Analysing Arithmetical and Geometrical Features of the Elements of Karbandies in Different Bases

All bases of Karbandies have their own exclusive geometrical features. Employing mathematics, one can proceed with reading geometrical proportions of Karbandi elements in different bases. Although in most of the researches in the field of Karbandies, the geometrical aspect is studied, in some cases, their structural aspect has been considered. In this paper, for the first time, arithmetic and geometric proportions in the plan and façade of Karbandies is studied. The drawing procedure is established on the rectangular dimensions and its peripheral circle divisions using graphic software. First, the Karbandies are drawn in different bases using AUTOCAD and 3D software. After the drawing is completed, Karbandies are classified based on their common dimensional features. as a result, Karbandies are categorized into two types: Karbandies with the same length, and Karbandies with the same width. After determining the characteristics of each category, the features of these two categories are compared to each other. The drawings presented in this study involved plan, vertical and horizontal sections of Karbandies. This research is based on documentary studies. In this comparative study, the relationship among the number of sides, the area of each Karbandi’s element and overall base through the analysis of geometric system and mathematical relations in Karbandies in different bases are determined (24, 20, 22, 18, 16, 14, 12, 10). Hence, the area and frequency of each element are calculated for each existing base and then they are compared in different Karbandies. The area of the Pa-Bariks, Toranjs, and Soosanies in Karbandies follows an inverse relationship with the area of Sanboosehs. The area of the central Shamseh is not necessarily be increased by increasing the number of sides in Karbandi and increasing the number of rows of Toranjs. In all of the mentioned Karbandies, the area of the consisting parts of the Karbandi is decreased by moving into the direction of the vault. In the cross-section of the Karbandies in which after dividing them by 2, the given number is even (Karbandies number 12, 16, 18, 20) there would be a single Toranj in the apex of the arc. However, in all other Karbandies, the position of Toranjs is on the two opposite sides of the arc’s apex. As the number of sides increases, the size of the shamseh increases. The higher the ratio of the span to the depth of the rectangle, the higher the height of the Karbandi. The height of the Karbandi is directly related to the connection distance of the points on the circle. As the distance increases, the dimensions of the karbandi ribs increase. The height of the Karbandi and the size of the shamseh are always inversely related. As the dimensions of the shamseh increase, the height of the Karbandi decreases.