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Jagadguru Sankaracharya Sri Bharati Krishna Tirthaji of Puri Mutt, a brilliant scholar of Sanskrit, who won the highest honours in several subjects simultaneously in Sanskrit, Philosophy, English, Mathematics, History and Science, etc proceeded to
Sringeri Mutt in pursuit of the highest
knowledge - Adhyatma Vidya, even giving up the Principalship of a college.
Through vigorous yoga sadhana and assisduous Tapas in the forests of Sringeri, he could achieve the reconstruction of 16 - Sutras (Aphorisms) and corollaries, stated to have been found in the parisishta of
Atharva Veda, to solve several topics in mathematics which include Arithmetics, Geometry, Conics, Solids,
Trignometry, Power series, Factorization, differential and integral, simultaneous equations, quadratic, Cubic and higher order equations, roots etc.
To quote Swamiji "The Sutras are easy to understand, easy to apply and easy to
remember". The time taken for solving the problems using these methods is much much smaller than that in the current (western) system.
A comparison of these methods with the Western methods is a welcome idea. The methods lead to different algorithms which are worthy to attempt on computer language.
We proudly announce the release of Lecture Notes on Vedic Mathematics in connection with Swarnajayanthi Celebrations (2002 - 03) of Vidya Bharathi - An all India Educational
Organisation.
Bharateeya Vidya Kendram (Visakhapatnam) has taken up the publication of series of Lecture Notes on Sri Jagadguru Sankaracharya Sri Bharathi Krishna Tirthaji Maharaj's work on Vedic Mathematics.
The Lecture Notes I is exclusively on Multiplication Lecture Notes II is on Division and Lecture Notes III (a) is on Equations.
These are prepared under the sponsorship of Dr. Smt. Gokula Kumari Ghanashyam Das Shah Vedic Mathematics project headed by the Director Prof. C. Santhamma jointly with the expert consultancy of Senior Professors of Mathematics, the assistance of project fellows and computer operators.
Lecture Notes - I on Multiplication explains different methods of multiplication on the basis of different Sutras and the modus operandi which are explained elaborately with a number of examples. These are compared with the working details of the existing
system and these include multiplication
(i) Left to Right
(ii) Series Multiplication
(iii) Introduction of Vinculum Multiplication
(iv) Polynomial Multiplication
(v) Method of Combined Operations
(vi) Moving Multiplier Method.
The multiplication of numbers in a single line is novel. A few method are also
computerised. The sutras mainly used are Urdhva Tiryagbhyam, Vinculum concept, Nikhilam Navatas Charamam Dastah, Ekadikena Purvena, Antya or Dasakepi.
The Lecture Notes - II deals exclusively with Division. The general Division method using the concept of Dhwajanka and Part divisor called the Straight division very elaborately. A reduction process by using the Vinculum process in Straight Division is also an interesting effort. The Decimal concept is considered in the divisor and the dividend also. A new method called Paravatya as envisaged by Swamiji is exemplified for numbers and
Polynomials. Division in Polynomials having three variables in fact, of any degree could be worked out including even successive remainders. An Argumental e\division method is another
interesting feature of the division, both in numbers and polynomials. Combined operation of division with multiplication or addition is also explained.
Some of these methods are also programmed. Some of the sutras that are used are Vinculum, Paravatya Yojayet, Argumentation, Vilokanam etc.
In almost all cases the existing method is also showing a comparison.
Volume III (a) deals with solving simple equations, Simultaneous simple equations. Multiple Simultaneous Equation including special types of Quadratic equations by using different methods through different sutras such as Vilokanam and using differential calculus, succesive differentiation. Methods using Purana
Apuranabhyam Sutram is clearly explained. In all these cases one could verify the results by using the sutram "Gunita Samuccayah Gunitaha" Factorisation of Quadratics, Harder Quadratics, Cubics, biquadratics and higher degree equations could be explained with a good number of examples. A comparison between existing method and Vedic
method that brings out the various sutras, that are applied for
solving the equation are
(i) Paravartya uyojayet (Paravartya)
(ii) Sunyam Samya Samuccaye
(iii) Sopantadvayamantyam
(iv) Antayoreva (Upasutram)
(v) Anurupyena Sunyam Anyat
(vi) Sankalana Vyavakalanabhyam
(vii) Adyamadyenantyamanthyena (Upasutram followed by Anurupyena)
(viii) Lopanasthapanabhyam (Upasutram)
(ix) Purana Apurnabyam
(x) Gunita Samuccayah Samuccaya Gunitah
(xi) Gunaka Samuccayah.
Volume III (b) starts with continuation of not only solving cubic equations but also higher order equations. Two different methods one is suggested by Swamiji and the other suggested by British Authors including Taylor's expansion and coupling with Swamiji's concept. All the Solutions are evaluated using factorization,
argumentation and different Sutras. A normal feature is an attempt of roots of any power of numbers and polynomials. Here too all the roots are evaluated. General methods for expansion of the forum (a + b + c + ...)n are detailed. It is found that the same expansion tables can be made use of in
numbers, decimals, polynomials and groups of expressions as well. Different methods are suggested by Swamiji for squaring, cubing and stated that these methods are extendable to higher orders as well.
A large number of problems are worked out by way of examples and the results are compared. Programming of solving equations are also attempted.
The other volumes which are in progress are:
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