What does the \var prefix stand for in \varphi and \varepsilon etc?

Question

What does the \var prefix stand for in \varphi and \varepsilon? Is it variable, or perhaps variant? I am thinking the latter, but it would be nice to clarify.

Sorry if this is an overly simple question. I am just after clarification.

Answer 1

There are several Greek characters that have different letter forms

• epsilon: ε or ϵ
• theta: θ or ϑ
• kappa: κ or ϰ
• pi: π or ϖ
• rho: ρ or ϱ
• sigma: σ or ς
• phi: φ or ϕ

In the list above, I put first the forms that Unicode classifies as letter, followed by the symbol form; not for sigma, where both shapes are actually used in common writing, the second one in final position.

I looked at all GFS fonts I have on my machine and the preferred form for phi seems to be the open one, except for GFS Porson (GFS is the Greek Font Society). The epsilon is lunate only in GFS Olga and GFS Porson. The theta is “open” in GFS Artemisia, GFS Bodoni, GFS Olga; it is “closed” in GFS Baskerville, GFS Complutum, GFS Didot, GFS Elpis, GFS Neohellenic, GFS Porson and GFS Solomos.

The variant of pi seems to be quite rarely used in common writing of Greek; however it is included in the math fonts because it was used as a math symbol. You know, mathematicians are always looking for new symbols!

What form to choose is a question of taste, maybe guided. My thesis advisor told me that there is just one form for rho (that is, ϱ). My own taste was immediately formed. ;-)

When assigning names, Knuth somewhat arbitrarily decided for “main form” and “variant form”, based on the tradition in scholarly studies in the US, very much influenced by the work of Richard Porson, after whom the GFS Porson font is named. So it's common in the US and UK to use the “lunate epsilon” and closed theta and phi; in continental Europe, the forms ε and φ are perhaps more common, as testified by the GFS fonts; for theta the situation is not so clearly distinguished. In Italian schools where Ancient Greek is taught, it's always ε ϑ, ϰ and ϕ.

The standard “member of” symbol comes directly from Peano, who used the (lunate) epsilon as abbreviation for ἐστί (is)

Eventually Knuth chose to use the Greek name, with the var prefix for what he considered to be variants of the main form:

• \varepsilon for ε and \epsilon for ϵ
• \theta for θ and \vartheta for ϑ
• \pi for π and \varpi for or ϖ
• \rho for ρ and \varrho for ϱ
• \sigma for σ and \varsigma for ς
• \varphi for φ and \phi for ϕ

for plain TeX and LaTeX followed suit. The Computer Modern fonts have just one form for kappa, but the package amssymb also provides \varkappa.

See also The history behind the broken epsilon for information about epsilon.

How to use the symbols?

In my opinion, one should stick with one of the letter forms; I'd avoid using both forms in one and the same document. If you want to follow Italian usage, do

\renewcommand{\epsilon}{\varepsilon}
\renewcommand{\theta}{\vartheta}
\renewcommand{\kappa}{\varkappa}
\renewcommand{\rho}{\varrho} % remember my teacher and friend Adalberto!
\renewcommand{\phi}{\varphi}

so changing back to the alternative letter form is just a matter of commenting out a line.

_{I know somebody would ask “Why not \let\phi\varphi?” Because \let is not a documented command in the LaTeX manual.}