On the Fair Use of an Image Offered as an Answer to a Stack Exchange Question About a month ago, I posted this question on the TeX Stack Exhange: https://tex.stackexchange.com/questions/570484/how-to-draw-a-rose-in-latex In it, I asked for assistance in producing the image of a rose using LateX (a software system for document preparation.) I also indicated that the motivation for the question was to use such an image in a book in order to introduce new chapters. Two people posted answers. My two-part question is: (i) Am I free to use any of these LaTeX images in a book I hope to have published in the future? (ii) Am I free to modify the LaTeX code posted as an answer---in order to produce an alternative, but similar rose image to use in my anticipated publication? Thank you.
Copyright Issues There are several issues here. The Original Rose Image and its Derivatives The image was apparently first posted to Stack Exchange as part of this question by user &quot;Ongky Denny Wijaya&quot;. That user did not say where the image came from. If that user created the image, whether by taking a photograph, or in an image drawing program (or in any other way), then s/he owns the copyright, and licensed it under the CC-BY-SA (4.0) free license by posting it to SE. However, if that user did not create the image but got it from somewhere else, it was quite probably protected by copyright and used without permission. If &quot;Ongky Denny Wijaya&quot; did not have the rights to the image, then s/he could not license them, and all uses on SE and deriving from SE are copyright infringements, and the copyright holder, whoever that is, could sue for damages. The first two answers to your SE question give LaTeX code for rose images only slightly resembling the original rose image. They are not derivatives of the original image. The third seems to be a transformation of the original, and so is a derivative work. It may not lawfully be used without the permission of the original copyright holder whoever that may be. Unless you can reliably determine who that is, and seek permission, you may not lawfully use that image, nor LaTeX code for it. Original SE Content When a user posts original contest to SE, it is automatically released under the CC-BY-SA (4.0) Creative Commons free license. That license allows anyone to reuse the content, and to create modified (derivative) versions of the content, but under some conditions. The most important of these are 1) that the content must be attributed properly to the copyright holder, and any copyright notice must be preserved. (That is the &quot;BY&quot; part.) And 2) the reused or modified work must be provided to others under exactly the same license. (That is the &quot;SA&quot; part.) The first part can be done by listing the user name of the original SE poster, and providing a link to the post. The second part is potentially trickier. If the modified work is &quot;merged into&quot; a new work, the entire new work must be released under CC-BY-SA, which would hinder any commercial publication. If the re-used or modified work is kept separate, at the very least it needs to have a separate license statement, making it clear that anyone can re-use or further modify the work, and making it clear just what is included in that release. That should be associated with the credit or attribution statement mentioned above. That would apply both to an image, and to LaTex code for generating the image. If this is not done, reuse of any such content is an infringement of copyright, and could be the subject of a lawsuit. Fair Use Use of the whole or the majority of an SE question or answer, or of the whole of an original image posted to SE, would probably not constitute fair use in the US, although that would depend on the rest of the facts. If such use did not qualify as fair use, that it must be used in accordance with the stated license, as described above.
Can he use another commercial product that is copyrighted, e.g. a map of a location (the map is a political map and has nothing to do with trees), for his tree research purposes, if such a map won't be part of the book he works on? Yes. Copyright protects particular expressions of ideas and knowledge, not the ideas and knowledge themselves. Using a map for research purposes when the map or a modified version of it does not appear in the final work does not make the final work a &quot;derivative work&quot; covered by copyright.
This is likely not fair use. At first blush it appeared similar to things one might see in The Onion (parody print and online newspaper) or other parody publications or shows (SNL, Key and Peele, etc.). In this case, the context would have likely been deemed transformative. However, since they are selling coffee called "Dumb Starbucks" while using their trademark, they would be be found liable if sued. You can parody a trademark brand, so long as the work is transformative such that the use of the brand goes from selling coffee to making a commentary in which the brand itself is relevant. Amendment I don't think this would pass the test as a parody/commentary. Originally, I failed to notice that they are actually selling coffee. This takes it out of fair use and they would almost certainly lose if sued. If they never sold the coffee, but just had it open as a performance art (like I had originally read this) giving the coffee away to complete the parody, I think they'd be fine. However, they are literally using the Starbucks logo, and selling the same product. This is clearly an infringement of their copyright and not fair use. Sorry for the confusion.
Your app is a simple case of copyright infringement. All the Pokémon are copyrighted, the lettering and names are also protect by trademarks. Trying to claim fair use will be outright impossible: you'll use huge portions of the individually protected Pokemon (the iconic ones like Pikachu) and you are usurping a market they are already in. They have given licenses for apps (Pokemon Go). Pokemon are artistic and some form of fiction. The last straw might be if you'd do a rather obvious parody, but even then, I see no way to show Fair Use with what you stated. No disclaimer can change that, and publishing your work might open you to a huge lawsuit with damages for each individually protected Pokemon you infringed on. With between 750 $ minimum and 150,000 $ absolute upper limit per infringed item (last is for willful infringement), you don't want to infringe on Pokemon, as you could be very easily liable for a number in the 6 to 9 digits! Even if Nintendo might only try to get the statutory damages for all the 900 Pokémon, that is a number of at least 675,4000 $. And that's before looking at Trademarks. Pikachu has about 6 live word marks and there are 111 different Pokémon trademarks filed (some expired or dead)!
The US does not provide copyright protection for font design. As long as you dont distribute font generating programs, that would themselves be copyrighted, you are not infringing. Your derived information is okay because it is derived from a non-copyrightable work and is therefore not a derivative work. https://law.stackexchange.com/a/25673/1340
Let’s work it through Is the work copyright? Yes. Are you making a copy or a derivative work? Yes. Do you have permission? No. At this point, it is prima facie copyright violation. However, various copyright laws have defences for breach. You don’t say where you are but as the USA is the most permissive in this regard we’ll use the USA. If it’s not legal there, it’s not legal anywhere. If it is legal there, it’s still likely to be not legal everywhere else. is it fair use? Almost certainly not. Wizards of the Coast (the copyright owner) already do this. While this service is free for creatures from the Monster Manual, it does drive traffic to their web site where they sell stuff. They also licence (presumably for money) others to do the same. Your usage would negatively affect the copyright owners market. This counts against fair use. Because it’s already being done, your work has virtually nil transformative value. This counts against fair use. You are copying a substantial part of the work. This counts against fair use. You are not using it commercially but neither is it for educational use. This is unlikely to matter. On balance: not fair use. TL;DR This is copyright violation.
Names of people, institutions, and events are not protected by copyright. Things that have occurred at events like math tournaments are facts, and may be recounted, in your own words, with no fear of infringing any copyright. Facts are never protected by copyright, although a particular description of facts could be, and so could a particular selection and arrangement of facts. Specific math techniques and their names are not protected either, and may be described without infringing copyright. The items you mention in the question are: video game / movie references and names No copyright issue here. common integration bee problems No copyright issue here. names of a university / math competition organizers No copyright issue here. integration techniques and formulas No copyright issue here, unless you copy an extensive description of a technique without rewriting it in your mown words.. using someone's Overleaf Latex package to format the book This depends on the license for the package, but there is not likely to be an issue. In short I think you are worrying over issues that are in fact non-issues.
The creator of the derivative work has copyright in the derivative work. The copyright would protect only the new elements of the derivative work. Wikipedia is a good place to start. In the case of a book with updated grammar, depending on the extent of the changes, it would probably be easier to copy the original directly than to eliminate the updates from a copy of the derivative work.