Gamma — Γ / γ
Γ γ
| Uppercase | Γ |
|---|---|
| Lowercase | γ |
| Transliteration | g |
| Pronunciation | GHAH‑mah |
| Numeric value | 3 |
Etymology and Origin
The name "gamma" comes from the Phoenician letter "gimel," which meant "camel" (referring to the camel's neck). The uppercase gamma (Γ) resembles an upside-down L shape. Gamma is the third letter of the Greek alphabet and third in line after alpha and beta.
Pronunciation
- Ancient Greek: [g] as in "go"
- Modern Greek: [ɣ] (voiced velar fricative) or [ʝ] before front vowels
- English usage: GAM-uh [ˈɡæmə]
The Gamma Function
One of the most important mathematical functions, the gamma function Γ(z) extends the factorial to complex numbers. For positive integers: Γ(n) = (n-1)! The gamma function appears throughout mathematics, from combinatorics to probability theory.
- Definition: Γ(z) = ∫₀^∞ t^(z-1) e^(-t) dt
- Key property: Γ(z+1) = z·Γ(z)
- Special values: Γ(1/2) = √π, Γ(1) = 1
Uses of Gamma in Mathematics
- Gamma Function: Γ(n) = (n-1)! for positive integers
- Euler-Mascheroni Constant: γ ≈ 0.5772... appears in number theory
- Christoffel Symbols: Γⁱⱼₖ in differential geometry and general relativity
- Third Angle: After α and β in geometry
- Gamma Distribution: Probability distribution in statistics
- Feferman-Schütte Ordinal: Γ₀ in proof theory
Uses in Science and Engineering
- Nuclear Physics: Gamma rays (γ-rays), highest energy electromagnetic radiation
- Particle Physics: Photons represented by γ
- Thermodynamics: γ = Cp/Cv (heat capacity ratio, adiabatic index)
- Special Relativity: Lorentz factor γ = 1/√(1-v²/c²)
- Surface Tension: γ (surface energy per unit area)
- Electrical Engineering: Propagation constant, conductivity
- Optics: γ-correction in image processing
Cultural and Symbolic Uses
- Fraternities/Sororities: Gamma Phi Beta, Delta Gamma, many others
- Photography: Gamma correction adjusts brightness/contrast
- Astronomy: Third brightest star in constellations (e.g., Gamma Cephei)
- Military: Third classification after alpha and beta
- Incredible Hulk: Gamma radiation created the character
Mathematical Examples with Gamma
Gamma function: Γ(5) = 4! = 24
Euler constant: γ = lim(n→∞) [1 + 1/2 + 1/3 + ... + 1/n - ln(n)] ≈ 0.5772
Lorentz factor: At v = 0.5c, γ = 1.15 (time dilation factor)
Heat capacity ratio: For ideal diatomic gas, γ = 1.4
Reflection formula: Γ(z)Γ(1-z) = π/sin(πz)
Copy Gamma
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Γ
γ
Unicode code points: U+0393 (uppercase), U+03B3 (lowercase).
Writing Tips
- Uppercase Γ: Like an upside-down L or right angle - vertical stroke with horizontal stroke extending right at top
- Lowercase γ: Like a "y" with a loop - descends below baseline with curved tail
- Common mistake: Don't confuse uppercase Γ with Latin L - Gamma has top bar, L has bottom
- Handwriting: Lowercase γ is one of the more distinctive Greek letters with its descender loop
Interesting Facts
- Gamma is the ancestor of the Latin letter C (and indirectly G)
- In ancient Greek numerals, Γ΄ = 3
- Gamma rays were discovered by Paul Villard in 1900
- The Euler-Mascheroni constant γ is one of mathematics' most mysterious numbers
- Gamma-ray bursts are the most energetic events in the universe
- The gamma function was introduced by Leonhard Euler in 1729
- Gamma correction was crucial for early television displays
- In relativity, γ approaches infinity as velocity approaches speed of light
- Gamma Cephei was one of the first stars discovered to have an exoplanet (1988)