Quadrilateral during Vedic Time

Quadrilateral during Vedic Time:-
Vedas are the rich source of our knowledge. During this period the rituals to please gods by means of Yagna were high. The rituals was an extremely important part of the ancient Hindu religion. Fire altars were constructed to perform yagna and they were made with precision in different shapes and size. Geometrical rules found in the Sulvasutras, therefore, refers to the construction of squares and rectangles, the relation of the diagonal to the sides, equivalent rectangles and squares, equivalent circles and squares, conversion, of oblongs into squares and vice versa, and the construction of squares equal to the sum or difference of two squares. In such relations a prior knowledge of the Pythagorean Theorem, that the square of the hypotenuse of a right-angled triangle is equal to the sum of squares of the other two sides, is disclosed.
Sulba means pieces of Chord or string and Sutra means formula. The Sulba sutras are the mathematical discoveries by famous Indian rishis turned mathematicians at about 1000 BC to 200 BC, using a piece of chord for constructions of various fire sacrifice altars.

Fire altar

The purpose of the rituals was to build an immortal body that would transcend suffering and death, both hallmarks of mortal existence. According to Plofker:-
Many of the altar shapes involved simple symmetrical figures such as squares and rectangles, triangles, trapezia, rhomboids, and circles. Frequently, one such shape was required to be transformed into a different one of the same size. Hence the Śulba-sūtra rules often involve what we would call area–preserving transformations of plane figures, and thus include the earliest known Indian versions of certain geometric formulas and constants. . In an article published in Indian Journal of Histroy of Science “Ritual Geometry in India and its Parallelism in other Cultural areas” – by Mr. A. K. Bag where he writes that the construction of altars having drawn on a base of different figures such as square, circle, semi- circle, isosceles trapezium, triangle, rhombus, falcon or tortoise shape and other led to the development of various geometrical figures, their transformations and calculation of areas involving many Pythagorean relations with rational and irrational numbers leading to its general statement, approximation of the value of √2 and others. Here is the shape of Mahavedi that is in shape of Isosceles Trapezoid trapezium of area 972 sq. units with 24 and 30 units of length for parallel sides and 36 units of length for altitude with the shape of Square and Rectangle within.

Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com