What is the relationship between research mathematics and the mathematics that arises in non-academic mathematical practices? I answer this question in terms of situated mathematical research, which comprises situated mathematical interpretations and situated mathematical applications. A situated mathematical interpretation of a practice takes into account both practitioners' procedures and mathematical ideas. A situated mathematical application occurs when an academic solution to a practice-based problem (that has been developed using practitioners' ideas and procedures) is welcomed by the practitioners. I illustrate these notions through the example of the construction of a regular pentagram by Torajan woodcarvers from Sulawesi, Indonesia.