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Math? It’s all Greek to me

By Murray Bourne, 03 Apr 2008

Why is there so much Greek used in mathematics?

Did you know that...

α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ σ τ υ φ χ ψ ω
  • Greek (ελληνκα) is probably the oldest European language (spoken for 4000 years and in written form for 3000 years)
  • Greek was used across the Middle East and as far away as India during the Hellenistic Period (330 BCE to 100 CE). The early Christian writers used Greek and one passage says God is the "Alpha and Omega" (Α and Ω, the first and last letters of the Greek alphabet) to mean he is the beginning and the end
  • It was the official language of the Byzantine Empire (the Roman civilisation centred on Constantinople − present-day Istanbul in Turkey − 380 to 1483 CE) which stretched around most of the Mediterranean and the Middle East
  • Importantly (for its common use in mathematics), Greek was used widely for publishing scientific discoveries during the European Renaissance (15th century)

Common Greek letters used in mathematics

Probably the first Greek letter any of us come across is π (pi), the value we get from dividing the circumference of a circle by its diameter. Pi was chosen to stand for 'perimeter'.

Trigonometry makes great use of θ (theta) as a variable for angles and also in statistics.

A close runner-up for angles is phi (lower case: φ, upper case:Φ). Phi is also the symbol used for the Golden Ratio (1.618... See Math of Beauty.)

The first 3 letters of the Greek alphabet, α (alpha), β (beta) and γ (gamma) are also used in trigonometry as variables for angles. You'll also come across upper case gamma (Γ) as a variable, or as a function name.

The 24th and last letter of the Greek alphabet, omega (ω, upper case: Ω) is commonly used in electricity. The unit for resistance is ohms (Ω) and the angular velocity of an object rotating on an axis is written ω and the units are usually radians/second. (See Applications of radians.) O-mega means "big O".

In Scientific Notation we use mu (μ), for the prefix "micro" or 10-6. So for example, a human hair has width of about 50 μm.

Delta (δ, upper case: Δ) is used a lot when writing about differentiation in calculus. It often means "a small change in" a quantity. So δx (or Δx) means "a small change in x". The 5th Greek letter ε (epsilon) is also used in calculus to mean "an extremely small quantity - almost zero".

Next up is lambda (λ, upper case: Λ) which is used for the wavelength of a periodic wave.

You'll come across sigma in probability and statistics. Upper case sigma (Σ) is used for "sum" (see Summation Notation) and lower case (σ) is used for the standard deviation of a population measure in statistics.

The density of an object is represented by rho (ρ, upper case: Ρ). Rho is also used in spherical polar coordinates to represent the radius.

Less commonly used Greek letters

You usually only see the following Greek letters in university-level mathematics. As such, they are more difficult to remember (and some of them are difficult to pronounce!). Hopefully this list of Greek letters (with their common letter-name pronunciations in English, not necessarily how the Greeks pronounce them) will help you.

Zeta, pronounced 'zeeta': Ζ, ζ - the 6th letter of the alphabet (not the last)

Eta, pronounced 'eeta': Η, η

Iota, pronounced 'eye-oh-ta': Ι, ι - used in the English saying "not one iota of difference" to mean "almost identical".

Kappa: Κ, κ

Nu, pronounced 'noo': Ν, ν

Xi, pronounced 'sigh': Ξ, ξ

Omicron: Ο, ο - O-micron means "small O". (Remember O-mega, or "big O" above?)

Tau, rhymes with 'how': Τ, τ - see Series R-L Circuit for one use of Tau as a unit of time.

Upsilon, pronounced 'oops-i-lon': Υ, υ

Chi, pronounced 'kai' rhymes with 'eye': Χ, χ

Psi, pronounced 'sigh' (yes, the same as Xi): Ψ, ψ - as used in the words psychology and psychiatry - the "p" is usually silent.


So now, after all that, hopefully you are in mathematical utopia. The word "utopia" comes from the Greek for "no where."

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