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Often a relevant image can supplement an answer and make it better. Sometimes I add a graph which is created using free tools like Matplotlib, but this can take a little while. I was wondering if it is allowed to draw the graph of a function using some online graphing calculator such as Desmos or WolframAlpha (or any other one) and add that image to the answer? If yes, should I attribute it in some way? I tried reading the Desmos terms of use but I was unable to reach a definite conclusion. WolframAlpha's terms of use have been clearer to understand and I think they would allow using their graphs on MSE if we add an attribution, but I'm not sure. My question is therefore threefold:

  1. Am I allowed to post graphs generated by Desmos and WolframAlpha as parts of answers?
  2. Are there other online graphing calculators that are easy to use and that allow incorporating their graphs without attribution?
  3. In case I should attribute those graphs to the graphing calculator which generated them, what would be the least intrusive way of doing so? Should one add a note at the end of the answer (or at a comment?). Would it be possible to add a tooltip when one moves their cursor over the image, or is there any other better idea?
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    $\begingroup$ What about this part: "Desmos does not claim ownership of any materials (other than the underlying software and other materials of Desmos and its licensors used to generate such materials), lessons, formulae, information, data, text or other materials you submit and create for display or distribution to others through the Desmos Services, or the graphs generated therefrom (collectively, “User Submissions and Generated Materials”). " (Emphasis mine) $\endgroup$ Apr 15 at 9:31
  • $\begingroup$ @CalvinKhor Great find. So seems they are saying we can use their graphs freely without any attribution? $\endgroup$
    – Snaw
    Apr 15 at 9:33
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    $\begingroup$ I think so, yes. Personally I have always given the link because the interactivity adds a rich experience $\endgroup$ Apr 15 at 9:34
  • $\begingroup$ @CalvinKhor Thanks. Do you add both the image and the link below it or just the link? Is there a way to make the image itself become the link? $\endgroup$
    – Snaw
    Apr 15 at 10:12
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    $\begingroup$ usually both image and link. I have no idea about the last question, I gave it a go and failed $\endgroup$ Apr 15 at 12:02
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    $\begingroup$ @CalvinKhor Does this syntax not work for you —? [![enter image description here][1]][2] where [1] is the URL of the image and [2] is the URL of the graph on Desmos. Perhaps I misunderstood what you need to accomplish, though... $\endgroup$ Apr 15 at 15:33
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    $\begingroup$ @TheAmplitwist, Yes that works, I just didn't understand Markdown. Thanks! $\endgroup$ Apr 16 at 3:02

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The title asks "Is it legal...?", but the body of the Question raises issues of attribution as well as copyright.

Software packages such as Desmos and WolframAlpha are copyrighted, and notices of the copyright ownership are provided to online users (see bottom of respective web pages). However US copyright in the software does not by itself entail US copyright or ownership in the output of programs; see this discussion of relevant US case law.

Whether a user of the program can claim copyright in the output is a separate issue, one not explicitly raised in the Question here. However the strength of such a copyright claim is related to the degree of creative expression a user exercises in operation of the program. Automatic translations or conversions from one medium to another are generally insufficient to support a claim of copyright. Courts have been pressed to draw fact-based conclusions in conflicts between software owners and users.

Attribution is a good practice. If you are posting an Answer, it is not only helpful to Readers to learn your conclusions but also how you reached them. Particularly if software is being used to solve problems, the identification of the software is important for reproducing results and for the reputational weight of its results.

I have used brief mentions such as "Here is a (Desmos prepared) graph that..." to provide such attribution. More elaborate explanation would be appropriate when inputs bear a complicated relation to the output.

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  • $\begingroup$ Thank you for this useful information. I just want to make sure I understand: one is allowed to attach images created by any software or website without attribution, regardless of their T&C? (I do agree that most often it is good to add this attribution, regardless of whether or not one is required by law to do so). $\endgroup$
    – Snaw
    Apr 19 at 18:53
  • $\begingroup$ @Snaw If you want legal advice, you have to ask a lawyer (and I'm not one). The broad sweep of my post was not to say "attach images ... without attribution, regardless of their T&C" but rather to have you think about the value of attribution from Math.SE's policy. We want attribution for the reasons I outlined. Moreover StackExchange contributions are shared by a Creative Commons license with required attribution, an example of where Terms and Conditions for using the site's content matter. $\endgroup$
    – hardmath
    Apr 19 at 19:11
  • $\begingroup$ @Snaw You could always ask a question on Law, where they'd be better placed to talk about the relevant legal considerations, although they might still stop short of saying "it is legal/illegal to do this". $\endgroup$
    – David Z
    Apr 25 at 20:01

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