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CALANA - KALANĀBHYĀM
In the book on Vedic Mathematics Sri Bharati Krishna Tirthaji
mentioned the Sutra 'Calana - Kalanabhyam' at only two places. The Sutra means
'Sequential motion'. i) In the first instance it is used to find the roots of a quadratic equation 7x2 – 11x – 7 = 0. Swamiji called the sutra as calculus formula. Its application at that point is as follows. Now by calculus formula we say: 14x–11 = ±√317 A Note follows saying every Quadratic can thus be broken down into two binomial factors. An explanation in terms of first differential, discriminant with sufficient number of examples are given under the chapter ‘Quadratic Equations’. ii) At the Second instance under the chapter ‘Factorization and Differential Calculus’ for factorizing expressions of 3rd, 4th and 5th degree, the procedure is mentioned as 'Vedic Sutras relating to Calana – Kalana – Differential Calculus'. Further other Sutras 10 to 16 mentioned below are also used to get the required results. Hence the sutra and its various applications will be taken up at a later stage for discussion. But sutra – 14 is discussed immediately after this item. Now the remaining sutras : 10. YĀVADŨNAM ( The deficiency ) 11. VYAŞŢISAMAŞŢIH ( Whole as one and one as whole ) 12. ŚEŞĀNYAŃ KENA CARAMEŅA ( Remainder by the last digit ) 13. SOPĀNTYADVAYAMANTYAM ( Ultimate and twice the penultimate ) 15. GUŅITASAMUCCAYAH ( The whole product is the same ) 16. GUŅAKA SAMUCCAYAH ( Collectivity of multipliers ) The Sutras have their applications in solving different problems in different contexts. Further they are used along with other Sutras. So it is a bit of inconvenience to deal each Sutra under a separate heading exclusively and also independently. Of course they will be mentioned and also be applied in solving the problems in the forth coming chapter wherever necessary. This decision has been taken because up to now, we have treated each Sutra independently and have not continued with any other Sutra even if it is necessary. When the need for combining Sutras for filling the gaps in the process arises, we may opt for it. Now we shall deal the fourteenth Sutra, the Sutra left so far untouched. |
