# According to which authoritative source, where in a conventionally ordered list of constants does $\pi$ go? (Eg, “$h\pi$” vs “$\pi h$”)

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Where in a conventionally ordered list of constants does $$\pi$$ go?

For example, if you look at the attached image, you can see that in my last answer, I’ve put $$h \pi$$. But in the answer section of the book I’m working out of, they put $$\pi h$$.

I’ve read that constants ($$ABCDEFG$$, etc…) should be ordered alphabetically, but how about for symbolic/non-variable constants (or whatever the correct terminology is) such as $$\pi$$, $$\phi$$, $$i$$, and $$e$$?

Is there any such rule for this?

Strictly speaking, it is mostly subjective; $$h\pi\equiv\pi h$$, so neither of them are wrong. But, some things just look nicer.

Of course, nobody is going to write $$x17\ (17x)$$, $$e^x2\ (2e^x)$$, or $$\pi3\ (3\pi)$$. But, it seems perfectly fine (to my eyes) to write $$e^xy$$ or $$\pi\sqrt6$$.

To make this slightly less biased, I did some tests on a Casio fx-82AU PLUS II. In the following table, I enter the expressions exactly as I entered them into the calculator. "N" means that the expression returned a syntax error and "Y" means that it evaluated. $$\begin{array} {|r|r|} \hline \text{Expression} & \text{Evaluated?} \\ \hline 3\pi & Y \\ \hline \pi3 & N \\ \hline (\pi)(3) & Y \\ \hline (\pi)3 & N \\ \hline \pi(3) & Y \\ \hline \pi\log6 &Y \\ \hline \log(6)\pi &Y \\ \hline \pi\sqrt6 &Y \\ \hline \sqrt6\pi & Y \\ \hline \frac23\pi & Y \\ \hline \pi\frac23 & Y^1 \\ \hline |3|2 & N \\ \hline |3|(2) & Y \\ \hline \pi|3|\pi & Y \\ \hline \pi|3|\pi\sqrt3e & Y \\ \hline \pi|3|\pi\sqrt3e\frac23 & Y^1 \\ \hline \end{array}$$ $$^1$$The calculator automatically added brackets around the fraction when I pressed $$=$$, for example the screen said $$\pi\left(\frac23\right)$$.

$$3\pi$$ looks better than $$\pi3$$, but $$\pi r^2$$ looks better than $$r^2\pi$$. $$a+bi$$ is the usual form for a complex number, but you'll almost always see $$e^{i\pi}+1=0$$, not $$e^{\pi i}+1=0$$. But (as mentioned in the comments), $$e^{2\pi i}$$ is preferred over $$e^{i2\pi}$$, although we write $$e^{i\theta}$$ not $$e^{\theta i}$$.

Basically, there is no precise set of rules to follow when ordering things. (Assuming the operation is commutative, that is.) The way I usually see things done is: if you're dealing with the Latin alphabet, write in alphabetical order. Usually, integers or fractions (put the integers in the fractions (multiply) if there are fractions) go first, numbers with "operations" ($$\sqrt,\ \log,\ \tan$$, etc.) go next, and variables go last.

Of course, this won't always work, just write whatever looks the neatest and conveys what you're trying to say the clearest. To avoid any possibility of ambiguity, use brackets; brackets also seem to "soften the blow" of bad ordering; $$x17$$ just looks disgusting, whereas $$(x)(17)$$ is acceptable.