# Phi, The Greek Letter, and It's Use in Mathematics

In the following inequality

$$\frac{1+c}{a+b}\leq\varphi$$

how do I say it in English?

I think that I should say: "The ratio of the sum of $1$ and $c$ to the sum of $a$ and $b$ is less than or equal to phi."

Is the Greek letter, phi, used to represent the golden ratio so that the meaning of the inequality is, "The ratio of the sum of $1$ and $c$ to the sum of $a$ and $b$ is less than or equal to the golden ratio."

• Looks like it in this case. Capital phi $\phi$ is usually used for denoting Euler's totient function. – barak manos Feb 1 '15 at 14:40
• I'd say it depends on the context. If you were to bring this up during teaching (which I'm assuming by the education tag), and it's the first time mentioning phi as the golden ratio you could say "The ratio of the sum of 1 and c to the sum of a and b is less than or equal to phi, where phi here is the golden ratio." Then the rest of the lecture you could just use phi. – PawnInGameOfLife Feb 1 '15 at 14:42
• Capital phi is this: $\Phi$. These two are merely alternate forms of the same thing: $\phi, \varphi$ – GEdgar Feb 1 '15 at 14:43
• – Lucian Feb 1 '15 at 15:29
• In fact capital $\Phi$ and lower case $\phi$, $\varphi$ were all alternate forms of the same thing up until the Renaissance en.wikipedia.org/wiki/Greek_alphabet#Letter_shapes. – Lee Mosher Feb 1 '15 at 16:13

Say: "One plus cee over ay plus bee is at most equal to phee$\ \ldots$"$\ \$ If $\phi$ has been defined before (e.g., is an angle in some figure) that's it. If $\phi$ is meant to be the golden ratio, close your sentence with "where phee is the number $(\sqrt{5}-1)/2$, also called golden ratio".