Friedrich II and the love of geometry (Q1903421)

In the last decade of his life the Holy Roman Emperor Friedrich II (1194-1250) had built the Castel del Monte in the northern part of Apulia. This famous architectural monument with its clear geometric concept has been of interest not only by historians of architecture but also by mathematicians [see \textit{M. Koecher}, Castel del Monte und das Oktagon, Miscellanea mathematica, Festschr. H. Goetze, 221-233 (1991; Zbl 0733.51013)]. The present paper gives a plentifully illustrated analysis of this concept based on the homothetic octagons: the large octagon of the main building, the octagon of the inner courtyard, and the eight octagonal towers, all in the same system of symmetry axes. The symmetry group is a planar group of type D16 [by \textit{J. M. Montesinos}, Classical tessellations and three-manifolds, Berlin etc.: Springer Verlag (1987; Zbl 0626.57002)]. Besides the construction of this configuration with compass and ruler an alternative way (due to M. Erné, Techn. Univ. Hannover) is given not requiring directly a compass. The use of octagonal system in other buildings, navigational charts, mosaics is discussed; a connection between it and Indo-Arabic geometry is pointed out. It is marked that Friedrich II himself had interest in mathematics, his court included Theodorus of Antioch and had close contact with Leonardo of Pisa.