Robert Bork A Geometrical Analysis of the Gothic Choir at Aachen Cathedral Excerpted and translated from Robert Bork and Norbert Nußbaum: Gotischer Baubetrieb am Aachener Münsterchor. In: „Sie glänzte wie ein kostbarer Edelstein, wie ein kristallklarer Jaspis." 600 Jahre Aachener Chorhalle, (Schriftenreihe des Karlsverein – Dombauverein, Band 16) Aachen 2014, pp. 22-42. The design of the Gothic choir at Aachen Cathedral can be readily understood in geometrical terms. Because the elevation generally develops out of the ground plan, it makes sense to begin with the latter. Like all complex Gothic structures, the choir can be understood as the physical trace of a dynamic design process, which generates intricate forms through combination of only a few geometrical procedures. Among the most important of the procedures in this widespread and long-lasting lingua franca of Gothic designers were the nesting and rotation of polygons, especially triangles, squares, and octagons, and the use of the Golden Section. 1 In the case of the Aachen choir, the design seems to have been conceived starting in the crucial area where the radial geometry of the hemicycle meets the axial geometry of the straight bays. Ground Plan (see Figure 1) The ground plan involves almost exclusively operations based on squares and circles. Out of these simple ingredients an elegant scheme soon develops. Red lines: We begin the development of the design in the center of the choir polygon, at the position of the keystone. The transversal rib that separates the polygon from the straight bays lies 3.155m west of this origin point. Four squares with this side length can be grouped around the north-south axis through this origin, so as to form a 2x2 grid. In this way, they together form a larger square 6.310m on a side. The half-diagonal of this larger square, which runs at an angle of 26.56°, measures 7.055m. Orange lines: This 7.055m-long half-diagonal defines the radius of a circle that sweeps through the interior corners of the hemicycle wall. Each of the seven eastern facets of the hemicycle has an angular width of 180°/7 = 25.71°. The span of the straight choir bays, measured between the window surfaces, equals the diameter of the hemicycle, which is thus 2 x 7.055m = 14.110m. Golden rectangle: The parts of the plan described so far together define a rectangle with the proportions of the Golden Section. This rectangle measures 7.055m to the east of the origin line, and 3.155m to its west, for a total length of 10.210m, while its width of 6.310m matches that of the red double square. The proportions of the square are thus 10.210/6.310 = 1.618. This perfect Golden Section proportion results from the unfolding of the diagonals in the red double square.