Folding in recreational mathematics during the 17th-18th centuries: Between geometry and entertainment

This article aims to present how paper-folding activities were integrated into recreational mathematics during the 17th and the 18th centuries. Recreational mathematics was conceived during these centuries as a way not only to pique one's curiosity, but also to communicate mathematical knowledge to the literate classes of the population. Starting with Leurechon's 1624 Récréation mathématique, which did not contain any exercise concerning paper folding, we show how two other traditions-Dürer's folded nets on the one hand and napkin folding on the other hand-prompted and influenced the integration of folding within subsequent books and manuscripts, especially those of Georg Philipp Harsdörffer and Daniel Schwenter. In Germany, but also to a lesser extent in France, folding was henceforth re-conceptualised within recreational mathematics as a way to transmit geometrical knowledge. Following Harsdörffer, the paper will claim that practising folding activities enabled the acquiring of a geometrical knowledge, which was haptic rather than symbolical or merely visual. This tactility reflects the Baconian conception of science and scientific experiment; and the paper will try to illuminate how folding, by advancing practice and tactility via experiments, was representing these traditions and conceptions.