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We often use that to connect two sentences. I want to pause somewhere when the sentence is long and complicated. Where do I pause in the following sentence? Before that or after that?

The Pythagorean theorem states that given a right triangle the square of the side opposite the right angle is equal to the sum of squares of the other two sides.

Moreover, I want to add commas.

The Pythagorean theorem states that given a right triangle, the square of the side opposite the right angle is equal to the sum of squares of the other two sides.

I want to add a comma around that, but somehow it seems weird. Is it OK to put one there? On the other hand, if I don't put comma it seems also weird, because the above sentence is basically the combination of two sentences before that and after that.

[Edit]: Thanks for many answers. It's hard for me to choose best one, so I guess it's better to leave it to users. Still I am not sure if I can pause around that, but it seems it's after that if it's allowed. And for commas, is it correct to think that I may pause even if there is no comma, but I must pause at a comma?

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  • Yes. In my opinion, you absolutely should have a comma there. I put commas wherever I find myself pausing/breathing in speech. However, I see many people not using commas very often, and in school, students are often discouraged from "breaking the flow" of the sentence with commas. I think they serve to make the sentence clearer, especially logically.
    – Alex K
    Dec 16, 2015 at 7:10
  • You can read more about commas here: owl.english.purdue.edu/owl/owlprint/607
    – Alex K
    Dec 16, 2015 at 7:21
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    You can write: The Pythagorean theorem states that, given a right triangle, the square of the side opposite the right angle is equal to the sum of squares of the other two sides.
    – user20792
    Dec 16, 2015 at 11:26
  • Let's pause for a moment, shall we? Here's an interesting Google query related to your introduction: comma for pauses myth. That will direct you to sites like this one and this one, which explain why I bristled when I saw that this question asks about pauses and commas – as though the two should maybe be tied together.
    – J.R. ♦
    Dec 17, 2015 at 0:05

3 Answers 3

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The Pythagorean theorem states that given a right triangle the square of the side opposite the right angle is equal to the sum of squares of the other two sides.

We put a comma after triangle and then we explain on what consists the theorem:

The Pythagorean theorem states that given a right triangle, the square of the side opposite the right angle is equal to the sum of squares of the other two sides.

Also, the other way you were provided below your question by NES also works:

The Pythagorean theorem states that, given a right triangle, the square of the side opposite the right angle is equal to the sum of squares of the other two sides.

This emphasises that it's important to have a right triangle.
Often, you'll see the theorems written where commas are placed on different parts of the text to emphasise some hypothesis and then to explain on what the theorem consists.

As a side note, we normally capitalise the t on theorem, as being an important result.

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The sentence is correct and understandable without any commas, although long. Your sense of breaking up the sentence in to smaller pieces is well placed, however you will need to use two commas to create a subordinate clause:

1) The Pythagorean theorem states that,
2) given a right triangle,
3) the square of the side opposite the right angle is equal to the sum of squares of the other two sides.

The sentence will still make sense without the subordinate clause (though becomes mathematically ambiguous, since a right triangle is necessary):

1) The Pythagorean theorem states that,
2) the square of the side opposite the right angle is equal to the sum of squares of the other two sides.

this may create the pause after that which you may be considering.

An alternative might be to use a ":"(colon), to mean note hereafter :

1) The Pythagorean theorem states, that given a right triangle:
2) the square of the side opposite the right angle is equal to the sum of squares of the other two sides.

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  • For some reason, when I say this, I say it without the comma after the "that." I think this may be because commas are indicative of logical pauses - they help separate the sentence out into logical chunks. To me, the "given a right triangle" part is required mathematical information that is needed for the sentence to make sense, not just an aside, so I don't treat it as such. Just an interesting sidenote.
    – Alex K
    Dec 16, 2015 at 7:20
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    It's a little confusing for me. The rule 4 in Alex's link says Do not use commas to set off essential elements of the sentence, such as clauses beginning with that. Does it mean that I should not pause there?
    – Hwang
    Dec 16, 2015 at 7:45
  • @Lucian Sava: sorry, I couldn't understand. One example in the link is She believes that she will be able to earn an A. Doesn't the sentence have the same structure as The theorem states that ...?
    – Hwang
    Dec 16, 2015 at 8:12
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    @Hwang I would never write versions 2 or 3 that Peter gives here. Version 2 is bad because of the rule you indicate, and Version 3 is just plain awkward.
    – user20792
    Dec 16, 2015 at 11:24
  • As a former mathematician, we wouldn't break up a theorem with a single fact. Normally this is done when the hypothesis of the theorem provides more results or when the propositions are equivalent.
    – Schwale
    Dec 16, 2015 at 12:30
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Unfortunately there is no way to put a comma by "that" which doesn't break a rule. The best way to add a pause is probably to rearrange the sentence.

Given a right triangle, the Pythagorean theorem states that the square of the side opposite the right angle is equal to the sum of squares of the other two sides.

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  • I believe this statement is inaccurate. Adding a comma after "that," as in "The Pythagorean theorem states that, given a right triangle, the square of the side opposite the right angle is equal to the sum of the squares of the other two sides" is a sentence that is grammatically valid and mathematically correct, although it's meaning is very slightly different than the version without the comma.
    – Ryan Jensen
    May 31, 2019 at 18:06
  • To elaborate; the sentence so constructed has the same basic form (the Pythagorean theorem states [the Pythagorean theorem]), and uses an unnecessary phrase to clarify. Omitting the phrase results in a statement that is both true and grammatically complete; the fact that the Pythagorean theorem is operative only on right triangles is apparent without being explicitly stated, as otherwise there could not be both "the side opposite the right angle" and "the other two sides."
    – Ryan Jensen
    May 31, 2019 at 18:12

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