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IntroductIon Geometry and the Gothic design ProcessExplaining thE Roots of thE gothic aEsthEticGothic church architecture powerfully conveys impressions of movement and restless growth. In many Gothic interiors, slender columns seem to soar heavenward, as if unconstrained by gravity, before sprouting ribs that knit together into complex vaults. Exterior elements such as spires and pinnacles further emphasize the sense of upward thrust, while leafy crockets and other foliate carvings literalize the organic growth metaphor. Gothic churches also have a crystalline quality that adds a dynamism of its own to the architecture. Both the buildings themselves and their small components generally have polygonal plans, with faceted surfaces meeting at sharp edges. The alignments between these surfaces define planes of reflection and axes of rotation about which the architecture seems to organize itself. The formal kinship between large and small-scale elements, meanwhile, recalls that seen in min...