A New Method for Depicting the Motifs of Acute and Obtuse 10 Point Girih

Islamic art mostly avoids figurative images to avoid creating objects of worship. This aniconism in Islamic culture caused artists to explore non-figural art, and created a general aesthetic shift toward mathematically-based decoration. Islamic patterns are created to lead the viewer to an understanding of the underlying reality, rather than being mere decorations, as writers interested only in pattern sometimes imply. In Islamic culture, the patterns are believed to be the bridge to the spiritual realm, the instrument to purify the mind and the soul.
These patterns in Islamic art are often built on combinations of repeated squares and circles, which may be overlapped and interlaced, as can arabesques (with which they are often combined), to form intricate and complex patterns, including a wide variety of tessellations. These may constitute the entire decoration, may form a framework for floral or calligraphic embellishments, or may retreat into the background around other motifs. The complexity and variety of patterns used evolved from simple stars and lozenges in the ninth century, through a variety of 6 to 13 point patterns by the 13th century, and finally to include also 14 and 16 point stars in the sixteenth century. So, many Islamic designs are built on squares and circles, typically repeated, overlapped and interlaced to form intricate and complex patterns. In all of these patterns, circle has a very important role because the circle symbolizes unity and diversity in nature, and many Islamic patterns are drawn starting with a circle.
Based on the shapes drawn from the circle, the earliest geometrical forms in Islamic art were occasional isolated geometric shapes such as 8-pointed stars and lozenges containing squares. These date from 836 in the Great Mosque of Kairouan, Tunisia, and since then have spread all across the Islamic world. The next development, marking the middle stage of Islamic geometric pattern usage, was of 6 and 8 point stars, which appear in 879 at the Ibn Tulun Mosque, Cairo, and then became widespread. A wider variety of patterns were used from the 11th century. Abstract 6 and 8 point shapes appear in the Tower of Kharaqan at Qazvin, Persia in 1067, and the Al-Juyushi Mosque, Egypt in 1085, again becoming widespread from there, though 6 point patterns are rare in Turkey. In 1086, 7 and 10 point girih (knot) patterns (with heptagons, 5 and 6 pointed stars, triangles and irregular hexagons) appear in the Jameh Mosque of Isfahan. 10 point girih which became widespread in the Islamic world is the subject of this paper.
Girihs are elaborate, interlacing patterns, formed of five standardized shapes. The style is used in Persian Islamic architecture and also in decorative woodwork. Girih designs are traditionally made in different media including cut brickwork, stucco, and mosaic faience tilework. In architecture, girih forms decorative interlaced strap work surfaces from the 15th century to the 20th century. Most designs are based on a partially hidden geometric grid which provides a regular array of points; this is made into a pattern using 2-, 3-, 4-, and 6-fold rotational symmetries which can fill the plane. The visible pattern superimposed on the grid is also geometric, with 6, 8, 10 and 12 pointed stars and a variety of convex polygons, joined by straps which typically seem to weave over and under each other.
A recurring motif is the 8-pointed star, often seen in Islamic tilework; it is made of two squares, one rotated 45 degrees with respect to the other. The fourth basic shape is the polygon, including pentagons and octagons. All of these can be combined and reworked to form complicated patterns with a variety of symmetries including reflections and rotations. Such patterns can be seen as mathematical tessellations, which can extend indefinitely and thus suggest infinity.
As it is cited above, in this article, the method of 10 point girih drawing is essayed and in order to maintain and ease the use of this lasting legacy in contemporary Iranian Islamic architecture, the question arises as to how to minimize the tools and stages of 10 point girih drawing, invent a method for drawing schematics in addition to speeding up the practice of drawing and applying the motifs. Authors, in response to this question, focusing on one type of girih (acute and obtuse 10 point girih), have developed a method called the Golden Star, which presented an original pattern for drawing shapes with a constant ratio in the resulting elements based on golden proportions and golden ratio.
In this research, a combinative method has been used. The data collection is based on library research method and published documents, and a kind of logical methodology based on mathematical relationships and mathematical proportions is used for presenting a suitable model for drawing the 10 point girih. Therefore, in this paper a new method for 10 point girih drawing is presented.