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...
- 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."
See the 7 Comments below.
4 Apr 2008 at 8:58 am [Comment permalink]
Oh those darn Greek letters, I don't understand why they cause the students to freeze. My seniors have now got me saying fish when I see α. I've mostly given up. It's just a name.
4 Apr 2008 at 7:57 pm [Comment permalink]
Should we continue to use so much Greek in mathematics?
I tend to avoid the least common Greek letters unless it breaks with strong conventions.
But I think it is reasonable for students to learn "alpha", already!
5 Apr 2008 at 3:38 am [Comment permalink]
I agree it is reasonable for students to learn "alpha" (I still remind them that it really isn't a fish). However getting them to learn the Greek letters is not my main goal.
You ask if we should we continue to use so much Greek in math. I don't know. What do you propose we use instead? There are times when I use other symbols instead. I've labeled angles as * or :), just to show them that the Greek letters aren't "magic". Then we go back to using the standard notation.
5 Apr 2008 at 11:19 am [Comment permalink]
Not forgetting ...
Ï‡ is used in a certain probability distribution.
ξ (and sometimes Î¶ since they look rather similar) is commonly used to represent the Universal Set in Venn Diagrams.
Lastly φ is used to distinguish Jφss Sticks from joss sticks! Sorry just had to do this! 😀
5 Apr 2008 at 11:31 am [Comment permalink]
JackieB: As an example of alternatives to Greek, I use h instead of Δx in the introduction to differentiation from first principles.
I used to find that students' eyes glaze over less if the notation is simpler.
Miss Loi: Thanks for your additions. That issue about Xi and Zeta looking very similar is one reason I avoid them.
And oh yeah - how could I forget to mention Jφss Stick's use of φ ? 🙂
5 Mar 2018 at 1:11 am [Comment permalink]
[…] This is a secular holiday. Not celebrating it is a missed opportunity to let students have FUN with math. So many kids dread math, think it’s tedious, boring, or “too hard.” Experiencing math in a fun setting is a way to light a fire of math love in kids. You can choose the level of rigor your students can handle. It may be that hands-on activities are the way to go, or they may be able to work with formulas. Language opportunities are another reason to celebrate Pi Day - where does “pi” come from, and why do we use Greek letters in math? […]
19 Dec 2019 at 7:57 pm [Comment permalink]
[…] great-granddaddy of all modern European alphabets, the Greek alphabet is used around the world, even by people who don’t speak any Greek. […]