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Exploring Śulbasūtras

Centre for Indian Knowledge Systems

Presents 

Exploring Śulbasūtras–An Overview of Cord Geometry

An online course that draws from the treasure trove of ancient Indian mathematical traditions


Prologue

Śulbasūtras, the manuals written around 800 BCE contain geometrical procedures for the construction of altars for ritual purposes. These are part of a vast literature called Kalpasūtras which are one among the six Vedāṅgas (auxiliaries to Vedas). Śulbasūtras are collections of aphorisms that help us appreciate how sophisticated Geometry was involved in the construction of fire altars starting from the construction of simple perpendicular bisectors to complicated altars of various sizes and shapes such as falcon, tortoise, etc. 

Introduction to the Course

The course takes learners to the ancient Indian Geometry knowledge systems where techniques to convert one geometrical shape to another while keeping the area constant. Learners also get to explore how ancient Indian mathematicians were able to devise a good approximation to the square root of 2, and more. 

The course is also designed to clearly convey the idea of how Cord Geometry laid the foundations for the development of Indian Mathematics in later centuries. 

Objectives: 

  • Understanding how sophisticated Geometry got developed in India in connection with simple to complicated construction of altars of various shapes such as Falcon, Tortoise, etc.
  • Study the original sūtras with translation in English along with Mathematical explanations and proofs wherever needed.
  • Provide exposure to how the Śulvakāras (geometers) judiciously integrated Geometry, Algebra, and Arithmetic. 

Learning outcomes:

  • Students will get an overview of the ancient text Śulbasūtra by going through the original sūtras. 
  • The course will aid students to appreciate the elegant geometrical techniques along with learning about their development a few thousand years ago using cords.

Topics covered:

  •  The Śulbasūtras – an overview. 
  • Tools involved in the construction of Vedis. 
  • Determining the east-west line using śaṅku.
  • To draw a perpendicular bisector of a given line. 
  • Theorem of the square of the diagonal. 
  • Construction of squares, rectangles, and trapezium. 
  • Area preserving transformations. 
  • Combination, and subtraction of geometrical areas. 
  • Properties of similar figures, areas, and rational right triangles. 
Teaching Hours60 minutes (Total 15hrs)
Starting from12th July 2023, 2 days a week, every Wednesday and Friday
Timings (tentative)Afternoon IST
Online platformMicrosoft teams
Medium of InstructionEnglish, Sanskrit
Course Fees INR 2000

Who can apply?

– Individuals keen to understand ancient Indian geometry and possessing a background in basic mathematics.
– No age limits
– The ability to read Devanagari is desirable.
– Background in Sanskrit is desirable, but not necessary.
Click here to register

Epilogue

The primary text for study: T. A. Saraswati Amma: Geometry in Ancient and Medieval India, Motilal Banarsidas Publishers Pvt. Ltd, Delhi,1991.

Additional texts for reference:

  1. A. K. Bag, Mathematics in Ancient and Medieval India, Choukhambha, Varanasi 1979.
  2. Bag, A. K., & Sen, S. N. (Eds. & Tr.) (1983). The Sulbasūtras of Baudhāyanā, Apastambā, Katyāyana and Mānava. New Delhi: Indian National Science Academy
  3.  B. B. Datta and A. N. Singh (revised by K. S. Shukla): Hindu Geometry, IJHS, 15, 121-188, 1980.
  4. Bibutibhushana Datta: The Science Of The Sulba, University of Calcutta, 1932, reprint 1991.
  5. G. G. Joseph, The Crest of the Peacock: The Non-European Roots of Mathematics, Penguin 1990; 3rd Ed., Princeton 2010.

Course Facilitator:  Dr. Vanishri Bhat 

Dr. Vanishri Bhat is currently a Research Associate at the Centre for Indian Knowledge Systems at Chanakya University. After finishing her graduation in science (PCM), she pursued M.A. in Sanskrit specializing in Śābdabodha and Language Technology from Rashtriya Sanskrit Vidyapeetha, Tirupati. 

Further, she went on to complete Ph.D. in the Cell for Indian Science and Technology in Sanskrit, Department of Humanities and Social Sciences, IIT Bombay under the guidance of Prof. K Ramasubramanian. 

She has more than eight years of research experience in the field of history of Indian Mathematics and Astronomy and has also published articles in reputed journals like Ganita Bharati. Having come from a Sanskrit traditional family background she has taught the Sanskrit language in various reputed Degree colleges.

She was one of the instructors for an online diploma in Bharatiya Ganita, offered by National Sanskrit University, Tirupati. Apart from academics, she has an avid interest in Sitar and continues practising it.