recognising various types of akhtari karbandi (discrete, continuous, tarkin) without the need for drawing, based on mathematical relationships

There are various classifications of karbandis, with akhtari karbandi as one of the most widely used classesin traditional architecture. the present research aims to establish a method to identify various types of akhtarikarbandi without the need for drawing based on mathematical relationships. moreover, it seeks to answerthe question whether there is a mathematical relationship between the number of base circle divisions and theconnection distance in the akhtari karbandi. using logical thinking and inductive reasoning, this researchinvestigates the mathematical relationship between the number of base circle divisions and the connection distancein the 8th to 28th bases of karbandi (including 102 karbandis) that can be drawn in these fields. the results revealthat the mathematical relationship between the number of base circle divisions and connection distance in akhtarikarbandi dictates its type: continuous if they share no common divisor, star-discrete if they share one, and discreteregular polygon grid if the number of base circle divisions is divisible by the connection distance.