From ancient times, the traditional architectural practice 'Vastusastra' is rigidly followed and practised in many parts of the Indian sub-continent and has a unique position in Indian architecture. In Indian traditional domestic architecture, a hand calculator table and an index number system are used for finding the proportion and orientation of the building. The mathematical and logical background of this traditional practice, which is not known at present, is investigated in this paper. The study reveals that there is a strong and complex mathematical background behind this traditional architectural practice.
Indian traditional architectural practice 'Vastusastra' (Vāstuśāstra) recommends some particular ratios as auspicious for the proportioning of domestic buildings. Similar ratios are found in some ancient buildings belonging to the classical ages in other parts of the world. Recent studies conducted by Dhileep, Kottuppillil, and Kurian [2019. "Orientation and Proportion in Indian Traditional Domestic Architecture." Interdisciplinary Science Reviews 44 (1): 97-109], show that the square and the rectangle formed by the basic auspicious ratio (breadth:length) are geometrically related to a circle with a diameter equal to the length of the rectangle. The mathematical aspects behind these geometrical relationships and other ratio groups given in 'Vastusastra' (Vāstuśāstra) are investigated in this paper. The study reveals that the auspicious ratios help to convert the area of a circle to a rectangle and vice versa, without any loss in accuracy, while using the methods of their age. The traditional social practices are incorporated into these ratios and are modified adequately to fit into the traditional engineering practice.
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