This chapter begins with the description of four methods or proofs for inscribing a square in a triangle. The first, by Nicolas Chuquet, dated 1484, describes the calculation of the side of an equilateral triangle inscribed in a square of side 4. This is followed by the calculation of the side of a square inside an equilateral triangle of side 8. The three other texts, from the nineteenth century, show algebraic, geometric and analytical techniques which facilitate the construction. We then suggest a sequence of several class activities on the same theme, suitable for 16- to 18-year-olds. To raise their awareness of the problem, we initially asked the students to construct a square within a triangle and after discussing their solutions we got them to work on a geometric method by Samuel Marolois (1616), then an algebraic method by al-Khwarizmi. In each case there were issues around the understanding of the texts and checking the proofs, even of completing or adding to them. Here we aim to show the conflict of ideas, the stages of the students' work, their reactions and the summary of their work.