Before going into the fourth chapter, which discusses two main traditions—firstly, the rise of the German tradition of folding in kindergarten, a tradition that spread throughout Europe starting from the mid-nineteenth century; secondly, the appearance of material mathematical models, including folded models, in the nineteenth century—another encounter between folding and mathematics occurred in the nineteenth century that deserves mention. The ramifications of this event are echoed in the attempts to prove parallel axioms (to be discussed in this chapter), as well as in Pacioli's earlier forgotten constructions with folding (which I discussed in the second chapter). Hence, I will discuss this third tradition as one that appears alongside the two other subsequent traditions that I have just mentioned above.