I'm currently writing my Masters thesis in English.
If I take some (small) German text snippets from some papers (I'm German-speaking) and just translate them into English, would this be plagiarism?
Secondly, if I have some English text snippet and just change most of the (specific) words, so that I didn't change the meaning, would this be plagiarism?
Thirdly, if I reuse math formulas (with the same variables etc.) is this plagiarism? What about just changing the variable names?
Well as most of the answers imply here, you should simply "cite" whatever that is not yours. What I mean by this is you should basically include references to snippets that you did not write and ones that you took from other sources. As long as you include proper citations, then you're on the safe side. (This basically refers to the idea of including a reasonable amount of translations to be cited, and by reasonable I'm referring to a paragraph, or two worth of translation.)
As for the translation you're asking about, you should also consider some sort of footnote at the bottom of the page where the translated text is, again to be on the safe side. The question is, are you going to literally translate the text you want or are you going to use an online translator for that because that's an important note, check the following blog post link for more info. (Note: It's an APA citation example for translated texts)
As for the math formulas you're asking about as well, again you should cite them because none of them are really yours (You're taking them from a source whether it's a research paper, or an online source, or a book for that matter). Regardless of changing the variables or not, you should always include citations to avoid falling in trouble.
I think the following link might be of help for you.
You seem to be asking for permission to plagiarize. Don't. Cite all of your sources in your bibliography.
It seems likely that your thesis advisor or chairperson explained this to you at some point. If you have more questions of this type, review the resources he or she gave you. Then, if it isn't covered, ask them in person.
If you use someone else's ideas in an academic paper without giving them credit, that is plagiarism.
If you have some hazy case and you're unsure, just give the original writer credit. It's easy to avoid committing plagiarism: just add a footnote. It's not that you can't use someone else's ideas. You just have to give the footnote.
You don't need to give credit for things that are "common knowledge". For example, if you say, "France is in Europe", you don't need to give a source. There are thousands of sources for that. When I was in school, I was taught that if you can find it in three sources, it's "common knowledge". That seems a little simplistic to me, but it might be a workable rule of thumb.
A math formula might or might not be common knowledge.
Note that plagiarism is not the same thing as copyright violation. If you're not sure of the difference, that's a different question.
For your first question:
This "translation" would likely be plagiarism. In academics, most researchers have a way to write and express ideas, independently of their writing language. Someone reading your paper, who is knowledgeable in your field (so most colleagues in your field), is likely to find the link between your 'translated ideas' from the original, with a resulting potential backfire on you, which would be a possibility even much later.
For example, a case along the lines of your was discussed here,
Further, when you submit your manuscript, some institutions, by default (mine is doing it), use commercial plagiarism detection software. If I created this type of software, I would include features to detect translations and plagiarism.
Second question: Please see the previous answer.
Third question: In my thesis there is a load of equations. I had some specificity in a context that required changing most variable names. But the meaning of the terms and what the equation does will of course not change the outcome of the equation (it is expected). Further, anyone reading your paper will guess, unless you are widely known to have developed yourself many of those equations, that you are a fraud, this without a software detecting plagiarism.
I would add another consideration when you are considering translation: copyright laws. Somewhat inconveniently, these vary from one jurisdiction to the other, so you will need to check that out.
You may need to obtain the copyright holder's permission to translate something, depending on the length of the passage and the reason you are using it. In some countries, such as the USA, you are allowed certain fair use, while in other countries there is no provision for fair use as such, unless you are using a work for criticism, parody and the like. Also, don't rely solely on the brevity of a text if you want to use it without permission. In poetry, for example, even a line or two may require permission.
Academic writing is about developing your own thougths and research, so yes, translation would probably be considered plagiarism, since it is not your own work (beside the translation part of course). I studied in Eastern Europe for a while and putting transtaled text without any references was the most popular way of cheating among students, since even Plagiarism Checkers couldn't recognize it as plagiarism. But yeah, it's definitely wrong, and they could've get into real trouble if cheating was revealed.
A math formula might or might be considered common knowledge, but it's better to use citation just to make sure you won't get in trouble.
