From the sixteenth century onwards

folding polyhedra—new epistemological horizons?

pp. 29-91

in: Michael Friedman, A history of folding in mathematics, Basel, Birkhäuser, 2018

Abstract

The end of the fifteenth century signaled a major shift regarding the representation of space: the rise of perspective, a "faithful" representation of three-dimensional objects on a two-dimensional plane, mediated through novel technical instruments and innovations and conceptions such as the "perspective machine" or Alberti's window. This exact drawing of geometrical forms in a painting—which can be regarded as a doubling of reality consisting of the seen, "outside" reality on the one hand, and the drawn, "flat" reality on the other—was based on mathematical calculations, even if this mathematics, and especially the implied geometry, was sometimes implicit. Folding a piece of paper—so it may seem—did not have a place in this new (doubled) geometrical order, even if this piece of paper were folded into a geometrical form, e.g., a polyhedron.