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Indian Mathematics: YAVDUNAM TAAVDUNIKRITYA VARGANCHA YOJAYET

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YAVDUNAM TAAVDUNIKRITYA VARGANCHA YOJAYET. This sutra means whatever the extent of its deficiency, lessen it still further to that very extent; and also set up the square of that deficiency. This sutra is very handy in calculating squares of numbers near(lesser) to powers of 10. For instance in computing the square of 98 we go through the following steps:. 1 The nearest power of 10 to 98 is 100. 2 Therefore, let us take 100 as our base. 3 Since 98 is 2 less than 100, we call 2 as the deficiency. Enter yo...

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Indian Mathematics: SAŃKALANA – VYAVAKALANĀBHYAM

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SAŃKALANA – VYAVAKALANĀBHYAM. This Sutra means 'by addition and by subtraction'. It can be applied in solving a special type of simultaneous equations where the x - coefficients and the y - coefficients are found interchanged. 45x – 23y = 113. 23x – 45y = 91. From Sankalana – vyavakalanabhyam. Ie, ( 45x – 23y ) ( 23x – 45y ) = 113 91. Ie, 68x – 68y = 204 i.e., x – y = 3. Subtract one from other,. Ie, ( 45x – 23y ) – ( 23x – 45y ) = 113 – 91. Ie, 22x 22y = 22 i.e., x y = 1. 1955x – 476y = 2482. 2x 3y = 17.

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Indian Mathematics: GUNÌTA SAMUCCAYAH - SAMUCCAYA GUNÌTAH

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GUNÌTA SAMUCCAYAH - SAMUCCAYA GUNÌTAH. In connection with factorization of quadratic expressions a sub-Sutra, viz. 'Gunita samuccayah-Samuccaya Gunitah' is useful. It is intended for the purpose of verifying the correctness of obtained answers in multiplications, divisions and factorizations. It means in this context: 'The product of the sum of the coefficients(sc) in the factors is equal to the sum of the coefficients(sc) in the product'. X 3) (x 2) = x. Now ( x 3 ) ( x 2 ) = 4 x 3 = 12 : Thus verified.

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Indian Mathematics: LOPANA STHÂPANÂBHYÂM

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Lopana sthapanabhyam means 'by alternate elimination and retention'. Consider the case of factorization of quadratic equation of type ax. Dxy eyz fzx. This is a homogeneous equation of second degree in three variables x, y, z. The sub-sutra removes the difficulty and makes the factorization simple. The steps are as follows:. I) Eliminate z by putting z = 0 and retain x and y and factorize thus obtained a quadratic in x and y by means of Adyamadyena. Step (i) : Eliminate z and retain x, y; factorize.

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Indian Mathematics: YAVADADHIKAM TAAVADAHIKIKRITYA VARGANCHA YOJAYET

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YAVADADHIKAM TAAVADAHIKIKRITYA VARGANCHA YOJAYET. This sutra means whatever the extent of its surplus, increment it still further to that very extent; and also set up the square of that surplus. This sutra is very useful in calculating the sqaures of numbers nearer(greater) to powers of 10. For instance: in computing the square of 103 we go through the following steps:. 1 The nearest power of 10 to 103 is 100. 2 Therefore, let us take 100 as our base. Hence the answer is 10609. 5 On the right hand side p...

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Indian Mathematics: Adyamadyena-Antyamantyena

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The Sutra ' Adyamadyena-Antyamantyena' means 'the first by the first and the last by the last'. Suppose we are asked to find out the area of a rectangular card board whose length and breadth are respectively 6ft . 4 inches and 5 ft. 8 inches. Generally we continue the problem like this. Area = Length X Breath. By Vedic principles we proceed in the way "the first by first and the last by last". Ie 6’ 4" can be treated as 6x 4 and 5’ 8" as 5x 8,. Where x= 1ft। = 12 in; x2 is sq. ft. Now ( 6x 4 )(5x 8 ).

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Indian Mathematics: ANTYAYOR DAŚAKE'PI

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The Sutra simply means - numbers of which the last digits added up give 10. This sutra is helpful in multiplying numbers whose last digits add up to 10(or powers of 10). The remaining digits of the numbers should be identical. Ie the Sutra works in multiplication of numbers for example:. 25 and 25, 2 is common and 5 5 = 10. 47 and 43, 4 is common and 7 3 = 10. 62 and 68,. And also for 425 and 475. The last example can be looked as digit 4 being common and 25 and 75 add upto 100. Example 1 : 57 X 53.