Indian Science Cruiser

P. J. Sindhurani ¹, V. P. N. Nampoori ²

Affiliations
1 Department of Mathematics, Cochin University of Science and Technology, Cochin-682022, IN
2 International School of Photonics, Cochin University of Science and Technology, Cochin-682022, IN

Abstract

The difference between Indian mathematics and Greek mathematics lies not only in the methods employed by them and the purpose of study, but also in their definitions, propositions and proofs. But the geometric constructions in both these cultures are almost similar. The present paper discusses a comparison between geometric constructions in ‘Śulbasūtras’ (800 BC-200 BC) and Euclid’s ‘Elements’ (300 BC). There are three types of constructions in both of these treatises. The first type is the construction of plane figures like squares, rectangles, parallelograms, triangles, trapeziums etc. The second type is the construction of geometric figures by transformation of another geometric figure without changing area. The third type is the construction of similar figures. Comparing the methods of constructions we see that the propositions behind the geometric constructions of the first type in ‘Śulba’ and ‘Elements’ are similar. But in the case of the second and third type of constructions, the methods are extremely different in both of these treatises.

Keywords

Sulbasutras, Elements, Geometric Constructions, Similar Figures, Transformation of Areas.

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P. J. Sindhurani ¹, V. P. N. Nampoori ²

Affiliations
1 Department of Mathematics, Cochin University of Science and Technology Cochin 682022, IN
2 International School of Photonics,Cochin University of Science and Technology, Cochin 682022, IN

Abstract

Problems of indeterminate equations first appeared in Baudhayana Sulbasutra (800-500 B.C.). But a general method of integral solutions of linear indeterminate equations is not described in it, except some geometrical solutions. Aryabhata I (476 A.D.) first gave a general method (kuttaka) of integral solution of linear indeterminate equations of two variables. The kuttaka method was subsequently discussed with modifications by several ancient and medieval Indian mathematicians. However, a general method of solving indeterminate equations of n variables is not available in kuttaka method. The present paper reviews the method used by earlier writers, and describes kuṭṭaka in terms of matrices and determinants. Generalizing this matrix kuttaka method, we present a general method of integral solutions of linear indeterminate equations of n variables. Using this method, we can evaluate all positive integral solutions of the indeterminate equations in Sulbasutras (800-200 B.C.).

Keywords

Linear Indeterminate Equations, Sulbasutras, Kuttaka, Karanapadhati, Aryabhaṭiya, Generalized Matrix Kuttaka.

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