions, which generate alkenes via E1 (unimolecular, carbocation intermediate) or E2 (concerted, base-promoted) pathways; for instance, in dehydrohalogenation of alkyl halides, Zaitsev's rule predicts preferential formation of the more substituted alkene from the beta carbon with fewer hydrogens, verified through kinetic isotope effects and product distributions in laboratory syntheses.^[42] These reactions underpin industrial processes, such as the production of ethylene from ethanol dehydration, where beta-hydrogen elimination occurs at temperatures above 300°C with catalysts yielding 95% selectivity.^[43]

Role in Statistics and Probability

The beta distribution is a continuous probability distribution defined on the interval (0, 1), suitable for modeling random variables representing proportions, probabilities, or rates bounded between 0 and 1.^[44] ^[45] Its probability density function is given by f(x \mid \alpha, \beta) = \frac{x^{\alpha-1} (1-x)^{\beta-1}}{B(\alpha, \beta)}, where \alpha > 0 and \beta > 0 are shape parameters, and B(\alpha, \beta) is the beta function normalizing constant, defined as B(\alpha, \beta) = \int_0^1 t^{\alpha-1} (1-t)^{\beta-1} \, dt.^[46] The mean is \frac{\alpha}{\alpha + \beta} and the variance is \frac{\alpha \beta}{(\alpha + \beta)^2 (\alpha + \beta + 1)}, with the parameters determining the distribution's skewness and concentration around the mode.^[46] For \alpha = \beta = 1, it reduces to the uniform distribution on (0,1); as \alpha, \beta > 1 increase equally, it approximates a normal distribution near 0.5; unequal values produce U-shaped, J-shaped, or unimodal forms reflecting prior beliefs about success probabilities.^[44] In Bayesian inference, the beta distribution functions as the conjugate prior for the binomial likelihood, enabling analytical posterior updates without numerical integration.^[47] Given a beta prior Beta(\alpha, \beta) and binomial data with k successes in n trials, the posterior is Beta(\alpha + k, \beta + n - k), where the updated parameters incorporate observed evidence as pseudo-counts, preserving the family form and facilitating credible intervals for the success probability p.^[48] This conjugacy supports sequential updating in models of binary outcomes, such as reliability testing or proportion estimation, grounded in the Dirichlet-multinomial generalization for categorical data.^[47] Parameters \alpha and \beta are typically estimated from data via maximum likelihood estimation (MLE), which maximizes the log-likelihood \sum \log f(x_i \mid \alpha, \beta) but lacks closed-form solutions, requiring numerical optimization like Newton-Raphson or expectation-maximization algorithms.^[49] For instance, in samples from Beta(\theta, 1), the MLE \hat{\theta} solves transcendental equations, often yielding consistent estimators under regularity conditions, though boundary issues arise for small \alpha or \beta.^[50] Empirical fitting aligns the distribution with observed moments, such as method-of-moments estimators setting \hat{\alpha} = \bar{x} (\bar{x}(1-\bar{x})/s^2 - 1) and \hat{\beta} = (1 - \bar{x}) (\bar{x}(1-\bar{x})/s^2 - 1), where \bar{x} is the sample mean and s^2 the variance.^[44] The beta distribution underpins statistical inference for bounded parameters, notably in A/B testing where it models conversion rates from randomized controlled trials, enabling causal estimates of treatment effects via posterior probabilities.^[51] In such designs, binomial counts from variant A (Beta(\alpha_A + k_A, \beta_A + n_A - k_A)) and B yield the probability P(\theta_B > \theta_A \mid data) = \int_0^1 \int_{\theta_A}^1 f(\theta_B) f(\theta_A) \, d\theta_B \, d\theta_A, quantifying superiority under randomization's exchangeability, which identifies causal impacts absent confounding.^[52] This approach avoids frequentist pitfalls like p-value variability, prioritizing empirical evidence from trials for decision-making in optimization problems.^[53]

Economic, Technical, and Applied Uses

Beta in Finance and Risk Measurement

In finance, beta (β) quantifies the systematic risk of an asset or portfolio relative to the overall market, representing the expected change in the asset's return for a one-unit change in the market return.^[54] The concept originates from the Capital Asset Pricing Model (CAPM), developed by William Sharpe in his 1964 paper "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk," which posits that asset returns are linearly related to their contribution to market portfolio risk under assumptions of investor rationality and market equilibrium.^[55] The beta coefficient is defined as \beta_i = \frac{\Cov(R_i, R_m)}{\Var(R_m)}, where R_i is the asset's return, R_m is the market return, Cov denotes covariance, and Var denotes variance; this measures the asset's sensitivity to non-diversifiable market fluctuations.^[56] Beta is typically estimated empirically through linear regression of an asset's historical excess returns against the market's excess returns, often using 36 to 60 months of monthly data from indices like the S&P 500 to capture covariance while minimizing noise from short-term anomalies.^[57] The regression slope yields the beta value, with the market proxy's variance in the denominator ensuring normalization; for instance, excess returns are computed as asset return minus risk-free rate (e.g., Treasury bill yield) regressed against market excess returns.^[58] This historical approach assumes stationarity in risk exposure, though adjustments for leverage or industry effects are sometimes applied via bottom-up estimation from firm fundamentals.^[59] A beta greater than 1 indicates the asset exhibits higher volatility than the market, amplifying both gains and losses in bull and bear phases—common in technology stocks, where sector betas often exceed 1.2 due to sensitivity to economic cycles and innovation risks.^[60] Conversely, betas below 1 signify defensive assets with muted responses, such as utilities or consumer staples, which provide stability during downturns; for example, many S&P 500 technology constituents like those in semiconductors display betas above 1.5, reflecting leveraged exposure to growth volatility.^[61] In portfolio management, beta guides diversification: investors seeking higher expected returns under CAPM tolerate elevated betas, while risk-averse strategies favor low-beta holdings to reduce drawdowns without sacrificing adjusted performance.^[62] Despite its ubiquity in cost-of-capital calculations and performance benchmarking, beta's reliance on CAPM assumptions—such as efficient markets, homogeneous expectations, and no transaction costs—faces empirical scrutiny, as real-world data reveals deviations like the low-beta anomaly, where low-beta stocks deliver higher risk-adjusted returns than high-beta counterparts predict. This anomaly, documented across U.S. and global equities, contradicts CAPM's linear risk-return tradeoff, potentially arising from investor overreach into high-beta assets during leverage-constrained environments or failure to capture tail risks from rare events like market crashes (black swans), which beta underestimates by assuming Gaussian return distributions.^[63] Alternatives, such as the Fama-French three-factor model (1993), augment beta with size (small-minus-big) and value (high-minus-low book-to-market) factors to better explain cross-sectional returns, empirically outperforming CAPM in regressions on historical U.S. data from 1963 onward.^[64] These multi-factor extensions highlight beta's limitations in causal risk assessment, prioritizing observable market data over theoretical equilibrium.^[65]

Implementations in Computing

Beta reduction, a core computational rule in lambda calculus developed by Alonzo Church in the early 1930s, substitutes the argument of a function application into the lambda abstraction's body, formalized as (\lambda x.M) N \to M[x := N], where a redex (reducible expression) is reduced to its normal form through repeated applications.^[66]^[67] This process underpins the semantics of pure functional computation, enabling term rewriting without side effects and serving as the basis for evaluating higher-order functions.^[68] In practical implementations, beta reduction is executed in interpreters for functional languages like Scheme and Haskell, often via graph reduction techniques that share subcomputations to avoid redundant evaluations; for instance, Church-Rosser confluence ensures unique normal forms regardless of reduction order.^[69] Efficiency is enhanced by strategies such as applicative-order versus normal-order evaluation, with benchmarks on lambda interpreters showing that lazy evaluation via graph reduction can reduce memory usage by factors of 10-100 for recursive terms like factorial computations.^[70] The β symbol also appears in algorithmic data structures, notably β-skeletons in computational geometry, which generalize proximity graphs by excluding edges longer than a β-parameterized lune or spindle; linear-time algorithms for β=1 (relative neighborhood graphs) extend to O(n log n) for general β via divide-and-conquer, facilitating applications in clustering and nearest-neighbor searches.^[71] In search algorithms, β denotes the upper bound in alpha-beta pruning for minimax trees, which discards branches exceeding β thresholds, empirically cutting evaluated nodes by up to √b (where b is branching factor) in balanced trees compared to unpruned minimax.^[72]

Betamax Format and Media Technology

Betamax is an analog videotape cassette format for consumer-level recording and playback of video signals, developed by Sony Corporation. Introduced in Japan on May 10, 1975, with the LV-1901 model released in the United States later that November, it utilized 1/2-inch-wide magnetic tape housed in a cassette measuring approximately 5.8 by 3.6 by 1.2 inches.^[73]^[74] The format supported one hour of NTSC color video recording at standard play speed, with horizontal resolution around 250 lines and a signal-to-noise ratio superior to early competitors due to narrower track width and helical-scan technology.^[75]^[76] Despite technical merits including higher video fidelity and compact design, Betamax's initial one-hour tape length proved limiting for feature films, prompting Sony to introduce extended-play modes reaching two hours by 1977.^[77] In September 1976, JVC launched the competing VHS format with the HR-3300 recorder, offering two hours of recording on larger cassettes using 1/2-inch tape but with wider tracks yielding about 240 lines of horizontal resolution.^[78] VHS's advantages stemmed from JVC's open licensing policy, which enabled manufacturers like Matsushita and Hitachi to produce compatible decks at lower prices—often $200–$400 less than Betamax units—and its longer baseline recording time, fostering broader availability and economies of scale.^[79] Sony's proprietary approach restricted Betamax to its own production, inflating costs and limiting distribution networks.^[80] The format war illustrated path dependence in technology adoption, where VHS's early market penetration—driven by pricing and tape length—created self-reinforcing effects through greater content availability and retailer stocking. By 1980, VHS captured 60% of the U.S. market, eroding Betamax's initial 100% share; VHS reached 75% by 1981 and 92.5% by 1984.^[76]^[80] Claims that adult video distribution decisively favored VHS due to its suitability for longer uncut films have been overstated, as pornography titles appeared on both formats proportionally to market share, with VHS's edge arising from preexisting availability advantages rather than causal preference.^[81] Betamax persisted in professional broadcast and editing applications into the 1990s and early 2000s, valued for durability and precision in nonlinear workflows before digital formats like DV supplanted it.^[82] Sony ceased Betamax tape production in 2016, marking the end of support for a format that, despite superior engineering, yielded to VHS's economic scalability and network effects.^[82]

Practical Applications in Meteorology and Sports

In geophysical fluid dynamics, the beta-plane approximation models the meridional variation of the Coriolis parameter f as f = f₀ + βy, where f₀ is the local value at a reference latitude and β = ∂f/∂y approximates the linear gradient due to Earth's sphericity. This simplification, valid for mid-latitude scales, underpins quasigeostrophic theory for atmospheric and oceanic flows, capturing effects like Rossby wave propagation essential to weather systems.^[83]^[84] The approximation's efficacy is demonstrated in simulations matching empirical observations, such as mid-latitude jet stream meanders and cyclone tracks, where β-driven planetary vorticity gradients align with satellite and radiosonde data for predictive accuracy in numerical weather models. Limitations arise near the equator or poles, where higher-order spherical effects dominate, prompting refinements like non-traditional beta-plane derivations for improved fidelity in global circulation models.^[85]^[86] In rock climbing, beta denotes the detailed sequence of handholds, footholds, body positions, and techniques required to complete a specific route or boulder problem, often verbally transmitted or visually demonstrated among practitioners. Originating from community practices emphasizing empirical problem-solving, beta sharing optimizes energy use and route efficiency, particularly on crux sections involving dynamic moves or precarious holds.^[87]^[88] This tactic-based knowledge transfer, refined through repeated ascents, enables climbers to bypass inefficient or high-risk maneuvers, as taller or shorter individuals may adapt personalized variants while adhering to core beta elements. While direct statistical linkages to reduced falls are sparse, beta dissemination correlates with lower injury rates in controlled settings by promoting technique-focused progression over forceful attempts, per anecdotal and gym incident reports highlighting poor beta as a factor in overuse and impact injuries.^[89]^[90]

Cultural, Symbolic, and Informal Uses

Organizational Naming (Fraternities and Societies)

Phi Beta Kappa, the oldest academic honor society in the United States, was founded on December 5, 1776, at the College of William & Mary in Williamsburg, Virginia, by five students seeking to promote scholarship through a secret society modeled on literary fraternities.^[91] Its name incorporates the Greek letters phi (φ), beta (β), and kappa (κ), derived from the motto Philosophia Biou Kybernētēs ("Love of learning is the guide of life"), with beta symbolizing the second letter in this sequence.^[91] Initially limited to seniors demonstrating excellence in liberal arts, the society expanded slowly amid secrecy and anti-fraternity sentiments, reaching 25 chapters by 1883 when the United Chapters of Phi Beta Kappa formalized national governance.^[91] Today, it maintains approximately 290 active chapters at accredited institutions, electing members based on academic merit without regard to field of study.^[91] Beta Theta Pi, a prominent social fraternity, was established on August 8, 1839, at Miami University in Oxford, Ohio, by eight undergraduates as the first fraternity founded west of the Allegheny Mountains.^[92] The name draws from the Greek letters beta (β) and theta (θ), reflecting classical influences in early 19th-century American collegiate culture, where Greek nomenclature evoked ideals of brotherhood and intellectual pursuit.^[92] The fraternity's symbols, including its badge (a diamond-shaped pin with intertwined beta and theta letters) and coat of arms featuring a dragon guardian, incorporate the beta letter in rituals, oaths, and paraphernalia to signify mutual trust and lifelong bonds among members.^[93] By the late 19th century, Beta Theta Pi had grown to dozens of chapters, emphasizing cultivation of character over mere social exclusivity, though like other Greek-letter groups, it faced criticism for secrecy and selective membership.^[92] Greek-letter organizations incorporating beta, such as these, proliferated in the 19th and early 20th centuries, with over 100 national fraternities and sororities by 1900, driven by students' desire for camaraderie amid expanding higher education.^[92] However, predominantly white groups like Beta Theta Pi historically enforced racial exclusions through explicit clauses or informal practices, barring Black students until mid-20th-century reforms prompted by civil rights pressures; for instance, many retained "white only" policies into the 1950s and 1960s.^[94] This paralleled the emergence of Black Greek-letter organizations, collectively known as the Divine Nine under the National Pan-Hellenic Council (formed 1930), which originated in the early 1900s—starting with Alpha Phi Alpha in 1906 at Cornell University—to provide fellowship for Black students denied entry to white societies amid widespread segregation.^[95] ^[96] Controversies surrounding beta-named organizations have included hazing practices, exemplified by the 2017 death of Penn State sophomore Timothy Piazza during a Beta Theta Pi pledging ritual involving excessive alcohol consumption, leading to the chapter's permanent ban and criminal convictions of members for involuntary manslaughter and related charges, with sentences handed down as recently as October 2024.^[97] Such incidents highlight persistent risks in initiation rites across Greek life, despite anti-hazing laws like Pennsylvania's Timothy J. Piazza Antihazing Law enacted in 2018.^[97] While reforms have addressed overt racial barriers, debates continue over de facto homogeneity in many chapters, contrasting with the Divine Nine's focus on cultural uplift for underrepresented groups.^[95] The alpha-beta distinction in social hierarchies traces its roots to mid-20th-century ethological observations of captive wolf packs, where unrelated animals formed dominance structures with "alpha" leaders securing priority access to mates and resources, and "beta" subordinates ranking below them.^[98] Subsequent research clarified that wild wolf packs operate as family units led by breeding parents, without the rigid hierarchies seen in captivity, challenging the model's direct applicability to natural canid behavior.^[99] Nonetheless, the framework influenced broader interpretations of animal dominance and mating success, where higher-ranking individuals exhibit traits like assertiveness correlating with reproductive advantages. In human contexts, "beta" emerged as slang in the 2010s within manosphere and pickup artist (PUA) communities, denoting men perceived as submissive, emotionally dependent, or lower in attractiveness compared to "alpha" counterparts who display confidence and leadership.^[100] This usage ties to empirical links between testosterone levels and dominance: studies show elevated testosterone promotes status-seeking and assertive behaviors in men, enhancing perceived mating viability, while lower levels align with submissiveness.^[101] ^[102] Evolutionary psychology supports related dynamics through hypergamy patterns, where women across cultures preferentially select partners of higher socioeconomic or status positions, reflecting adaptive preferences for resource-providing traits over passive ones.^[103] ^[104] By 2024-2025, "beta" permeates teen and online slang as a pejorative for passivity or weakness, often juxtaposed against "alpha" assertiveness in social or romantic scenarios.^[105] ^[106] Proponents cite evo-biological data on sex-differentiated attraction—women's hypergamy and valuation of dominance versus men's emphasis on physical cues—as evidence for real hierarchies in mating markets, countering narratives that equate such observations with pathology.^[103] Critics, frequently from academic and media outlets, decry the framework as fostering "toxic masculinity" by rigidifying gender roles, though this perspective often discounts cross-cultural empirical consistencies in mate choice disparities.^[107] ^[108] Causal analysis reveals these hierarchies stem from proximate mechanisms like hormonal influences and ultimate selection pressures, rather than solely cultural constructs.^[109]

Digital Encoding and Unicode Representation

The uppercase Greek letter beta (Β) is assigned the Unicode code point U+0392 (GREEK CAPITAL LETTER BETA), while the lowercase form (β) uses U+03B2 (GREEK SMALL LETTER BETA). These code points reside in the Greek and Coptic block (U+0370–U+03FF), which facilitates encoding for both ancient Greek texts and Coptic script variants that reuse Greek-derived letters, including beta for phonetic representation.^[110] The block's core Greek characters, encompassing beta, originated in Unicode version 1.0 (October 1991), with expansions in version 1.1 (June 1993) to include additional diacritics and symbols compatible with polytonic Greek and early Coptic needs. A distinct variant, the cursive or lunate Greek beta symbol (ϐ), is encoded at U+03D0 (GREEK BETA SYMBOL) within the same block, preserving a historical form from medieval manuscripts and occasionally used in modern mathematical or stylistic contexts to differentiate from the standard upright beta. In mathematical and scientific applications, Unicode's Mathematical Alphanumeric Symbols block (U+1D400–U+1D7FF) offers typographic variants of beta for enhanced equation rendering, including mathematical bold small beta (𝛃, U+1D6C3), mathematical italic small beta (𝛽, U+1D6FD), and mathematical bold italic small beta (𝜷, U+1D737). These forms decompose to the base U+03B2 via font styling, enabling precise control in digital typesetting systems like LaTeX or MathML while maintaining compatibility across rendering engines.^[111] Prior to Unicode 3.1 (2001), such variants were unavailable, often requiring custom font hacks or approximations in legacy software.

References

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Beta Symbol in Greek Alphabet Β β
Beta is the second letter of the Greek alphabet. In the Greek numeral system, it has a value of two. Beta is transliterated as b (beta) in Classical Greek.
[2]
The Origin of the Alphabet
Beth, the house, may have derived from a more rectangular Egyptian alphabetic glyph of a reed shelter (but which stood for the sound h). The Greeks called it ...Missing: etymology | Show results with:etymology
[3]
The ABG's of History - 1320
In the Greek alphabet zeta comes rather early, immediately after epsilon (the Greek equivalent of E). While early Italians had inherited zeta along with the ...
[4]
Beta - Symbols.com
In the system of Greek numerals it has a value of 2. In Ancient Greek, beta represented the voiced bilabial plosive /b/.
[5]
Pronouncing the Greek Alphabet - ThoughtCo
May 29, 2024 · Letters in the Greek Alphabet ; Letter Upper, Lower, Name, Pronounced ; A, α, Alpha, AHL-fah ; Β, β, Vita, VEE-tah ; Γ, γ, Gamma, GHAH-mah ; Δ, δ ...
[6]
Beta Symbol (β) - wumbo.net
The Greek letter beta (β). In mathematics and science, it is often used to denote a variable or a parameter, such as an angle or the beta coefficient in ...<|control11|><|separator|>
[7]
Alphabet Origins: From Kipling to Sinai
Dec 22, 2014 · ... letter B were floor plans of a house (Hebrew bayit; Phoenician bt). This meant that the alphabet would have been created by speakers of a ...Missing: bet meaning
[8]
Expedition Magazine | The Alphabet - Penn Museum
The earliest known Greek alphabetic inscriptions date to the 700s BCE, when Phoenician ships sailed the Mediterranean. ... Proto-Sinaitic and Proto-Canaanite: The ...
[9]
Phoenician alphabet and language - Omniglot
Dec 11, 2023 · The Phoenician alphabet developed from the Proto-Canaanite alphabet, during the 15th century BC. Before then the Phoenicians wrote with a cuneiform script.
[10]
The Origins of the Alphabet | ArmstrongInstitute.org
Nov 30, 2021 · ... Phoenician letters aleph and bet. In Hebrew, it is called the “Alephbet,” spelled “alpbit.” Second line is ancient Hebrew (reading left to ...Missing: meaning | Show results with:meaning
[11]
Did the Phoenicians Even Exist? - Archaeology - Haaretz
Jul 28, 2016 · The Phoenicians are believed to have invented the 22-letter alphabet in about 1300 BCE. As they spread, other nations saw the advantages of the ...
[12]
[PDF] the rise of the greek alphabet - Deep Blue Repositories
148 The signs 𐌔 ᴤ Σ, 𐊑, 𝈿, Μ, 𐌔 ᴤ Σ, Χ and 𐌙 stand for. 'crooked iota', xi, san at Caere versus san elsewhere, sigma with three or four bars, chi and psi ...
[13]
The Dipylon Oinochoe Graffito - jstor
The famous Dipylon oinochoe furnishes a tantalizing glimpse of the. Greek alphabet while it was still in its infancy.1 This early view, however,.
[14]
Archaic Letters - Kata Biblon Greek Grammar Reference
The earliest known Greek alphabet is the Fayum Alphabet, a ninth-century BCE (ca. 800) abecedarium found in Egypt inscribed on a set of four copper tablets* ...
[15]
Introduction | The Early Greek Alphabets: Origin, Diffusion, Uses
Alphabet and Language. Alphabetic inscriptions of the Archaic period play a crucial role in reconstructing the development of the Greek language.
[16]
8. THIRTEENTH-CENTURY HANDS | Greek Paleography
263-7) proposed to call "Beta-Gamma Style", because here the letters which are enlarged are beta and gamma. This script has a better claim to be considered ...
[17]
Kiwi Hellenist: 'No one knows how ancient languages were ...
Feb 29, 2016 · But our timeframe for when the pronunciation shifted from b to v is at least a 300-year window: we know it was pronounced b in the 2nd century ...
[18]
At what point in time did the pronunciation of the Greek β change ...
Aug 13, 2017 · The first unequivocal evidence is the differentiation between б and в in Cyrillic in the 9th century AD. It turns out though that at the same ...
[19]
Isopsephy.com – Cipher Mysticism in Greek Antiquity
Isopsephy (ἰσοψηφία: meaning literally, “equal pebbled” or “equal count”) is the technique of (1) calculating the numerical value of Greek words by adding ...
[20]
Pronunciation - Duke People
Β β beta, pronounced like the b in boy. Γ γ gamma, pronounced like the g in go. The letter γ is pronounced like the ng in sing when it comes before γ, κ, χ, or ...
[21]
beta in Greek alphabet - Katerina Sarri webtopos
The initial ancient greek pronunciation was [b]. The example of the lambs that bleat, written as: BH, BH, BH in comedy texts by Aristophanes and Cratinus is ...
[22]
Diphthongs and Digraphs - Greek Language and Linguistics
ΜΠ μπ. Mu Pi. Modern. b as in back,. or sometmes mb. Hellenistic Koiné. b as in back,. or sometmes mb. Classical. μ + π pronounced as a consonant blend ...
[23]
The Details of Modern Greek Phonetics and Phonology
In the page of the Greek alphabet it was explained that the letters μπ, when found together, are pronounced as [b]; the letters ντ, also together, are ...
[24]
Phonetic symbols
β, voiced bilabial fricative, Spanish haber ; c, voiceless alveolar affricate; IPA [ʦ] or [ts], Italian zucchero, German zu, Yiddish tsimmes ; č, voiceless ...
[25]
IPA: Labials
[β]: the voiced bilabial fricative, symbolized by the Greek letter beta. Examples: Spanish: [sɛɾβesa] cerveza 'beer' ([β] is an allophone of /b/ in Spanish.).
[26]
Entry - IPA: voiced bilabial fricative - ScriptSource
Mar 20, 2017 · At the current time, the IPA gives the encoding for the voiced bilabial fricative as U+03B2 GREEK SMALL LETTER BETA. This character is in the ...Missing: Alphabet | Show results with:Alphabet
[27]
[PDF] Phonetic characters_ Greek and Latin 2024-08-17 - Unicode
Aug 17, 2024 · IPA uses Greek β, θ, χ (03B2, 03B8, 03C7) be- cause they unify various forms since Unicode 1.1. IPA has a history of having Latin forms ...Missing: adoption | Show results with:adoption
[28]
A primer on Greek type design - ATypI
Although types were cut in Greece throughout the period of mechanical typesetting, any original designs were limited to display typefaces; very few typefaces ...
[29]
[PDF] U0370.pdf - Unicode
Variant letterforms. 03CF Ϗ GREEK CAPITAL KAI SYMBOL. → 03D7 ϗ greek kai symbol. 03D0 ϐ GREEK BETA SYMBOL. = curled beta. ≈ 03B2 β greek small letter beta. 03D1 ...
[30]
[PDF] Linotype's design of new Greek typefaces for photocomposition in ...
Helvetica Greek: Optima Medium Greek, Cadmus, Century Schoolbook Greek and Baskerville. Greek, all designed between 1972 and 1980. These are only some of the ...
[31]
[PDF] Keeping Greek Typography ALive - HAL
Apr 26, 2019 · Greek, and especially the transcription of epigra- phical material, is a typesetter's challenge since additional symbols are needed (for example ...
[32]
Greek number systems - MacTutor - University of St Andrews
The first Greek number system we examine is their acrophonic system which was use in the first millennium BC.
[33]
Gematria, Isopsephy, and Stoicheia - The Digital Ambler
A big difference is the number of characters: Hebrew has 22 letters with 5 extra, adding to 27, while Greek has 24. To make up for the lost characters, Greek ...
[34]
Trigonometric Addition Formulas -- from Wolfram MathWorld
Angle addition formulas express trigonometric functions of sums of angles alpha+/-beta in terms of functions of alpha and beta.
[35]
Beta Function -- from Wolfram MathWorld
The beta function B(p,q) is the name used by Legendre and Whittaker and Watson (1990) for the beta integral (also called the Eulerian integral of the first ...
[36]
Lorentz Transformation - HyperPhysics
Much of the literature of relativity uses the symbols β and γ as defined here to simplify the writing of relativistic relationships. For v = c. β = and γ = .
[37]
Beta decay | Definition, Examples, & Facts - Britannica
Sep 8, 2025 · Beta decay was named (1899) by Ernest Rutherford when he observed that radioactivity was not a simple phenomenon. He called the less penetrating ...
[38]
The discovery of the α-helix and β-sheet, the principal structural ...
PNAS papers by Linus Pauling, Robert Corey, and Herman Branson in the spring of 1951 proposed the α-helix and the β-sheet, now known to form the backbones ...
[39]
Beta Sheet - an overview | ScienceDirect Topics
Beta sheet is defined as a significant secondary structure of proteins consisting of beta strands linked laterally by hydrogen bonds, forming a zig-zag and ...
[40]
The Pancreatic Beta Cell: Editorial - PMC - PubMed Central
Mar 8, 2023 · Pancreatic beta cells play a critical role in maintaining glucose homeostasis by serving as the primary source of insulin.
[41]
Beta Blockers - StatPearls - NCBI Bookshelf
Beta-blockers also decrease blood pressure via several mechanisms, including decreased renin and reduced cardiac output. The negative chronotropic and inotropic ...Continuing Education Activity · Indications · Mechanism of Action · Contraindications
[42]
4.1: β-Elimination Reactions - Chemistry LibreTexts
May 3, 2023 · β-Elimination involves the transfer of a leaving group from a ligand to the metal center, forming a π bond in the ligand, and requires an open ...β-Hydride Elimination · Other β-Elimination Reactions
[43]
Illustrated Glossary of Organic Chemistry - Beta elimination
Beta-elimination is a reaction where atoms or groups are lost from adjacent atoms, forming a new pi bond, like A-B-C-D ---> A + B=C + D.
[44]
Beta Distribution: Uses, Parameters & Examples - Statistics By Jim
The beta distribution is a continuous probability distribution that models random variables with values falling inside a finite interval.
[45]
Beta distribution | Properties, proofs, exercises - StatLect
The Beta distribution is a continuous probability distribution often used to model the uncertainty about the probability of success of an experiment.How the distribution is used · Definition · Distribution function · More details
[46]
1.3.6.6.17. Beta Distribution - Information Technology Laboratory
Probability Density Function. The general formula for the probability density function of the beta distribution is. f ( x ) = ( x − a ) p − 1 ( b − x ) q − 1 B ...
[47]
[PDF] Conjugate priors: Beta and normal Class 15, 18.05
In this section, we will show that the beta distribution is a conjugate prior for binomial,. Bernoulli, and geometric likelihoods. 3.1 Binomial likelihood. We ...
[48]
[PDF] 18.05 S22 Reading 15: Conjugate priors: Beta and normal
We saw above that the beta distribution is a conjugate prior for the binomial distribution. This means that if the likelihood function is binomial and the ...<|separator|>
[49]
Maximum Likelihood Estimation of the Parameters of the Beta ...
Apr 30, 2012 · Numerical methods, useful with high-speed computers, are described for obtaining the maximum likelihood estimat.es of the two (shape) parameters of a beta ...
[50]
Fitting Beta Distribution Parameters via MLE
Describes how to estimate beta distribution parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel.<|separator|>
[51]
Introduction to Bayesian A/B Testing — PyMC example gallery
A/B testing (also known as split testing) is a process of showing two variants of the same web page to different segments of website visitors at the same time.
[52]
Bayesian A/B testing — a practical primer - UX Collective
Jun 10, 2025 · Bayesian A/B testing for conversion rates typically uses the Beta distribution as a conjugate prior for the binomial likelihood (see above).
[53]
Use the Beta Distribution · A/B Testing Statistics
It's simply the correct distribution to use when you're modeling a true rate after observing k successes out of n trials.
[54]
CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM ...
In equilibrium, capital asset prices have adjusted so that the investor, if he follows rational procedures (primarily diversification), is able to attain any ...Introduction · II. Optimal Investment Policy... · III. Equilibrium in the Capital...
[55]
Capital Asset Prices: A Theory of Market Equilibrium under ... - jstor
The implica- tions for the relationship between the prices of individual capital assets and the various components of risk are described in Part IV. II. OPTIMAL ...
[56]
CAPM Beta Explained | Risk-Free Beta & Formula Examples
Dec 15, 2020 · ... Beta calculation uses the correlation between the security and the market. The Beta formulae for company i is the following: βi=Cov(i,m) ...Quick Reference: CAPM Beta... · Beta · The Capital Asset Pricing...
[57]
How to Calculate Beta in Excel - Investopedia
Beta is essentially the regression coefficient of a stock's historical returns compared to those of the S&P 500 index. This coefficient represents the slope of ...What Is Beta? · Methodology · Calculating Beta · Formulas
[58]
[PDF] Estimating Beta - NYU Stern
Regression parameters are always estimated with error. The error is captured in the standard error of the beta estimate, which in the case of Disney is 0.10.
[59]
Beta Coefficient - Definition, Formula, Calculate
The Beta coefficient is a measure of sensitivity or correlation of a security or an investment portfolio to movements in the overall market.
[60]
2025 High Beta Stocks List | The 100 Highest Beta S&P 500 Stocks
Jun 26, 2025 · We created a list of S&P 500 stocks with the highest beta values. You can download your free High Beta stocks list (along with relevant financial metrics)
[61]
S&P 500 High Beta Index | S&P Dow Jones Indices - S&P Global
The S&P 500 High Beta Index measures the performance of 100 constituents in the S&P 500 that are most sensitive to changes in market returns.
[62]
What Beta Means for Investors - Investopedia
A security's beta is calculated by dividing the product of the covariance of the security's returns and the market's returns by the variance of the market's ...
[63]
A behavioral explanation of the low-beta anomaly - ScienceDirect.com
We show that the low-beta anomaly can be explained by a return reversal following adverse beta herding, as high beta stocks underperform low beta stocks.
[64]
[PDF] The use of CAPM and Fama and French Three Factor Model
The main alternative to CAPM is the Three Factor Model suggested by Fama and French (1992). In this mod- el, size and book to market factors are included, in ...
[65]
Fama-French Three-Factor Model - Components, Formula & Uses
Learn how the Fama-French Three-Factor Model expands CAPM by adding size and value factors to better explain stock returns and portfolio performance.
[66]
Alonzo Church > D. The λ-Calculus and Type Theory (Stanford ...
The λ-operator is a monadic variable binding “abstraction” operator that allows one to build complex expressions that designate functions.
[67]
Lambda Calculi | Internet Encyclopedia of Philosophy
Alonzo Church first introduced the λ -calculus as “A set of postulates for the foundation of logic” in two papers of that title published in 1932 and 1933.3. Expressiveness · 4. Philosophical Importance · A. The Church-Turing Thesis
[68]
[PDF] lambda calculus
There are two key reduction rules in the lambda calculus. Alpha reduction allows you to rename variables uniformly. Beta reduction is the essence of computation ...
[69]
Beta Reduction (Part 1) - Programming Research Laboratory
Nov 2, 2016 · The λ-Calculus. The λ-calculus is a simple model of computation developed by Alonzo Church. The λ-calculus has three different syntactic forms: ...
[70]
[PDF] Optimal Interpreters for Lambda-calculus Based Functional
Aug 10, 1990 · It takes a A-expression to be evaluated as argument, and if it terminates, it returns the normal form of the input expression. interpreter exp = ...
[71]
Fast algorithms for computing β-skeletons and their relatives
In this paper we present fast algorithms for computing β-skeletons (Kirkpatrick and Radke, in: Toussaint (Ed.), Computational Geometry, North-Holland, ...<|separator|>
[72]
Alpha-Beta pruning in Adversarial Search Algorithms - GeeksforGeeks
Jul 23, 2025 · Alpha-beta pruning is an optimization technique for the minimax algorithm. It reduces the number of nodes evaluated in the game tree by eliminating branches ...
[73]
June 7, 1975: Before Digital, Before VHS ... There Was Betamax
Jun 7, 2011 · 1975: Sony introduces the Betamax video recorder. Revolutionary for its day, the Betamax format was on its way to becoming the industry standard ...
[74]
What Is Betamax? A Guide To The Betamax Tape - EverPresent
WHEN DID BETAMAX COME OUT? ... Sony's Betamax system was first released in Japan on May 10, 1975, and reached America in November of the same year. In both ...
[75]
On this date: going Beta - Yahoo
May 10, 2024 · On May 10, 1975, Sony introduced the Betamax videocassette recorder. The Betamax cassette could record an hour of video on 1/2-inch wide tape.
[76]
The Format Wars History: Betamax vs. VHS - Two Squares
Apr 25, 2023 · In 1975, Sony introduced the first Betamax devices, which made use of cassette tapes with an internal tape width of 0.50 inches. Although ...
[77]
https://legacybox.com/blogs/analog/vhs-beat-betamax
[78]
Milestones:Development of VHS, a World Standard for Home Video ...
Jun 14, 2022 · Finding a niche in this area, JVC on 9 September 1976, released a VHS-format home VTR, HR-3300. With a weight of 30 pounds, it was smaller ...
[79]
Chapter2 Sony Goes to Battle for Its Favorite Child
By 1976, the year following the launch of Betamax, the Vietnam War had ended and North and South Vietnam were reunified. Sony celebrated its 30th ...
[80]
Betamax vs. VHS Videotape Wars - Everything Everywhere Daily
Jul 30, 2023 · By 1980, VHS had 60% of the market in the United States. By 1981, VHS had 75% of the market, and by 1984 they had 92.5% market share.
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VHS vs Betamax: How influential was the pornography industry in ...
May 11, 2011 · Ultimately, VHS won the battle, and tech lore has it that the porn industry played a big role in that victory.Missing: legacy | Show results with:legacy
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Betamax is dead, long live VHS | Sony - The Guardian
Nov 10, 2015 · Sony announces end of production of Betamax cassettes for March next year, 40 years after its introduction and 28 years after losing format ...
[83]
Beta-Plane - an overview | ScienceDirect Topics
A β-plane model is defined as a simplified representation of the variation of the Coriolis parameter, expressed as f = f₀ + βy, where β is treated as a constant ...
[84]
On the Validity of the β-Plane Approximation in the Dynamics and ...
Jan 1, 2015 · In geophysical fluid dynamics the β-plane approximation plays a central role as the basis of large-scale quasigeostrophic dynamics. The idea ...
[85]
On the Beta Plane Approximation in - AMS Journals
We show that the difficulty can be overcome by basing the derivation of the beta plane approximation on a suitably chosen spherical coordinate system.
[86]
[PDF] derivation of non-traditional beta-plane equations from Hamilton's ...
Starting from Hamilton's principle on a rotating sphere, we derive a series of successively more accurate β-plane approximations.
[87]
What does 'Beta' mean in climbing (and what is the origin)?
Jun 21, 2022 · Beta is a climbing term used when information is consumed about a boulder problem or climbing route that will be helpful towards an ascent. For ...
[88]
https://boulderflash.com/climbing-beta-origins-and-what-you-need-to-know/
[89]
Ever Flipped Upside-Down While Falling? Here's How to Avoid That
Oct 22, 2024 · Upside-down whippers falls are both very dangerous and almost always avoidable. Here's how to keep your climbing falls safe.Missing: reduce statistics
[90]
Risk factors and injury prevention strategies for overuse ... - NIH
Dec 12, 2023 · Higher climbing intensity, bouldering, reduced grip/finger strength, use of a “crimp” grip, and previous injury were associated with an increased risk of ...
[91]
History of Phi Beta Kappa - PBK
Phi Beta Kappa was founded by five students at William & Mary in 1776, with its first meeting in Williamsburg, Virginia. Its name comes from the motto "Love of ...
[92]
History - Beta Theta Pi Fraternity
Beta Theta Pi, commonly known on campuses across North America simply as Beta, was founded on August 8, 1839, at Miami University in Oxford, Ohio.
[93]
Archives & Heraldry - Beta Theta Pi Fraternity
Beta Theta Pi's symbols include a coat of arms, great seal, pink and blue colors, a flag, a rose, a badge, and a pledge pin.
[94]
Greek Letter Discrimination: Fraternities Without Brotherhood
By 1928, more than half of the national college fraternities and sororities had specific rules requiring exclusion along racial and religious lines, while ...
[95]
The Divine Nine: History of Black Sororities and Fraternities
Aug 3, 2023 · The Divine Nine is the nickname of a group of nine historically Black Greek-letter organizations called the National Pan-Hellenic Council (NPHC).
[96]
The history and impact of Black Greek letter organizations - ABC News
Feb 28, 2023 · The Divine Nine, according to the National Pan-Hellenic Council website, "evolved during a period when African Americans were being denied ...
[97]
Penn State frat leaders sentenced in hazing death - USA Today
Oct 2, 2024 · Ex-leaders of Penn State frat sentenced in 2017 hazing death of Timothy Piazza · Brendan Young, 28, and Daniel Casey, 27, were sentenced to two ...
[98]
[PDF] Alpha Status, Dominance, and Division of Labor in Wolf Packs
In captive packs, the unacquainted wolves formed domi- nance hierarchies featuring alpha, beta, omega animals, etc. With such assemblages, these dominance ...<|separator|>
[99]
Wolf packs don't actually have alpha males and alpha females, the ...
Apr 26, 2021 · Doesn't work for wolves in the wild. Calling wolves alpha and beta animals comes from research on wolves in captivity, says Barbara Zimmermann.
[100]
Hegemonic masculinities in the 'Manosphere': A thematic analysis of ...
Apr 1, 2022 · Betas are defined as weak men who rely upon trading money, power, or (worse) emotional intimacy for sex. This is reflected in the terminology “ ...
[101]
Testosterone promotes either dominance or submissiveness in the ...
Jul 13, 2017 · Our results suggest that testosterone may enhance socially dominant behaviour among high-status persons, but strategic submission to seniority among lower- ...
[102]
Testosterone promotes dominance behaviors in the Ultimatum ... - NIH
Oct 21, 2023 · Our analysis reveals that individuals with higher baseline salivary testosterone levels exhibited more dominance as their position in the hierarchy increased ...
[103]
The Economics of Hypergamy - Journal of Human Resources
Jan 1, 2023 · We have presented empirical evidence that hypergamy is an important feature of mating patterns in Norway, and we have shown that there are no ...
[104]
Hypergamy reconsidered: Marriage in England, 1837–2021 - PMC
Feb 3, 2025 · It is widely believed that women value social status in marital partners more than men, leading to female marital hypergamy (“marrying up”), ...Methods · Average Bride And Groom... · Marriage Rates By Social...
[105]
100 Teen Slang Words and Phrases To Know in 2025
Feb 19, 2025 · Beta. Beta. Someone who is weaker, passive, not assertive. Example. “She's such a beta for letting him walk all over her.” 31. Cheugy. Cheugy- ...
[106]
Beta Meaning Slang in 2025: Examples & Safety Tips
Mar 9, 2025 · Unfortunately, some individuals use “beta” as an insult to belittle others, particularly in online spaces where cyberbullying is common.
[107]
[PDF] The manosphere, the red pill and alpha males: toxic masculinity in ...
Toxic masculinity began to be used as a category of analysis in the 1990s, referring primarily to relations between men and masculinities instead of between men ...
[108]
(PDF) Alphas, Betas, and Incels: Theorizing the Masculinities of the ...
The analysis reveals that, while there are some continuities with older variants of antifeminism, many of these new toxic assemblages appear to complicate the ...
[109]
Male Testosterone Linked to High Social Dominance but ... - PubMed
Boys perceived as socially dominant by unfamiliar peers were found to have concurrently higher levels of testosterone than boys perceived as less socially ...
[110]
https://codepoints.net/greek_and_coptic
[111]
https://fileformat.info/info/unicode/char/1d6fd/index.htm