# How to draw greek letters on paper / blackboard?

For $\gamma$ (gamma), I've noticed people doing a sort of $\alpha$ (alpha) rotated by ninety degrees, which seems to be the standard on-paper-or-blackboard equivalent of $\gamma$.

But for letters like $\zeta$ or $\xi$, I'm stumped. Anyone have any advice?

On an unrelated note, I've noticed that there are two lower case phis: $\phi$ (\phi) and $\varphi$ (\varphi) ... these are used interchangeably by some physics professors - is there any history or convention relating to these two phis?

EDIT: There are also two lower case epsilons: $\epsilon$ (\epsilon) and $\varepsilon$ (\varepsilon). I've noticed most mathematicians write the second epsilon on paper or on blackboards, and that makes sense; it's easier to draw.

• I write zeta and xi exactly the same (well anyway as near as I can) as their printed versions. I'm not sure why anyone would want to do anything different, but perhaps I misunderstood your question. – David Nov 19 '14 at 13:00
• I walked past the office of a Ph.D. student I know a few weeks ago, and his blackboard was full of attempts at drawing $\xi$. He still didn't have it down. I am also convinced that one of my first lecturers thought of $\xi$ as a downward zig-zag squiggle. They were not in any way consistent. – Arthur Nov 19 '14 at 13:02
• One of the advantages of using Greek letters as variables in math, from personal observation, is that most letters can be written with a single continuous stroke of the pen, which helps with speedy writing, e.g. $\alpha, \gamma, \delta, \varphi, \vartheta, \rho,\sigma , \nu$. However, this is not quite the case with $\zeta$ or $\xi$! (PS - one wonders if the actress signs off as Catherine $\zeta$-Jones... :)) – hypergeometric Nov 19 '14 at 14:37
• mathoverflow.net/a/5968/3948 – Willie Wong Nov 19 '14 at 14:40
• I was once present for a conversation between a professor who was teaching a class which was open to “graduate students, or undergraduates with mathematical maturity” and an undergraduate who wasn't sure if he had ‘mathematical maturity’. “Well,” asked the professor, “can you write a lowercase zeta?” – MJD Nov 19 '14 at 17:23

This site about modern Greek has a guide for handwriting the Greek letters apparently based on how people actually write in modern Greece and Cyprus.

It can sometimes be useful to think about how the lowercase letter might have developed from the uppercase letter through people attempting to write it faster, smaller and without lifting the pen off the page.

The uppercase zeta is just a Z and when writing it smaller and faster you can imagine emphasising the angle at the top and curving the angle at the bottom, then adding a little kick so it doesn't look like a 7. The uppercase xi is three horizontal lines and the lowercase xi is an attempt to draw these three horizontal lines without lifting your pen, but in the end is just a zeta with an extra kink in the middle.

Lowercase sigma is a bit tricky to make it not look like a 6 and I still haven't perfected that yet. The webpage above draws the circle anticlockwise and then changes direction to put the top line. I see other people drawing something like a capital u starting from the right hand side and then making a sharp bend (but not a kink) to draw the flat top. I like to start at the far right and draw the flat top right-to-left then do the loop, imagining that you started to write a capital sigma from the top but then gave up after the first bend.

Concerning epsilon, I don't like to use $\epsilon$ because it looks too much like the "in" symbol $\in$. It also really really bugs me when people use the curly epsilon instead of an in symbol.

Finally I have noticed the use of the two phis, but never both by the same lecturer. I would not recommend indiscriminately switching between them but sticking to one so as not to confuse whoever was watching.

• I have seen $\phi$ and $\varphi$ used by the same lecturer in the same lecture (in physical chemistry). One was pronounced "fee" and the other "fie". I found this lecture essentially impossible to follow because I thought of those two glyphs as interchangeable. – Michael Lugo Nov 19 '14 at 19:08
• very nice link +1! One cannot add much to it. – Jimmy R. Nov 20 '14 at 10:40
• Two Greeks I know have disagreed on this description of writing lowercase sigma. I have to admit this way is easier for me to produce good looking sigmas, but it doesn't seem to be authentic. – PrimeRibeyeDeal Jun 29 '15 at 21:37
• Which of the three descriptions of lowercase sigma are you referring to? – DavidButlerUofA Jun 29 '15 at 22:45
• @MichaelLugo - and two other alternative representations pronounced "fo" and "fum"? :) – hypergeometric Dec 19 '16 at 16:22