Should there be a period after an equation?

This isn't a pure English question, but it is about writing style: Sometimes entities that aren't words end up being in sentences.

I know that when mathematical expressions are inline as follows:

We used the equation x + y = z. This is the next sentence.

they are treated as any other word, and the sentence needs to end with a period.

But suppose I have text in a paper such as:

We used the equation

x + y = z

This is the next sentence.

Notice that the equation isn't inline. Should there still be a period after the equation (right after z) to indicate the end of the sentence?

I don't know if LaTeX is considered a definitive source for mathematics writing style (although it was developed for typesetting math equations), but this link and this one seem to indicate that, yes, a period would be inserted after the equation in the example

We used the equation

x + y = z.

This is the next sentence.

The Wikipedia Manual of Style (Mathematics), which cites several published mathematics style guides, offers this wisdom (emphasis added by me):

Just as in mathematics publications, a sentence which ends with a formula must have a period at the end of the formula. This equally applies to displayed formulae (that is, formulae that take up a line by themselves). Similarly, if the conventional punctuation rules would require a question mark, comma, semicolon, or other punctuation at that place, the formula must have that punctuation at the end.

The reference for this section is Higham, Nicholas J. (1998), Handbook of Writing for the Mathematical Sciences (second ed.), SIAM, ISBN 0-89871-420-6. The notation states that this is the style adopted by "many mathematics journals," so it is probably a safe choice.

Alternatively, you could use

We used Equation 1.

Equation 1.

x + y = z

This is the next sentence.

For there to really be a "should" means that you're following some particular style guide/typographical charter that specifies either way. If you're not following such a style guide, or it doesn't specify either way, then I would suggest:

• it's unusual, and looks a little jarring, to omit a full stop at the end of what is still a sentence at the end of the day;
• so, if it doesn't look more jarring/confusing to add the full stop, add the full stop;
• if it looks jarring to add the full stop, rearrange your sentence so that the equation isn't at the end.

I write a fair amount in the area of computing, and a similar issue arises with things like variable names, method names etc occurring at the end or indeed beginning of a sentence. I often find myself ending up opting for the latter option.

In mathematics and physics papers, the equations are viewed as part of the sentence. If they come at the end of a sentence, they should have periods after them. I know I have seen some papers where they put equations on separate lines, not considering them part of the sentence. You should check the style of other papers in the same area to decide which style to use.

No, but I would change "the" to "this" and add a colon after the start of the sentence.

We used this equation:

x + y = z

This is the next sentence.

Think of it this way: if the equation was a photograph, you wouldn't add a period, right?