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Several papers that I have read only indent paragraphs that are not the first paragraph of a section:

1.1 Introduction

This is the first paragraph.

    This is the second paragraph.

    This is the third paragraph.

Is this a common convention? Are there rules for when to indent like this?

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    Yes, it's a fairly common typographical convention. It generally looks nicer, but someone with a better knowledge of typography (there should be at least one copy editor around here) can probably give you a sounder reason for that.
    – Massimo Ortolano
    Jan 29 '16 at 22:30
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    I'm voting to close this question as off-topic because it is about typsetting and has nothing to do with academia. Jan 30 '16 at 7:56
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Copied from this answer on writers.SE:

[...] in Robert Bringhurst's Elements of Typographic Style, he states that "opening paragraphs" should be "flush left" because "[t]he function of a paragraph indent is to mark a pause, setting the paragraph apart from what precedes it. If a paragraph is preceded by a title or subhead, the indent is superfluous and can therefore be omitted".

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    "to mark a pause, setting the paragraph apart from what precedes it" - a more tangible reason is to tell apart a mid-paragraph pagebreak from one that coincides with a new paragraph, while looking at the second page. Jan 30 '16 at 11:32

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