Geometry in Royal Tomb Art of Ancient Eurasia
Scythian, Xiongnu and Chinese ethnomathematics from
Ukraine, Russia, Mongolia and China
Sz. Bérczi
Eötvös University, Institute of Physics, Budapest, Hungary
Geometry of ornamental structures can be described by the symmetries of the patterns. Complex
structures contain more than one plane symmetry group for the arrangement of different pattern
elements in their positions in the unit cell. Some technological structures triggered development of 2D
complex crystallographic structures, which were discovered even in the 2500 years old Eurasian Royal
Tomb ornamental arts. This paper collects several complex structures from the archaeological finds in
royal tombs of Scythians (Kul Oba, Ukraine; Pazyryk, Altai-Mts, Russia), Xiongnu Huns (Noin Ula,
Mongolia;) and Chinese (Urumchi and Mawangdui, China). This topics is also interesting both for
geometry education and ethnomathematics research. Both symmetry and cellular automata principles
in forming the operations of complex patterns and structures help to describe in a new way the friezes,
double friezes, the woven 2D symmetry patterns and finally the complex (composite) plane symmetry
patterns. Complex patterns of Coxeter-type (Coxeter, 1985), and Curie-type (Bérczi, 2004) are shown
in the Royal Tomb archaeological finds. The composite symmetry patterns help is teaching the
mathematical background of symmetry groups, their relations to technologies, and composite
symmetry patterns also demonstrate, that ancient masters of technologies were intuitive enough in
structural knowledge to give ideas for materials science, architecture and geometry knowledge
developments of the next millennia.
Ref: Bérczi Sz. (2000): Katachi U Symmetry in the Ornamental Art of the Last Thousands Years of
Eurasia. FORMA, 15/1, 11-28. Tokyo
Bérczi Sz. (2004): The Role of Curie Principle in Understanding Composite Plane Symmetry Patterns:
New Ethnomathematic Relations in Ancient Eurasian Ornamental Arts from Archaeologic Finds of the
Period 1. M. B. C. and 1. M. A. D. FORMA, 19/3. pp. 265-277. Tokyo
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Coxeter-type (colored) pattern from Pazyryk (Source: Rudenko, 1953).