Orientation and proportion in Indian traditional domestic architecture

Abstract

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.

Aspects of proportions in Indian traditional domestic architecture

“…While choosing the length and breadth from the Padhadhikam (pādādhika) group, practical functional requirements are considered and a suitable ratio from the group is selected. The methodology used in Vastusastra (Vāstuśāstra) to arrive at the ratios used for proportioning the dimensions of the domestic buildings is explained in detail by Dhileep, Kottuppillil, and Kurian (2019). Their studies show that these ratios correspond to the first few partial sum terms, excluding the first term in the mathematical expression of π , given by Madhava of Sangamagrama in AD 1400 and Leibniz in AD 1674 (Hayashi, Kusuba, and Yano 1990; Roy 2004; Katz 2004) is expressed as: …”

“…The first few positive terms in the series except the first term are grouped as Padhadhikam (pādādhika) and the negative terms except the first negative term are grouped as Padhonam (pād na). This expression for the π series is represented in Figure 3 (Dhileep, Kottuppillil, and Kurian (2019)).

Figure 3 An explanation for the expression for π (Dhileep, Kottuppillil, and Kurian (2019)).

…”

“…The construction of a square or rectangle having the same area as that of a circle is impossible because it involves the square root of π and is an unsolved problem even today. The studies on the proportioning of buildings using traditional domestic architectural practice by Dhileep, Kottuppillil, and Kurian (2019) show that the ratios considered and omitted for the dimensioning of the buildings belong to the first few positive and negative partial sum terms, except the first term in the mathematical expression for π. Further, it is observed that the base ratio of the Padhadhikam (pādādhika) group recommended for the proportioning of the buildings are in such a manner that, 'the area of the corresponding rectangle is equal to the area of a circle having a diameter equal to the longer side of the rectangle and perimeter equal to the perimeter of a square formed using the shorter side'.…”

“…The measurement and proportion in Hindu temple architecture have been extensively studied by Meister (1985). In a recent article for this journal, Dhileep, Ajesh and Kurian turned to the ‘Orientation and proportion in Indian traditional domestic architecture’ (2019), focusing on the mathematical background of traditional architectural practice in Kerala, a state on the southwest coast of India. Like the temple architecture, the traditional domestic kind has followed the Vastusastra (Vāstuśāstra), an ancient system of architecture practiced religiously in many parts of the Indian subcontinent, providing separate guidelines for temples and domestic buildings.…”

“…Figure4. Derivation of higher ratios from basic ratio given in Padhadhikam (pādādhika) group(Dhileep, Kottuppillil, and Kurian (2019)). …”