Investigating Numerical Sequences in Decagonal Geometric Ornamentation

Marvelous geometry of geometric arabesque (girih), and their traits has been praised for centuries. These traits are still of researchers’ interest, across the world, and much is to be known about their geometric properties. This paper aims to introduce a feature of a family of Iranian girih works previously unknown to the literature of the field. This research is seeking to answer a main question. That is “With what mathematical or geometric pattern does subdividing girih goes on?”  Data needed for the research is gathered from library sources.Results show that in repeatedly subdividing them, by maintaining the polygons size, their frame grows in a sequence with Fibonacci properties. This has been proved geometrically in the paper and has been shown in rectangular frames. Some real world samples, that put together, show the same properties has been presented. This feature could in the future be used to design and analyze girihs. These applications are discussed in latter sections of the paper.