The Sulbasutras, being an important part of Kalpa Sutras are the rules for the measurement and construction of Vedis (fire altars), Citis, Mandaps etc. The seers of the ancient period wrote these sutras to carry out different ritual activities effectively.
The Baudhayan Sulbasutras per-taining to the relation among sides and angles of right-angled triangles have been discussed extensively in this book.
Accordingly, the triples for angles, points, lines, complex numbers and vectors have been defined. The operations, addition and subtraction on triples have been applied in plane geometry, trigonometry, coordinate geometry (2-D), complex numbers and vectors as well.
This approach has made the study of the subjects easy, less time taking and interesting. In each unit the illustrations along with figures have been discussed in detail. The sets of a variety of questions have been provided for practice.
The approaches followed in the book will certainly be useful to the readers.
Dr. S.L. Maurya Got awarded M.A (Maths) degree from Allahabad University and Ph.D from Banaras Hindu University, Varanasi. Served the then Hindalco Vidya Niketan, Renukoot, Sonebhadra (U.P.) and thereafter Central Hindu Boys School, Kamachha, B.H.U., Varanasi as Post Graduate Teacher (Maths). Retired from active service in 2014 but continued services to the school till 2019. Recently, extending services to the Centre for Vedic Sciences, B.H.U., Varanasi as guest faculty teaching Vedic Mathematics.
I am extremely happy to dedicate this book to enthusiasts learning geometry-based problems of mathematics. The triples under consideration are named after their redactor Maharshi Baudhayan and consist of three numbers in order such that the sum of squares of first two numbers equals the square of third number. The triples associate angles, coordinates of points in coordinate geometry, trigonometric ratios, complex numbers and vectors as well. They bear multifarious applications in two and three-dimensional geometry, transformations, solution of trigonometric equations, measurement of area of rectilinear figures etc. The triples exhibit a unifying character among different branches of mathematics.
The first unit of the book deals entirely with the formation of Triples in general and elaborate the nature of such triples. The addition and subtraction of triples is defined and is justified geometrically. Based on these operations the triples for multiples of angles are obtained. In particular triples for angles of right-angled triangle, the sides bearing specific relations, are also determined. The operations are interesting, easy and inspiring and prepare a sound base for advanced work in geometry, trigonometry, astronomy etc. Illustrations along with geometrical figures exhibit the clarity of the content of the subject to comprehend.
The second unit on trigonometry reflects the easy, effective, and interesting approaches for finding the trigonometric-ratios for different angles, formation and justification of trigonometric identities, solution of trigonometric equations and the problems on heights and distances. The work is going on in different corners of the world to make it widely adaptive and supportive in other parts of trigonometry. The arithmetic of triples for inverse trigonometric functions makes the study of such functions easy and less time taking in comparison to the conventional methods which are not only time-taking but cumbersome also.
The third unit is on coordinate geometry, vectors and complex numbers. It is endeavored that the new chapters on complex numbers and vectors may easily be assimilated by beginners having no sound background of mathematics at early stages. The triples associated with the line, points and complex numbers help a lot to solve the difficult and cumbersome problems in easy, effective and error free ways. The measurement of area of linear geometrical figures could be obtained in few steps without any chance of errors taking place. The transformations in geometry play a significant role in solving tricky problems. The application of triples makes such solutions easy and takes less time. Such transformations could subsequently be applied in vectors as well as complex numbers. At the end of each unit a set of variety of questions too has been provided to the learners for practice. Further efforts are under way to make the application of triples more effective, inspiring and confidence building tool to deal with the problems of sciences also.
I express my deep gratitude to the editor Prof. Upendra Kumar Tripathi, coordinator, Centre for Vedic Sciences and professor, Department of Veda, Faculty of Sanskrit Vidya Dharma Vigyan, Banaras Hindu University, Varanasi whose cooperation, guidance and inspiration paved the way for me to carry on the shaping my work in the form of this book. I extend my heartiest thanks to Dr. D.S. Tripathi for valuable suggestions and encouragement. Constructive suggestions from readers end will be gracefully accepted. Computational errors, if any, should kindly be brought to our notice so that same can be removed in future editions.
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