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How to decide when \left( and \right) are necessary?

Here is my code that shows various ways to format the same formulae:

\documentclass{article}
\begin{document}
Example 1.1:
\[
    \frac12 \left( p + \frac{((a + b)^2 + c)^2}{2} \right)
\]

Example 1.2:
\[
    \frac12 \left( p + \frac{\left( (a + b)^2 + c \right)^2}{2} \right)
\]

Example 1.3:
\[
    \frac12 \left( p + \frac{\left( \left( a + b \right)^2 + c \right)^2}{2} \right)
\]

Example 2.1:
\[
    \frac12 \left( p + \frac{((a + b)^2 + \frac12)^2}{2} \right)
\]

Example 2.2:
\[
    \frac12 \left( p + \frac{\left( (a + b)^2 + \frac12 \right)^2}{2} \right)
\]

Example 2.3:
\[
    \frac12 \left( p + \frac{\left( \left( a + b \right)^2 + \frac12 \right)^2}{2} \right)
\]
\end{document}

Here is the output:

enter image description here

Among examples 1.1, 1.2, and 1.3, is there a preferred format?

Among examples 2.1, 2.2, and 2.3, is there a preferred format?

How do you decide when we need to employ \left( and \right) to format formulas? Is it just a matter of taste or are there any typography rules for it?

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7
  • 1
    In this particular case, probably the best way to typeset is \frac{1}{2} \biggl( p + \frac{\bigl( (a + b)^2 + \frac{1}{2} \bigr)^2}{2} \biggr) or \frac{1}{2} \biggl( p + \frac{\bigl( (a + b)^2 + 1/2 \bigr)^2}{2} \biggr); that is, not a single \left...\right pair…
    – Ruixi Zhang
    Jul 5, 2020 at 21:02
  • A general guideline: Use \left...\right for “genuinely large” blocks of maths (matrices, for example). Try to use \bigl, \bigr, etc. based on the hierarchy of the nested parenthesized expressions (and to gain complete control on how large the delimiters should grow). This is indeed “just a matter of taste”, but there are good and bad taste. Also, it depends on the journal/editor style…
    – Ruixi Zhang
    Jul 5, 2020 at 21:11
  • IMHO in case 2.x \frac {1} {4} \bigl( 2p +.... and getting rid of the inner fraction leads to a much more readable thing, unless you want to highlight that p +... thing. Basically, the best way to typeset a math formula depends on the context, and where you want to out the accent... Including brackets' size.
    – Rmano
    Jul 5, 2020 at 22:10
  • please write \frac{1}{2} !!
    – David Carlisle
    Jul 5, 2020 at 22:29
  • 1
    @LoneLearner the latex syntax as specified in the latex book says the braces (for all commands) are mandatory. When using tex you can drop them but it looks weird/horrible if done with a command like frac that can take arbitrary content (it's OK with commands that can only take a single token,\setlength\textwidth{..} instead of \setlength{\textwidth}{...} but as it essentially is only happening due to low level parsing rules, it will often fail in latex2xx convertors eg conversion to html, as they do not have a full tex parser and normally expect some reasonable markup for the arguments.
    – David Carlisle
    Jul 6, 2020 at 14:23

1 Answer 1

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3

If you can get yourself to replace all (direct or indirect) instances of \frac12 with 0.5, some obvious ways arise to display both terms much more compactly and -- I would argue -- more legibly. I will call these ways "Example 1.4" and "Example 2.4", respectively. Observe that they employ \mleft and \mright instead of \left and \right for improved, i.e., more-compact spacing.

enter image description here

\documentclass{article}
\usepackage{mleftright} % for \mleft and \mright macros
\begin{document}
Example 1.4:\quad $0.5 \mleft( p + 0.5[ (a+b)^2 + c ]^2 \mright)$

\bigskip
Example 2.4:\quad $0.5 \mleft( p + 0.5[ (a+b)^2 + 0.5 ]^2 \mright)$
\end{document}
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  • 1
    usually (for different reasons) in mathematics I have been involved in, 0.5 and 1/2 aren't the same thing:-)
    – David Carlisle
    Jul 5, 2020 at 22:34

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