On this site we have many questions about triangular numbers, pentagonal numbers, pyramidal numbers and probably also some other related topics. (We might also consider square numbers, although at least some of the questions about them will fall under and we also have a separate tag .)

Would it be useful to have a separate tag for figurate numbers?

My personal opinion is that such tag might be useful, as there are many problems related to such numbers in number theory, in recreational mathematics and maybe also in some other areas.

EDIT: I have noticed only today that there is (hence my addition above). I think that this tag should stay separate from , since squares have somewhat special character.

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    $\begingroup$ If we create such a tag, should we make triangular numbers etc. synonyms of it? I can more easily imagine somebody adding a tag triangular-numbers to a question than figurate-numbers, unless it's an exceptionally tag-savvy editor/asker. $\endgroup$ Commented Jan 15, 2015 at 12:47
  • $\begingroup$ @DanielFischer That seems to be a very reasonable suggestion. (To some extent related to what I wrote here. TL;DR: Let's use synonyms if they can help correct tagging.) $\endgroup$ Commented Jan 15, 2015 at 12:50
  • $\begingroup$ Hmm, maybe one should rather subsume triangular numbers, squares etc. under polygonal-numbers rather than figurate-numbers? But then, what would be the proper relation between the polygonal and figurate numbers tags? $\endgroup$ Commented Jan 19, 2015 at 12:43
  • $\begingroup$ @DanielFischer What would be figurate numbers which are not polygonal numbers? There are pyramidal numbers. Are there also some other classes of numbers which appear at least occasionally on this site? Personally, I would prefer to have them under one tag. Of course, creating an additional synonym for (polygonal-numbers) might be a good idea. $\endgroup$ Commented Jan 22, 2015 at 9:41
  • $\begingroup$ There are also cubes ;) But except of cubes and pyramidal numbers, I'm not aware of any type of figurate numbers commonly used that aren't polygonal. $\endgroup$ Commented Jan 22, 2015 at 11:04
  • $\begingroup$ Polytopic numbers are quite commonly studied, and are figurate numbers which are not polygonal. $\endgroup$ Commented Apr 9, 2015 at 19:41


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