Omega — Ω / ω
Ω ω
| Uppercase | Ω |
|---|---|
| Lowercase | ω |
| Transliteration | ō |
| Pronunciation | oh‑MEH‑ghah |
| Numeric value | 800 |
Etymology and Origin
Omega literally means "great O" (ὦ μέγα) to distinguish it from omicron ("little o"). It was the last letter added to the Greek alphabet around 800 BCE to represent the long "o" sound. The phrase "alpha and omega" (beginning and end) comes from the Christian Book of Revelation, where God declares "I am the Alpha and the Omega."
Pronunciation
- Ancient Greek: [ɔː] as long "o" in "door"
- Modern Greek: [o] as in "go"
- English usage: oh-MAY-guh or oh-MEE-guh [oʊˈmeɪɡə] or [oʊˈmiːɡə]
The Ohm - Unit of Electrical Resistance
The uppercase omega (Ω) is the standard symbol for ohm, the SI unit of electrical resistance, named after German physicist Georg Ohm. One ohm is defined as the resistance through which a current of one ampere flows when a potential difference of one volt is applied.
- Ohm's Law: V = IR, where R is measured in ohms (Ω)
- Common values: kΩ (kilohms), MΩ (megohms), mΩ (milliohms)
- Symbol origin: Chosen because Ohm starts with O, and Ω looks distinctive
Uses of Omega in Mathematics
- Big-Omega Notation: Ω(n) describes lower bound of algorithm complexity
- First Uncountable Ordinal: ω₁ in set theory
- Solid Angle: Ω measured in steradians
- Omega Constant: Ω ≈ 0.5671432904 (solution to Ω e^Ω = 1)
- Wright Omega Function: Inverse of f(w) = we^w
- Chaitin's Constant: Ω represents algorithmic probability
Uses in Science and Engineering
- Physics: Angular velocity (ω = 2πf), angular frequency
- Electrical Engineering: Impedance (measured in ohms Ω)
- Cosmology: Ω (density parameter) determines universe geometry
- Particle Physics: Omega baryon (Ω⁻), omega meson
- Biochemistry: Omega-3 and omega-6 fatty acids
- Astronomy: ω for argument of periapsis in orbital mechanics
Cultural and Symbolic Uses
- "Alpha and Omega": Beginning and end, used in Christianity
- Omega Watches: Luxury Swiss watchmaker (est. 1848)
- Fraternities/Sororities: Final letter, symbolizes completion
- Video Games: Omega Weapon (Final Fantasy), Omega symbol in Undertale
- Comics: Darkseid's Omega Effect (DC Comics)
- Brands: Often used to suggest finality, completion, excellence
Mathematical Examples with Omega
Ohm's Law: If V = 12V and I = 2A, then R = V/I = 6Ω
Angular velocity: ω = 2πf, where f is frequency in Hz
Big-Omega: Algorithm with runtime Ω(n²) takes at least quadratic time
Solid angle: Full sphere = 4π steradians ≈ 12.566 sr
Cosmology: If Ω > 1, universe is closed; if Ω < 1, universe is open
Copy Omega
Click the buttons below to copy the uppercase or lowercase letter to your clipboard:
Ω
ω
Unicode code points: U+03A9 (uppercase), U+03C9 (lowercase).
Writing Tips
- Uppercase Ω: Looks like a horseshoe or open circle with two feet extending downward
- Lowercase ω: Like a rounded "w" - three curved strokes forming valleys
- Common mistake: Don't confuse Ω with the astrological symbol for Aries (♈)
- Handwriting: Lowercase ω should have smooth, flowing curves - practice the three-bump shape
- Similarity: Uppercase Ω resembles inverted horseshoe magnet symbol
Interesting Facts
- Omega is the 24th and final letter of the Greek alphabet
- In ancient Greek numerals, Ω΄ = 800
- Omega Watches was the first watch worn on the Moon (1969, Apollo 11)
- Omega-3 fatty acids are essential nutrients found in fish oil
- "Alpha and Omega" appears in Revelation 1:8, 21:6, and 22:13
- The ohm symbol (Ω) was standardized in 1861
- Georg Ohm discovered his law in 1827 but faced initial skepticism
- Omega Nebula (M17) is a star-forming region in Sagittarius
- In horseshoes, omega-shaped shoes provide extra support