Mu — Μ / μ
Μ μ
| Uppercase | Μ |
|---|---|
| Lowercase | μ |
| Transliteration | m |
| Pronunciation | mee |
| Numeric value | 40 |
Etymology and Origin
Mu comes from the Phoenician letter "mem," meaning "water." The uppercase mu (Μ) looks identical to the Latin letter M, and both descended from the same ancient source. Mu is the twelfth letter of the Greek alphabet and represents the "m" sound, unchanged from ancient to modern Greek.
Pronunciation
- Ancient Greek: [m] as in "mother"
- Modern Greek: [m] as in "mother" (unchanged)
- English usage: MYOO [mjuː]
Mu as the Micro- Prefix
The lowercase mu (μ) is used as the symbol for the metric prefix "micro-" (μ), meaning one millionth (10⁻⁶). This is one of the most common uses of mu in everyday science and engineering, appearing in measurements from micrometers to microseconds to micrograms.
- Micrometer: 1 μm = 10⁻⁶ m = 0.000001 meters
- Microsecond: 1 μs = 10⁻⁶ s (one millionth of a second)
- Microgram: 1 μg = 10⁻⁶ g (common in chemistry and medicine)
- Microampere: 1 μA = 10⁻⁶ A (electrical current)
Uses of Mu in Mathematics and Statistics
- Population Mean: μ represents the true mean of a population in statistics
- Expected Value: E[X] = μ for random variable X
- Möbius Function: μ(n) in number theory (values -1, 0, 1)
- Measure Theory: μ for general measure in advanced analysis
- Normal Distribution: N(μ, σ²) with mean μ and variance σ²
Uses in Science and Engineering
- Coefficient of Friction: μ = F_friction/F_normal (μ_s = static, μ_k = kinetic)
- Magnetic Permeability: μ₀ = 4π × 10⁻⁷ H/m (permeability of free space)
- Dynamic Viscosity: μ in fluid mechanics (Pa·s)
- Particle Physics: μ⁻ (muon), an elementary particle like heavy electron
- Reduced Mass: μ = m₁m₂/(m₁+m₂) in two-body problems
- Chemical Potential: μ in thermodynamics
- Amplification Factor: μ in vacuum tube electronics
Coefficient of Friction
- Definition: μ = F_friction/F_normal, dimensionless ratio
- Static Friction: μ_s typically 0.5-1.5 (prevents sliding)
- Kinetic Friction: μ_k typically less than μ_s (during sliding)
- Examples: Ice on ice μ ≈ 0.02, rubber on dry concrete μ ≈ 1.0
Mathematical Examples with Mu
Micrometer: Human hair diameter ≈ 50-100 μm
Population mean: If SAT scores have μ = 1050, that's the true population average
Friction: 10 kg block, μ_s = 0.6: Maximum static friction = 0.6 × 10 × 9.8 = 58.8 N
Magnetic permeability: B = μ₀H relates magnetic field B to H-field
Muon lifetime: μ⁻ has mean lifetime τ ≈ 2.2 μs before decay
Writing Tips
- Uppercase Μ: Identical to Latin M - two vertical strokes connected by V at top
- Lowercase μ: Like "u" with tail extending below baseline on left
- Common mistake: Don't confuse μ with "u" - mu has descender on left side
- Handwriting: Start lowercase μ like "u", then extend left stroke downward
Interesting Facts
- Mu is the ancestor of the Latin letter M
- In ancient Greek numerals, Μ΄ = 40
- The muon (μ⁻) is about 207 times heavier than an electron
- Magnetic permeability μ₀ is an exact defined constant in SI units
- Human eye can resolve details down to about 100 μm without magnification
- Typical bacteria are 1-10 μm in length
- In Zen Buddhism, "mu" (無) means "nothingness" (different origin)
- The Möbius function μ(n) is multiplicative and crucial in analytic number theory
- Rubber on concrete has one of the highest friction coefficients (μ ≈ 1.0)
- Muons created in upper atmosphere reach Earth's surface due to time dilation
Copy Mu
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Μ
μ
Unicode code points: U+039C (uppercase), U+03BC (lowercase).