Geometry and Construction of Fire Altars in Ancient India Shobha Bagai ILLL University of Delhi
1 GEOMETRY AND CONSTRUCTION OF FIRE ALTARS IN ANCIENT INDIA Construct a square with the same area as a given circle using only a compass and a straightedge. From our school geometry knowledge we know that if the radius of the circle is one unit then the side of the square must be √π . But imagine encountering this problem when people had only a rope to serve as a straightedge and a compass. It has now been established that this problem cannot be solved. But the Aryans in the Vedic period had solution to construct a square whose area is nearly equal to the area of the given circle. INTRODUCTION The basis and inspiration for the ancient Indian mathematics is geometry. The first use of mathematics was in the Indus valley and dates back to 3000 B.C. Excavations at Mohenjodaro and Harappa present knowledge of basic geometry. In 2000 B.C. the Aryans invaded and destroyed the Harappan culture. They founded the Vedic religion. During this age (known as the Vedic period ), the Vedas, the oldest sacred texts of Hinduism were composed. The four Vedas were 1. Rigveda , containing hymns to be recited by the chief priest 2. Yajurveda , containing formulas to be recited by an official priest 3. Samaveda , containing formulas to be sung by a chanting priest 4. Atharveda , collection of magic spells and healing charms The only source of knowledge of Indian mathematics from the Vedic period are the Shulba Sutras . They are a part of a larger text Shrauta Sutras , appended to the Vedas. The word ' shulba ' is derived from the Sanskrit root ' shulb' meaning 'to measure' and hence its etymological significance is 'measuring' or 'act of measurement'. Geometry was also known as ʻ Rajju ʼ . The word ' Rajju ' literally means a 'rope' or an instrument of measuring. Therefore the rules of geometry were known as 'Shulba-Sutra' , the Sanskrit word 'sutra' meaning an 'aphorism' or a short rule. Excavated ruins of Mohenjo-daro, Pakistan [ link ]
2 The only instruments used for measurements were chords with knots and bamboos with cuts . With the help of these a wealth of mathematics was produced, all required for the preparation of fire altars. The fact that these altars were considered sacred might have led to great emphasis on the accuracy in measurement right down to details of construction. Eight of the Shulba Sutras have been traced which are as follows: • Baudhyayana • Vadhula • Apastamba • Hiranyakesin • Manava • Varaha • Laugaski • Katayana All these are named after the authors belonging to different schools. Out of these, Baudhyayana, Apastamba, Manava and Katayana have been translated and an in depth study of them conducted . SHULBA SUTRAS Number of geometrical results is either explictly mentioned or clearly implied in the construction of the altars of the prescribed shape and sizes in the Shulba Sutras . Some of the important ones are 1. The quadrilateral formed by joining the midpoints of the sides of the rectangle is a rhombus whose area is half of that of the rectangle.
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