![]() The Basics Of Circle Divisions The First Division. There are many more approximate constructions not mentioned.Ĭoincidentally these exact methods are likely to be the same methods used by historical artists geometry has not changed in the last 3,000 years. Only the exact divisions and two approximate divisions are presented here. ![]() Some discussions will be added in another post for the cases where a specific size and orientation is needed, as for constructing a figure with a specific side dimension. These discussions will also, as a bonus, construct the exact Compass Constructible Polygons: 3, 4, 5, 6, 8, 10,12, 16, 20 and 24 sides. This document attempts to answer the questions- how are the divisions of the circle accurately and efficiently drawn? Constructions are presented for the common symmetries of pattern 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16 and 20 fold. It is not possible to discuss the foundations and drawing of Islamic geometric pattern without a good understanding of this basic material. Grids are drawn based on divided circles. Patterns which appear to depend only on a “grid” are also defined by the divided circle. In many cases this is obvious, in some cases less obvious. The divisions of the circle define the fourfold, fivefold, sixfold and higher symmetries and create the pattern by interacting with the layout we create through added radial structures, pattern layout circles. This summary introduces the creation of those divisions of the circle, without which geometric pattern cannot exist.Īll repeating patterns, not only star pattern, depend at their roots on the divided circle. Only very rarely do we see the deepest layer in the final pattern, the divisions of the circle which provide the foundation of it all. We usually do not see the underlying structural layout of the patterns in the finished work. We see the final pattern lines, often as interlaced designs. In contrast, all of the geometric pattern layers are tightly related structures based on progressively deeper geometric foundations. It is related to, but not intimately linked to, the underlying geometry. Historical patterns very often show a layer of complex biomorphic design which enriches the pattern. This website deals with geometric pattern, but currently has a heavy emphasis on Islamic star patterns- tiled simple star polygons and complex rosettes. ![]() They could have been drawn with compass and straight edge. They comply, however, with the traditional rules of compass and straight edge geometric construction. The illustrations used here were created with a drafting program. This introduction collects many of the common operations of the division of the circle and polygon construction in one place.
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